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Solutions
Chapter 1 - Microeconomics: A Working Methodology 1. As the water shortage model developed in Section 1.2 illustrates, equilibrium and optimality are quite separate concepts. As we saw, the equilibrium of the water shortage model under the non-metered scheme is not Pareto-optimal. Nor is it cost-benefit optimal. Similarly, under either of the price support programs at which we looked, the equilibrium of the market for butter is neither Pareto-optimal nor cost-benefit optimal. That is, "equilibrium" and "optimum" are definitely not synonymous terms. 2. a. Initially, equilibrium price is 30 and equilibrium quantity is 20.

b. Subsequently, with decreasing income, equilibrium price falls to 25 and equilibrium quantity falls to 15. c. With the changed supply curve due to a new technology, equilibrium price will be 20 and equilibrium quantity 20 as well.

Diagram:
p 50 XS c 40 Eqa Eqb Eq 10 XD b 0 40
c

XS

XD

50

3. The restriction in supply means that the supply curve for drugs will shift up and to the left, resulting in an increase in equilibrium price and a decrease in equilibrium

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quantity. One would anticipate an increase (decrease) in street crime if the amount drug users spend on drugs is larger (smaller) in the subsequent equilibrium than in the initial equilibrium. (As we see in Chapter 3, the amount spent on drugs will increase if the demand for drugs is inelastic with respect to the price of drugs.) 4. a. Allocation is done by waiting in line. b. Usually by the direction of the mother or father. c. By grade point average, hours completed, special course requirements, and first come first served. d. Standing in line, paying a marginal fee, and then passing a test e. Judge makes the decision. 5. a. The Rolling Stones may be using the line to generate free advertising for a CD. b. Family members dont use prices because it is so easy to cheat and blame failure of performance on other family members. c. Presumably qualified students are wanted in the classroom. d. An individual who just paid for his license would not pay for the added risk to others if he did not know how to drive. e. The costs and benefits of an individual case may not reflect social costs and benefits, so you would not want decisions based on individual willingness to pay. 6. From an economist's perspective, the institution of a fine for late books is the solution to the following important incentive problem that all libraries face: How can the library ensure that borrowed books are returned promptly so other library users will have a chance to borrow the books? If the institution works well, then most people do return borrowed books on time, and other users do have the chance to borrow them. The fact that few fines are paid (because few people return their books late), is an indication that the system is working well, not that the fines serve no purpose. To put the point differently, the fact that most people return borrowed books on time when they face a fine for late return does not imply that they would continue to return books on time if the fine were eliminated. Many instructors use a similar institution to ensure that students complete assignment on time they deduct say 10% from the total mark for each day
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the assignment is late. Should they conclude that the institution serves no purpose because they get few late assignments, or should they conclude they get few late assignments precisely because of this institution? 7. There is now considerable evidence that the total amount of refuse generated is significantly smaller under the fee-for-service institution. However, the institution does create a perverse incentive for people to dispose of their trash by illegally dumping it. And there is also evidence that the amount of trash left by the roadside is larger and a bag of trash will be heavier under the fee-for-service institution. The amount hauled to the dump will, of course, be larger in the case where there is no fee for service. 8a. The price of newspaper will increase and the quantity will decrease. Newspapers would be induced to economize on the amount of paper they used. Hence, one would expect smaller papers and tighter formats. The price of advertising space in newspapers would increase, inducing advertisers to substitute away from newspapers and toward magazines, radio, and television. b. All users of paper would be induced to economize on their use of paper. Hence, less paper would be produced and there would be less paper to dispose of. However, one would expect users of paper to substitute other materials plastics, for example for paper. The disposal problems associated with these materials would be exacerbated by the tax on paper. c. There are many possibilities here. For example, paper manufacturers could be required to use a specified portion of recycled fiber in the manufacture of paper products, which would create a demand for used paper, thereby creating private economic incentives to recycle paper. The key to any successful recycling scheme is to somehow create a demand for used paper. 9. While trying to sound objective, the mayor is ignoring the fact that what is the best option for one person may not be the best option for another. 10. The person who splits the food knows that the other will take the better half, so the splitter is best off splitting the serving equally. 11. 12. All possible allocations are Pareto optimal. The bill will likely be higher. This is an example of the common property problem.

13. This may be more of a discussion question than an exercise. The announcement generates forces to donate both more and less. A donor could chose to donate more, since, as in the common property problem, the additional cost is spread
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across more people. Also, a donor could choose to donate less since he will face additional tax costs and the donation he would have made will be made up by the government. The net force of these factors will be determined by factors such as a person's preferences, their exposure to the tax increase and their natural level of donation (with no government intervention) relative to the population.

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Chapter 2 A Theory of Preferences 1. This question can lead to a great class discussion. Does maximization mean purely selfish or does it only mean self-interested. In other words, do people help others only because there is something in it for them, or is altruism possible? In either case, the economist would say her behavior is not refuting the maximization assumption. 2. In equilibrium the rate of return to each stock must be the same. Hence the one that does not pay dividends must have a higher expected capital gain. 3. Gordon Tullock claims that this is the acid test question that tells if someone thinks like an economist or not. The answer is no. 4a. Dizzy's indifference curves are vertical lines.

b. The following are utility functions for Dizzy: x1, 10x1, (x1)2. Indeed, any monotonically increasing function of x1 will represent Dizzy's preferences. 5a. Assuming you dont mind the bulk of all the nickels, the indifference curves are straight lines with a slope of -5 (assuming nickels are on the vertical axis). b. If the consumer has two hands, the indifference curves will have right-angled kinks along the line x1 = x2. Above the kink, they will be vertical, and to the right of the kink, they will be horizontal. If the consumer has only one hand, the indifference curves will be vertical or horizontal, depending on which hand the consumer has. c. Let x1 represent quantity of cocaine and x2 represent money. The indifference curve will be downward sloping and concave to the origin. In moving from left to right along the indifference curve, MRS will increase. d. Letting x1 represent quantity of lobster and x2 represent money, the indifference curve will be U-shaped. In the upward-sloping portion, if the individual is forced to eat more lobster, more money is required to get him or her back to the indifference curve. With free disposal, the upward-sloping portion of the indifference curve is replaced by a horizontal line. e. f. The indifference curve will be a straight line with a slope equal to - 1. The indifference curve will be upward sloping.

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g. The indifference curves will again be downward sloping and concave to the origin, as in (c), but the preference ordering will be increasing towards the origin. 6a. All three indifference curves are coincident.

b. The second utility function can be derived from the first by dividing by8, and the third can be derived from the first by dividing by 2 then squaring. Hence, all three functions represent the same preference ordering because they maintain the MRS. They are just monotonic transformations of each other.

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7a. Her indifference curves have right-angled kinks along the line 4 x1 = x21/3, and they are vertical above the kink and horizontal to the right of it.

b. Her preferences do not satisfy the diminishing marginal rate of substitution assumption the marginal rate of substitution is not even defined at the kink in the indifference curve, it is infinite along the vertical segment of the indifference curve, and it is zero along the horizontal segment. 8a. First plot the indifference curve for utility number 10. It passes through the following consumption bundles: (0,5), (1,4.5), (4,4), (16,3), (25,2.5), and (100,0). To get the indifference curve for utility number 15(20), move the first one vertically up by 2.5 (5) units.

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b. Along any vertical line, all three indifference curves have the same slope. In other words, MRS is determined exclusively by quantity of good 1. To put it another way, for these preferences, MRS is independent of quantity of good 2. 9a. The logic is wrong. Many goods are free to the user, but they are still scarce and someone pays for them. Whether or not water and air are scarce depends on the quantity supplied and demanded at a zero price. b. Even the richest man on earth faces scarcity of something. For many wealthy people the binding constraint is time. c. Smallpox is rare, it is not scarce. Scarcity implies that someone wants the good.

10. One of the implications of maximization is that individuals cannot systematically learn from others how to make above normal returns. Teachers of this type of knowledge would just make the money themselves. Hence, individuals who at a young age think they have what it takes to be great stock brokers, just enter the industry. Marginal brokers are more likely to go to school. It is not that universities make reduce the human capital of brokers, but that we observe a sample that is filtered by individual maximization. 11a. This indifference curve is composed of two segments: the line x2 = 10, for x1 the line x1 = 10, for x2 10. The two segments intersect at (10,10). 10;

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b. U(x1,x2) = max (x1,x2) where "max" means "the maximum of." Jack's indifference curves are nonconvex, they do not satisfy the non-satiation assumption, and they are kinked. 12. They make it clear that the first person to attack is killed. Hence no one moves first, and the plane is held. 13. The general must make certain that the probability of death is low enough for the soldier to be willing to fight. If the soldiers were in a single column, the first would be killed for sure, and like the people on the airplane, no one would be first. 14. When you fire your weapon you draw attention to yourself. The best way to get killed in battle is to draw attention to yourself. 15. Assuming that boys and girls are not viewed as perfect substitutes (we dont care what the sex is, as long as the child is healthy) then those families with only girls or only boys, should be more likely to have a third child because the marginal value of the child is higher. 16. Contractors are profit maximizers, which means they must minimize costs. As a result they build male and female washrooms adjacent to one another in order to use the same set of plumbing. 17. If the constraint is binding then Carl will certainly have all three drinks before 10. However, he will also substitute into harder liquor in order to maximize the amount of alcohol over the three drinks. 18. This is both maximization and substitution. Building straight buildings is costly and if one can get away with doing a poor job, one does. 19. You may have fewer armed robberies, but of the ones committed they would be much more violent. Essentially this would eliminate any marginal deterrence to the law. 20. Frequent flyer programs are mostly designed for business travelers who do not pay for their flights. Lower prices would benefit the firms, but the choice over which flight to take is often made by the traveler. Hence the points are a way of rewarding the decision maker.

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21a. b.

MU1= 3/5x1-2/5x22/5 MU2= 2/5x13/5x2-3/5 MRS = MU1/MU2 = 3x2/2x1

c. MRS goes to zero. MRS tends to infinity. In general, as the relative quantity of good 1 goes up (x1/x2 increases), the MRS goes down. That means that the individual wants more and more units of good 1 to give up one unit of good 2, if she has good 1 already in large quantities d. Yes.

22a. All of the MRS are equal to x2/x1. The MRS is independent of a monotonic transformation of the utility function. b. (i) MU1=2x2, (ii) MU1=x2/4, (iii) MU1=2x1x22 Unlike the MRS, the MUs are not independent of transformations of the utility function. This result occurs because MRS only depends on the quantity of the goods, not the level of utility. 23. MRS=.25x1-1/2 which does not depend on x2. If you knew one indifference curve you would know them all since this means that the indifference curves are vertically parallel. 24a. b. c. d. Sure. MRS=(x2-12)/(x1-25). Nothing, it is not defined. See Figure S2.20

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25a. b.

(i) Indifferent (ii) (5,6) (iii) (3,4) Slope of 1 but horizontal when r > 2n and vertical when n > 2r.

26a.

Yes.
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b. No. This is not a marginal change anymore diminishing marginal rate of substitution implies that the offer is too low. 27. (a) Yes. (b) No. (c) Yes, by the money pump strategy. Joe will pay a small amount (or zero if indifferent) to trade your Mars Bar for his Mr. Big bar. Hell then pay a small amount (or zero if indifferent) to trade your Mr. Big bar for his M&Ms. Hell then pay a small amount (or zero if indifferent) to trade your M&Ms for his Mars Bar. At least one of the trades will earn you a positive amount of money, and you end up with your Mars Bar. Continue this cycle of trades until you get his entire dollar.

28. Banks like to receive high interest payments, but they also like high probabilities that they will be repaid at the end of the term. Longer terms give borrowers more opportunities to get into financial trouble, and therefore the probability that they will repay the loan falls with the length of the term. Therefore, banks tradeoff lower interest rates for shorter terms.

29a.

b. Clearly Pizza is a bad for John. Given the shape of the indifference curves E=B>C>A>D. However, Bundles C and A could reverse if the indifference curves were steeper in that region.

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30a. b. 31.

Yes. For example, Anne could trade all of her Chocolates for Beth's flowers. Yes, same as part (a). (i) U(x1, x2) = x1 + x2 (ii) U(x1, x2) = x1x2 (iii) U(x1, x2) = min(x1 + x2) (iv) U(x1, x2) = max(x1 + x2)

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Chapter 3 Demand Theory 1. If Joe's indifference curves are smooth and convex, he will prefer the lump-sum tax, and he will smoke more cigarettes with that tax than with the sales tax. If his indifference curves are kinked, then it is possible that he would be indifferent between the two taxes, and if he is indifferent, then he would consume the same number of cigarettes under both taxes. Figure S3.1a Figure S3.1b

2. Assuming that the other good is a composite commodity C, we get the following graph:

Figure S3.2

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3. MRS is identical and equal to -p1/p2 at these two bundles, assuming that indifference curves are smooth. 4. Figures S3.1a and S3.1b are useful here. In Figure S3.1a, indifference curves are smooth and convex, and the individual strictly prefers the lump-sum subsidy. In Figure S3.1b, indifference curves are kinked, and the individual is indifferent between the two subsidy schemes. 5. We know the following and nothing more: one of the goods is inferior and the other is normal. 6a. The following bundles are on the indifference curve: (2,1), (0,3), (0.5,2), and (5,0.5).

b. Each of Jack's indifference curves intersects the x2 axis but not the x1 axis. Hence, good 1 is inessential and good 2 is essential. 7a. Ted's demand functions are x1 = 0.4M/p1 and x2 = 0.6M/p2.

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b. The income-consumption path is the line x2 = 3x1/2. The Engel curves are x1 = 0.4M and x2 = 0.6M. 8. No. The price of beer went down relative to the price of whiskey, and yet he drank less. This assumes no radical change in preferences or income occurred between the two evenings. 9a. Because the price-consumption path is horizontal, we see that Nancy's expenditure on good 2 does not change as p1 changes. Hence, her expenditure on good 1 does not change as p1 changes. b. Let the portion of income spent on good 1 in this exercise be z. Then, her demand for good 1, given p2, is x1 = zM/p1. c. d. Good 2 is neither a substitute nor a complement for good 1. Price elasticity of demand for good 1 is 1.

10. If a good was perfectly inelastic at low prices, then as prices increase the quantity demanded must eventually fall as the individual runs out of income. 11a. As p1 increases, we move from left to right along the price-consumption path (since good 1 is not a Giffen good). As we do so, expenditure on good 2 increases. Hence, expenditure on good 1 decreases, indicating that the demand for good 1 is elastic with respect to the price of good 1. b. As p1 increases, demand for good 2 increases, indicating that good 1 is a substitute for good 2. 12. Since the income-consumption path is positively sloped, both goods are normal.

13. Mr. Lucky's budget line is 1.1x1 + x2 = 55 000. The opportunity cost of $1 spent today is $1.10 that cannot be spent tomorrow. The opportunity cost of $1 spent tomorrow is $.91 that cannot be spent today.

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14. 15a.

Not-So's budget line is identical to Mr. Lucky's. Yes.

b. The amount consumed should fall, but other countries will start producing more due to the rise in price. c. When land is set aside in BC, it induces more timber cut in places like the Amazon. 16. Figure S3.3 is useful here. The worst point on the budget line is the point of tangency at F. The utility-maximizing bundle is at E, where quantity demanded of good 2 is 0, and all income is spent on good 1. If the budget line were steeper, the utilitymaximizing bundle would include 0 units of good 1, and all income would be spent on good 2.

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Figure S3.3

17. Consider some bundle A on the budget line, and suppose that the indifference curve through bundle A is locally concave (that is, nonconvex). If the budget line is steeper than the indifference curve at point A, then bundles on the budget line immediately to the left: of A are preferred to bundle A. If the budget line is flatter than the indifference curve at point A, then bundles on the budget line immediately to the right of A are preferred to bundle A. And if the budget line is tangent to the indifference curve, then bundles immediately to the right and to the left of A are preferred to A. Hence, bundle A cannot be a utility maximizing bundle. 18a. If we graph these preferences with F on the horizontal axis, then the indifference curves are vertical until F=100, and then flat after that. For prices of food less than 1 F*=100 and T*=100-100pf. For food prices more than 1 F*=M/pf and no T is purchased. b. 19. See part a. No, Tammy would be indifferent.

20. Let x2 be a composite commodity with price equal to $1, and m the profit per meal under the first option; that is, let m = p1 50. In Figure 3.6, m is, by construction, the profit per meal required to cover the cost per member; that is, mx1* = 1000. Given this pricing scheme, the representative member chooses bundle D on the blue indifference curve. Notice that DC = $1000 = mx1*. If the club chooses to sell meals at the $50 per meal cost and to cover overhead costs by a membership fee equal to $1000, the consumer will choose some bundle on segment DE of the associated budget
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line. Notice, all bundles in the interior of segment DE are strictly preferred to bundle D, so the club member is better off under the second option. 21a. Given the excise taxes, suppose Laura buys bundle ( x1',x2'). The lump-sum tax is then equal to t1x1' plus t2x2', the amount Laura pays in excise taxes. Hence, given the lump-sum tax, she can still buy the bundle (x1',x2'), and she therefore can be no worse off with the lump-sum tax. b. She will be better off with the lump sum tax when the slopes of the two budget lines are different that is, when p1/p2 is not equal to (p1 + t1)/(p2 + t2). This case is shown in Figure S3.4. c. If Laura's indifference curves were kinked, and if her preferred consumption bundle under the excise tax regime was at a kink, then she might be indifferent between the two tax regimes even when the slopes of the two budget lines were different. d. If good 1, for example, was inessential, and if Laura chose to buy none of good 1 under either tax regime, then she would be indifferent to the two taxes regardless of the slopes of the two budget lines.

Figure S3.4

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22a. A cash gift simply shifts the budget constraint out. A gift in kind shifts the budget constraint out as well, but it is truncated at the point where all income is spent on the good not used in the transfer. b. The recipient is better off under the cash scheme since his opportunity set is larger. c. For a number of possible reasons. Often we wish to direct the type of consumption made by the recipient. Probably not, unless the gift is from a parent. Presents in kind may be a signal that the giver knows the person well enough that they dont spend a lot of time finding the actual gift. That is, it is a signal that an investment has been made in the relationship. 23a. b. 24a. b. c. 25a. b. c. L = (x1 + 1) (x2 + 5) + [50 2x1 4x2] x1 = 17, x2 = 4 L = (x1 + 1) (x2 + 5) + [M p1x1 p2x2] x1 = (M p1 + 5p2) / 2p1, x2 = (M + p1 5p2) / 2p2 The answers are the same. L = x12(x2)3 + [200 p1x1 p2x2] x1 = 80 / p1, x2 = 120 / p2. Both goods are normal.

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d.

Both goods have a price elasticity of 1 everywhere along the demand curve.

e. The price consumption path is a flat line for changes in p 1, and it is a vertical line for changes in p2. The income expansion path is a straight line from the origin. Hence for a given percentage change in the price of one good, there is an equal percentage change in the quantity demanded. 26a. b. x2 = 135 p2. 20/7, 16/11, 4/5, 8/19, 4/23

27a. The demand for good 1 is x1 = aM / (a+b)p1. A similar result holds for good 2. If we multiply this by p1, we get the amount spent on x 1 which is aM / (a + b). b. 28a. b. c. 29a. The are equal to 1. 30p1 + 40p2 = x1p1+x2p2. L = (x1 3) (x2 4) + [30p1 + 40p2 p1x1 p2x2] x1 = 3(11p1 + 12p2) / 2p1, x2 = (44p1 +27p2) / 2p2. L = lnx1 + 3 x2 + [M p1x1 p2x2]. The choice variables are x1 and x2, the

parameters are M, p1, p2. The FOC are (i) 1/x1 p1= 0, (ii) 3 p2 = 0, and (iii) M p1x1 p2x2 = 0. b. x1 = p2 / 3p1, x2 = (3M p2) / 3p2. Yes the first law of demand holds. What is unique here is that good 1 does not depend on income, and good 2 does not depend on the price of good 1. c. 30a. 1. L = 1/x1 - 1/x2 + [M p1x1 p2x2]. The FOC are (i) 1/x12 = p1, (ii) 1/x22 = p2, and

(iii) M p1x1 p2x2 = 0. b. x1 = M/(p1 + p1.5p2.5), x2 = M/(p2 + p2.5p1.5). The law of demand holds for values of p1 > p2/4. c. 31a. Both x1 and x2 are normal. Slope = 2/5
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b. Intercept of 29, moving down like steps

c. Intercept of 24, moving down like a saw

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d. Kinked at (16.667,13.333)

32a. b. c.

He will not accept the trade. X1* = 40 and X2* = 120 His income elasticity is greater than 1.

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33.a. Drawing a graph of two parallel budget lines. Non-satiation implies that consumption of at least one good must increase with an increase in income. b. Yes it is possible. If this is good 1 on the horizontal axis, then the expansion path would look like an S, and if it is good 2 on the vertical axis it would look like tilda. 34. A major cost of attending university is the value of forgone time. In Canada tuition averages between $3000-$6000 per year, depending on the university. Most university students, however, are probably sacrificing $30,000-$40,000 per year in lost income. Hence the tuition is approximately 10% of the full cost. A doubling of tuition might mean the full price only increased by 10-15%.Thus only looking at the tuition will cause a bias in the elasticity measure.

35.

(a) Vertical intersect is 6, horizontal intercept is 18, slope is -1/3. (b) We know that x2* must be on the budget line M=p1 x1* + p2 x2*, so x2*=14/3. (c) The new optimal bundle must be on the new budget line above and the right of the original bundle. So, x1* must be in [4,16/3] and x2* must be in [14/3,6].

36.

(a) Solve for good 1: x1*=1, then use budget line equation to get x 2*=2. (b) Yes. (c) Substitute the demand equation of good 1 into the budget equation: x 2* = (M/p2) - (p1/p2)[M/(p1+2p2)].

37.

(a) (b) (c) (d)

x1* = 5, x2* = 2. Budget line runs from (0,10) to (4, 0). New budget line from (0, 9) to (18/5). x1* = 9/2, x2* = 9/5. New budget line from (0,10) to (2,0). x1* = 5, x2* = 1. He'd prefer part (b)

38.

(a) All croissants. (x1*, x2*) = (15/2, 0). (b) Still all croissants. (x1*, x2*) = (45/4, 0). (c) Now, all tarts. (x1*, x2*) = (0, 6).

39.

(a) x2, x3, x4. (b) x1. (c) x2, x4. (d) x3. (e) x4, x5.

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Chapter 4 More Demand Theory 1. Paper is inexpensive relative to cloth in North America, hence consumers substitute into the cheaper good. 2. If the employees are allowed to sublet, then the cost of using the space does not change (even though the cash flows might), and as a result there is no change in the relative price, and no expected change in the quality of cars parked. 3. He doesnt know how far each individual walked. If the closest people have coffee to go, he will have the experiment backwards. 4. Think of the students as forming a coffee club, and review in-chapter Problem 4.2. Assuming that the representative student's indifference curves are smooth and convex, the reasoning outlined in that problem reveals that the representative student will be better off with the $10 loan and coffee at $0.25 per cup than he or she would be with Marya selling coffee at $0.75 per cup until she recovers her $490. 5. Those in the economics department will have more dinners since the price of dinners relative to other meals has fallen. The quality of meal should fall, however, because the relative price of the inexpensive meals has fallen. 6. Figures S4.6a and S4.6b are useful here. The crucial price differential is a) distance EF in Figure S4.1a, and b) it is the cross-hatched area in Figure S4.1b, assuming that Julis demand for instant photographs is independent of her income.

Figure S4.1a

Figure S4.1b

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7a. b. c.

$2250 $600 $1134

8. To maximize profit, Walt should sell weekly passes for $50, and charge nothing for each fide. His profit will be $5000 per week, and each kid will take 10 rides per week. 9. Alisons father apparently loves the car more at the margin, but Im sure he loves Alison more in total. 10. If more seats were made available, more students would attend, and students could arrive somewhat later to get the same quality of seating. If average quality increased and the number of seats remained the same, then the student section would fill up somewhat earlier. This method lowers the value of the seats if everyone has different values of time. This is because those with the lowest time costs get the seats rather than those willing to pay the most dollars. 11. Since Buford could have bought bundle (8,2) when both prices were $1 but chose instead to buy bundle (4,8), we can infer that Buford prefers (4,8) to (8,2). It is, of course, necessary to assume that Buford's preferences are the same in both periods. 12. In case a, Juan was better off in period 0, and in case b, he was better off in period 1. In case c, we cannot be sure in which period he was better off. In the diagram for case a, the consumption bundle chosen in period 1 must lie below the period-0 budget line, and the consumption bundle chosen in period 0 must lie above the period-1

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budget line. In the budget line, and the consumption bundle chosen in period 0 must lie above the period-1 budget line. 13. The crucial thing to notice is that Norm's utility-maximizing bundles, B0 and B1 always lie on the line x1 = x2 when his preferences are described by this utility function. Hence, the statements that "B0 is below the period-1 budget line" and that " B1 is above the period-0 budget line" are equivalent in the sense that either one implies the other. But the first statement means that P > 1, and the second statement means that L > 1. Hence, P > 1 and L > 1 are equivalent statements: either one implies the other. The other results can be derived in the same way. 14. By buying 80 litres at a time, I minimize the time cost of buying gasoline and therefore maximize the income available for other goods. If I buy gasoline 80 litres at a time, in Becker's framework, the full price per gallon is p + w/8 where p is the money price and w is the value of a minute to me. If I buy it 60 litres at a time, the full price is p + w/6; if I buy it 30 litres at a time, the full price is p + w/3. 15. It will not work because in equilibrium everyone must wait 1 hour. It doesnt matter if this hour is spent with 55 minutes in line and 5 minutes filling out the form, or just one hour in line. 16. It is not Mustard since this would imply inconsistent preferences.

17. No matter which way the price goes, the individual is better off. Consuming an endowment insulates one from a price change in either direction. 18. No. The tax would reduce the consumption of all gas, but the fixed tax lowers the relative price of the expensive gas with more lead. Therefore, the effect on pollution is ambiguous. 19. The sharing rule creates a common property problem over the meal. Each participant faces a lower cost at the margin of consuming higher quality, and does so. 20. At the grocery store the owner of the store faces uncertain demand. It would be costly to constantly adjust prices to avoid the minor lines. Rock bands are probably using the free advertising that results from reports of the lines to promote CD sales. Both of these examples motivate the discussions in Chapters 17-20.

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21. Of course not. The law effectively raises the cost of harvesting the crop. If demand is inelastic the total revenue of berries will also increase. 22a. b. $4.00 $3.00

23. Since they both face the same prices, and since they both set the price of the goods equal to their MRS, they both end up having the same MRS. 24. Those who have to pay shipping on damaged and undamaged goods will face a lower relative price for the undamaged goods, and will therefore demand more of them. Thus the damaged seconds are sold closer to the point of production. 25. Students view courses taught in different semesters as substitutes. When the cost of a semester increases, and the cost of a given course within a semester is zero, the student will take more courses per semester and graduate sooner. 26. There will be more cats. Individuals with high time costs are more likely to have cats than dogs. 27a. The demand curve is a rectangular hyperbola. The height of the demand curve is the marginal value, and the area underneath is the total value.

b. The compensated demand function lies exactly on top of the ordinary demand function because x1* does not depend on income.

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c.

The indifference curves must be vertically parallel.

28a. b.

x1 = 9w, x2 = 9w / (p2 + 3w) Positive: 9p2 / (p2 + 3w)2, negative: 9w / (p2 + 3w)2.

c. E2w = p2 / (p2 + 3w), E22 = p2 / (p2 + 3w). The elasticity with respect to the full price is 1. 29a. b. c. x1 = 15(3p2 p1) / p2 The same as in a. With no income effect, the two demand curves are identical.

30. Assuming p2 = 1, then for 5 units MV = 8/3, TV = 85/6; for 15 units MV = 2, TV = 75/2; for 30 units MV = 1, TV = 60; for 45 units MV = 0, TV = 135/2 31a. b. c. d. 32a. X1* = M/2P1, X2* = M/2P2, X1u = U(P2 / P1)1/2, X2u = U(P1 / P2)1/2 X1* = 30 and X2* = 45, U = 36.74 $72.38 SE = 6.76, IE = 5.24 X1* = 10 and X2* = 0
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b.

CV = $15, EV = $0

33.

(a) x1 = x2 = 5 (b) 10 2

34a. (b) $16

(c) (d) x1* < 6 35. For p1=$1, x1= 10. For p1=$3, x1= (10/3) 36. (a) Straightforward. (b) CV = $64 (c) EV = $576 (a) None.
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(b) p2 > 16

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Chapter 5 Intertemporal Decision Making and Capital Values 1. If Howard put $20 000 in a savings account today, at a 6% annual rate of interest, it would be worth $23 820 in three years. The present value of $25 000 payable in three years is approximately $20 990 when the interest rate is 6% per year. Howard should take the $25 000 and borrow against this future income. 2a. Sarah should take Package B if the interest rate is more than 20%, and she should take Package A if it is less than 20%. b. If we assume that her inheritance is Sarah's only source of income, then we infer that given a 25% rate of interest Sarah is better off if she chooses to spend more than $15,000 in the first year. More generally, she is better off if she consumes more than her income in the first year, because in this case she is borrowing and benefits from a decrease in interest rates. c. See Figure S5.1. Figure S5.1

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d. If both rates are less than 20%, then the present value of Package A is greater than the present value of Package B, and the future value of Package A is greater than the future value of Package B. Sarah should therefore choose Package A. Similarly, if both rates exceed 20%, Sarah should choose Package B. However, if the borrowing rate exceeds 20% and the deposit rate is less than 20%, we need to know Sarah's preferences before we can determine which package she should choose. 3. The present value of the stream of payments promised by this bond is exactly $100.00 when the interest rate is 5%, approximately $84.15 when the interest rate is 10%, and $71.45 when the interest rate is 15%. If all participants in the auction were thinking only about investing in these bonds or investing their money at the specified rate of interest, and if they anticipated a constant rate of interest over the four-year time horizon, and if they regarded both options as riskless, and if there were no transactions costs, then the bonds would sell at a price equal to the present value of the promised stream of payments. This exercise suggests that the price of bonds ought to vary inversely with the rate of interest, a pattern that is widely observed in real bond markets. 4a. Apples are not a capital good, and so the price is determined in the spot market and the interest rate will have no effect. The rise in the interest rate may lower the profitability of the firm, in which case the stock price will fall (it may have no impact). The value of the bonds will fall. b. Same as a.

c. The future price of apples will be lower. The value of the stock should fall because the current trees are worth less. The value of the bonds remains unchanged. 5. Once the announcement has been made I regret that I didnt sell the stock earlier, but now the price has adjusted such that the stock is expected to earn a normal rate of return. 6. The separation theorem allows us to analyze firm behavior independently of the preferences of the owners. This makes the analysis of supply possible, or at least a lot simpler. 7a. Present values of costs under the two options are

PV(A) = 9000 + 12000/(1 + i) + 15000/(1 + i)2 + 18000/(1 + i)3 + 21000/(1 + i)4 + 24000/ (1 + i)5 + 27000/(1 + i)6
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PV(B) = 45000 + 3000/(1 + i) + 6000/(1 + i)2 + 9000/(1 + i)3 + 12000/(1 + i)4 + 15000/(1 + i)5 + 18000/(1 + i)6 Which is the cheaper option clearly depends on the interest rate. If it small enough (below 13%), option B is cheaper, and if it is large enough option A is cheaper. b. She should consider other options - for example, using here current truck for two more years and then buying a new truck to be used until she retires. 8a. Unless the interest rate is more than 100%, Jerry should wait until the deposit increases. b. These sorts of expectations create an incentive for people to hoard cans until the deposit increases. 9a. The wealth of current homeowners would increase.

b. Prospective homeowners at the margin would be indifferent since the savings would be capitalized into the price of the home. c. There would be an increase in housing due to intra-marginal transfers and this would benefit those in the construction industry. 10. 11. Because the property tax savings is capitalized into the value of the farm. If technology allows things to grow faster, then the real interest rate should rise.

12. It would seem that as long as individuals still were impatient, then there still should be a positive interest rate. 13a. It depends on the interest rate.

b. 399 + 50/(1+i) + 50/(1+i)2 50/(1+i)5 = 99 + 150/(1+i) + 150/(1+i)2 150/(1+i)5 The solution is approximately i = 20%. 14. The price of the book would go up to reflect the future resales of the book. Not unless they could somehow commit to the strategy. The optimal strategy is to put out new editions every couple of years. Yes, since it is costly to reinvent the book. 15. About 21%. No.

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16. Suppose that all of ones income is in the next period. A mortgage transfers income to the current period along the budget line. When interest rates increase the budget line rotates in. However, those that have fixed mortgages remain on the same budget line and therefore have a higher wealth level. 17. False. A higher interest rate causes borrowers to reduce the quantity they borrow.

18a. The opportunity cost of using your own $1000 is the forgone interest. The cost of using the credit card companies $1000 is the interest they charge you. Though there is a difference in the cash flow, the cost is the same. b. The interest rate charged by credit companies is huge, much larger than the return on a savings account. 19. Ignoring issues of risk, nothing should happen to their wealth. The price of art work is the present value of the stream of services. If the art is expected to sell for a high price in the future, this is capitalized into the price today. If the future high price must be shared with the artist, then the price paid today simply falls until the wealth level is the same. 20a. b. The wealth at the beginning of your life is $156 536.44. You can consume $49 382.68 each year.

c. You borrow in the first period, save in the second and third, and use up the remaining savings in the fourth. d. At the beginning of the second period your wealth is $122 807.41. At the beginning of the third period it is $85,705.47. And at the beginning of the last period it is $44 893.34 21a. b. 22a. b. c. Harvest when MV=1.10, t=10 V(10) = $25.33, PV = $9.77; he could charge up to $9.77 Both PV and FV are higher for A. He will choose A. He will consume (C0,C1) = (5400, 5400) i = 143.75%

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23. For 10% t = ln(2) / ln(1.1) = 7.2 years. For 5% t = ln(2) / ln(1.05) = 14.2 years. For 20% t = ln(2) / ln(1.2) = 3.8 years. The rule of 72 says divide 72 by the interest rate (times 100) and you get the number of years it takes to double your money. It is only an approximation. 24. Because Wanda gets a tax credit on her initial investment, the entire $5000 earns 10% for 44 years. This amounts to $5000(1.1)44 = $331 320. Katie will have to pay taxes on her $5000, and her after tax interest is only 5%, so she ends up with $2500(1.05)44 = $21 392.

25. When food is abundant the marginal value of consumption is low. The opposite is true in times of want. Hence, it pays to shift consumption from low value periods to high value periods. Or, which is the same thing, to save when times are good.

26.

(a) 23.8% (b) 11.7% (c) Cannot say which hed choose given the information. (a) C0(1+i)2 + C1(1+i) + C2 = M0(1+i)2 + M1(1+i) + M2 (b) M0 + M1/(1+i) + M2/(1+i)2 (c) (1+i)M0 + M1 + M2/(1+i) (d) (1+i)2M0 + (1+i)M1 + M2

27.

28. 21.5%

29.

(a) Annuity is preferred. (b) $315.47

30.

(a) PV = 10,000zw0 + 10,000(1-z)w1(1.10)/(1.08) (b) 0.9818

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Chapter 6 Production and Cost: One Variable Input 1. a. True, b. Uncertain, c. True, d. True, e. Uncertain, f. True, g. True, h. True, i. True 2. 3. a. True, b. True, c. False, d. False, e. True, f. Uncertain, g. True a. True, b. Uncertain, c. True, d. True, e. True, f. Uncertain, g. True

4. No, profit maximization implies that production should always take place where there are diminishing marginal returns. 5. TP(z1) = z1 MP(z1) = 1 AP(z1 = 1 VC(y) = y SMC(y) = 1 STC(y) = 100 + y if z1 if z1 if z1 if y if y if y 100, and TP(z1) = 100 100, and MP(z1)= 0 100, and AP(z1) = 100/z1 100 100 100 100 100 100 if z1 > 100 if z1 > 100 if z1 > 100

SAC(y) = 1 + 100/y if y AVC(y) = 1 AFC(y) = 100/y FC = 100 if y if y

Since it is impossible to produce more than 100 units when z2 = 100, these costs functions are not defined for y > 100. 6a. b. TP(z1) = z1 1/4, VC(y)=2y4, AVC(y)=2y3, STC(y)=2y4 + 5 TP(z1) = 2z11/4, VC(y) =y4/8, AVC(y) = y3/8, STC(y) = y4/8 + 80

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c. Y Z2 = 1 VC STC Z2 = 16 VC STC 7a. b. two. 1 2 7 0.1 80.1 2 32 37 2.0 81.0 3 162 167 10.1 90.1 4 512 517 32.0 112.0

It should produce 14 units in plant one and 6 units in plant two. It should produce seven-tenths of its output in plant one and three-tenths in plant

8. We know that the firm 'minimizes cost by allocating output so that SMC is identical in the two plants. But SMC is just the price of the variable input divided by MP of the variable input. Hence, equality of SMC for the two plants implies equality of MP for the two plants. 9. The Blue Jays knew that going to arbitration was going to end up costing them something around $5 million a year in salary to Cruz. The opportunity cost was the players they could otherwise sign with this money. When a team gives up one athlete, it replaces him with another one. *10a. VC(y) = y = 2y 80 = 4y 400 SMC(y) = 1 =2 =4 AVC(y) = 1 = 2 80/y for y 80 160 240

for 80 < y for 160 < y for y 80

for 80 < y for 160 < y for y 80

160 240

for 80 < y

160

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= 4 400/y b.

for 160 < y

240

To maximize profit, produce 160 widgets and work 16 hours per day.

11. Absolutely. If the cost of remaining in ones current job goes to zero, then the wage is likely to follow. When other firms increase their bids for your service, the cost of remaining in the current job increases. 12. The cost of losing a finger is much higher for a surgeon than it is for a teacher. So, even though Tim is more likely to cut himself, it is less costly. 13. The cost of an airplane seat is sunk, and so if one is available, it costs the airline nothing to let the passenger fly. 14. This depends on how driving affects the alternatives of teenagers between the age of 16 and 18. If, for example, the teen lives in a rural community where it is necessary to drive to work, and this community has ample employment opportunity for the teen, then the cost of completing high school falls if the age is raised. 15. The time spent waiting is sunk. Since it is worth your while to wait one minute, you wait until the elevator comes. 16. Yes, since the cost of the pads is sunk.

17. Only if the cramp remains when Emily wakes up and therefore effects her alternatives. 18a. 3010 cars. No this is not efficient since the marginal cost is greater than the average cost. b. Conrad would set the marginal cost equal to the opportunity cost. In this case the optimal number of drivers would be 3000, and the optimal toll would be $10. c. 19. Then the optimal toll would be $6. Because at the margin, it is more productive to catch speeders.

20. Public pools do not maximize profits, and often dont even try to cover average costs. The lower prices lead to more crowded pools. For identical pools, the average and marginal products are lower at the public pools.

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21.

Because at the margin, the other players are more productive in scoring.

22. It may be more costly not to put locks in all cars when the cost of setting up lock installations at the factory have been put in place. 23. There is a fixed cost in making the buttons that get used in all applications. It is too costly, therefore, to make special buttons at the drive through bank, given that the braille lettering does not lower the value of the buttons. 24. It simply points out that there is value to attending classes. Students who skip classes feel that the extra performance isnt worth the cost of attendance, so there is nothing irrational in their behavior. 25. For plant 1 we have TP = z21/4, AP = z2-3/4, MP = 1/4z2-3/4, VC = 7y14, AVC = 7y13, MC = 28y3. For plant 2 we have TP = 33/4z21/4, AP = (3/z2)3/4, MP = (1/4)(3/z2)3/4, VC = (7/27)y24, AVC = (7/27)y23, MC = (28/27)y23. 26. y1 = 2, y2 = 6. The minimized VC is approximately $448. The marginal products across the two plants are equal.

27.

That allocation that equates the marginal cost between the two plants. a. y1 = 1/4y, y2 = 3/4y. b. (7/64)y4 TP = Z11/3 + 4 , MP = (1/3)Z1-2/3 VC(y) = W1(Y 4)3, STC(y) = W1(Y 4)3 + 8W2, SMC(y) = 3W1(Y 4)2

28a. b. 29.

(a) F1 is preferred. (b) F3 is preferred. (c) (2,1,1)

30. (a) $100 (b) $50, $100 (c) $170

31. (a) 5, 7, 4, 2, 0, -3

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(b) 5, 6, 5.33, 4.5, 3.6, 2.5 (c) TP(6) = 18 since the 6th cook can be kept out of the kitchen. 32. (a) 2 (b) AFC(2) = 2/3, AFC(5) =2/4, AFC(7) =2/7, AFC(11) =2/11 (c) AVC(2) = 1/3, AVC(5) =2/4, AVC(7) =3/7, AVC(11) =4/11

33. (a) (b) (c) (d) VC(y) = 4y2z1 AVC(y) = 4yz1 SMC(y) = 8 yz1 Same as part (c).

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Chapter 7 Production and Cost: Many Variable Inputs 1. a. True, b. Uncertain, c. True, d. False, e. Uncertain, f. Uncertain

2. a. True, b. Uncertain, c. Uncertain, d. Uncertain, e. Uncertain, f. True, g. True, h. True, i. True, j. True 3. 4. a. False, b. Uncertain, c. False, d. True, e. False, f. True a. Certainly false, b. Possibly true, c. Possibly true

5.

FC 2400

VC 600 1550 3300 5000 6300 7950 8800 10 500 12 700 14 900

AVC 60 77.50 110 125 126 132.5 125.7 131.3 141.1 149

TC 3000 3950 5700 7400 8700 10 350 11 200 12 900 15 100 17 300

MC 300 95 175 170 130 165 85 170 220 220

ATC 300 197.5 190 185 174 172.5 160 161.3 167.8 173

6a. b.

$3.25, $3.25, $2.5 See Figure S7.1

c. When w1 < w2, the cost-minimizing bundle is (0.7y,0.3y), and when w1 > w2, it is (0.3y,0.7y). d. C(w1,w2,y = y[0.7min(w1,w2) + 0.3max(w1,w2)] Figure S7.1

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7a. Letting z1, z2, z3, and z4 denote hours of Liz's time, litres of gasoline, hours of the smaller mower, and hours of the large mower respectively, the production functions are min(z1, z2, z3) and min(z1/3, z2, z4/3). b. If Liz uses the smaller mower, the conditional input demand functions are z1* = y, z2* = y, and z3* = y. If she uses the larger mower, they are z1* = y/3, z2* = y, and z3* = y/3. The cost functions are y[w1 + w2 + w3] and y[w1/3 + w2 + w4/3]. c. The smaller mower entails lower costs if w1 + w2 + w3 is less than w1/3 + w2 + w4/3, or if 2w < w4 3w3. The price of gas is irrelevant because the gas costs per unit of lawn mowed are the same for the two mowers. d. If the smaller mower is the cheapest way to cut grass, the price Liz gets for cutting a unit of lawn must exceed w1 + w2 + w3. If the larger mower is the cheapest way to cut grass, the price she gets for cutting a unit of lawn must exceed w1/3 + w2 + w3/3. 8a. Yes, both inputs are variable.

b. No, the cash flow is different because one firm rents capital, but the opportunity cost of owning means that the costs are the same. 9. this. We should never have anything worse than constant returns to scale because of

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10. When wage rates are low, as in small towns, labour is used more often. Hence candy and newspapers are sold using sales people. In urban centers, where wages are higher, firms substitute into capital to dispense these goods. 11. 12. 13. No. 7 percent. False, this ignores the higher marginal product of input 2.

14. False. The marginal products are set equal to their cost in order to minimize costs. 15. 16. No. (a.) (b.) (c.) (d.) (e.) MP1 = uz1u-1z2v and MP2 = vz1uz2v-1 MRT = MP1/MP2 On a straight line. c* = 5y/2(w11/3w22/3), and AC = 5/2(w11/3w22/3) c* = y1/(u+v)[w1(uw2/vw1)v/(u+v) + w2(vw1/uw2)u/(u+v)] AC = y1-u-v/(u+v)[w1(uw2/vw1)v/(u+v) + w2(vw1/uw2)u/(u+v)] (f.) (g.) (h.) MRT = uz2/vz1 u + v > 1 IRS, < 1 DRS, = 1 CRS. MRT decreases as z1 increases. Figure S7.2

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17.a. Figure S7.2 is relevant here. b. The Lagrangian method finds an interior tangency and the second order condition assures a maximum. With the first function, the second order condition is violated and a tangency gives the solution with the maximum cost. With the second function there is no tangency. c. The marginal product of input 1 for the first function is 4z 1/(z12+z22). For input 2 the marginal product is 4z2/(z12+z22). The MRTS is z1/z2. For the second function the marginal products are 1 as is the MRTS. d. No. In the first case there is increasing MPs, and in the second case there is constant MP. e. Nothing. RTS is a statement about the movement from one isoquant to another.

f. For w1 not equal to w2, we have the following results for both production functions: Z1* = y and z2* = 0 if w1 < w2 z1* = 0 and z2* = y if w1 > w2

g. For all input prices, and for both production functions, we have the following cost function: C(w1, w2,y) = ymin(w1,w2) The only differences arise when w1 = w2. In this case, either of the input bundles identified above is cost-minimizing for both production functions, and for the second
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production function, any other input bundle on the appropriate isoquant is costminimizing. h. True. A firm will never operate there. It can lower costs by moving to the convex portion or to a corner. 18a. Aside from the fact that there is no output for the small levels of inputs, the isoquants are simply Cobb-Douglas shaped, but shifted over. b. c. d. The function is not homogeneous, therefore it does not have any returns to scale. F1 = 1/3(z1 5)-2/3(z2 7)2/3 F2 = 2/3(z1 5)1/3(z2 7)-1/3 MRTS = (z2 7) / 2(z1 5)

e. Setting the MRTS = 1, we see that the expansion path is given by x 2 = 2z1 3. Note that this is a straight line that passes through the point (5,7). f. No. It has linear expansion paths, but they do not pass through the origin. This function is known as quasi-homothetic. g. The conditional input demands are:

z1* = 0 and z2* = 0 if y = 0. z1* = 5 + y(w2 / 2w1)2/3 and z2* = 7 + y(2w1 / w2)1/3 if y > 0. The cost function is C* = w1z1* + w2z2*. Therefore, C* = 0 if y = 0, and C* = y(w11/3w22/3)(2-2/3 + 21/3) + 5w1 + 7w2 if y > 0. 19a. MPL = 2/3L-1/3 MPK = 1/2K-1/2. The MRTS = 4K1/2 / 3L1/3

b. The cross marginal products are zero, and the isoquants are concave to the origin as usual. Otherwise there is nothing abnormal.

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c. If wL < wKy then you should use labour instead of capital. With the numbers given, labour is the cost minimizing input, therefore you need L* = 2000(2 1/2). d. 20. 21a. b. The function is not homogeneous. Yes for (16), no for all the others. STC = W1(y/ Z20) + W2 Z20 Z1* = [ y (W2/W1) ]1/2 , Z2*= [ y (W1/W2) ]1/2 , TC = W1[ y (W2/W1) ]1/2 + W2 [ y (W1/W2) ]1/2 c. 22a. b. c. If Z20 = Z2* = [ y (W1/W2) ]1/2 STC larger 39, 65, 91. Output levels irrelevant Z2* = (7/13) Z1* No, we need to know the production function.

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d.

No. Implied by homotheticity.

23. The electrical industry has been dominated by enormous firms running large power plants and controlling the grid. If small power plants become more economical, the industry will become extremely competitive, with no large power generators.

24. (a) Graph of z2 = 9/ z1. (b) min w1 z1 + w2z2; choosing z1 and z2; subject to z1z2 = 9. (c) z1* = z2* = (y)1/2 (d) TC(9, w1, w2) = 6w (e) Graph of z2 = 6 - z1. (f) One unit of z2.

25. (a) Increasing returns (b) Constant: F(az1, az2) = aF(z1, z2) for 0 < a < 1. Increasing: F(az1, az2) < aF(z1, z2) for 0 < a < 1. Decreasing: F(az1, az2) > aF(z1, z2) for 0 < a < 1. 26. (a) F(z1, z2) = 3z1 + 5z2. (b) MP1 = 3; MP2 = 5. (c) MRTS = 3/5. 27. (a) z1* = 5; z2* = 10/3; TC(10, 1, 3) = 15 (b) z1* = 5; z2* = 0; TC(10, 1, 3) = 5 (c) z1* = 5; z2* = 0; TC(10, 1, 3) = 5 28. (a) Adam with Debby and Ben with Claire. (b) 80/120 67% (c) No, with Claire and a equal share he gets 54, but with his offer to Debby he only gets 40.

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Chapter 8 The Theory of Perfect Competition 1a. True, b. False, c. True, d. False, e. True, f. Uncertain, g. True, h. True, i. False, j. Uncertain, k. True, l. Uncertain 2a. Equilibrium price and quantity are $5 and 7500. There are 1500 firms in equilibrium, each producing 5 units and earning 0 profit. b. Equilibrium price and quantity are $5 and 15 000. There are 3000 firms in equilibrium, each producing 5 units and earning 0 profit. c. Long-run equilibrium price would exceed $5, and equilibrium quantity would be less than 15 000. 3a. Revenue increases by $24 999.625. If the firm ignored the slope of the demand curve and assumed it was flat, it would have guessed at an increase of $25 000. b. c. It would be $100,000. No.

4. This is a major short coming of the competitive model. As we see in the chapter on general equilibrium, the historical solution has been to introduce an imaginary auctioneer that works for free. This fictional character sets the price. 5. LAC(y) = 50/y + 2y. The efficient scale of production is 5 crates of berries per day. Minimum average cost is 20, which is the long-run equilibrium price. 6. Notice that LAC(y) is independent of y; that is, average cost is identical for all levels of output. Hence, there is no unique efficient scale of production. Long-run equilibrium price is equal to (w1w2 / 300)1/2, and equilibrium quantity is just the quantity demanded at this price. Since there is no unique efficient scale, the sizes and number of firms in equilibrium are indeterminate. 7a. The firm will produce 15 units, and its profit will be $400. It is possible, though clearly not necessary, that this price is a long-run equilibrium price and that this firm has the wrong scale of production. b. y* = (p 10)/2

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c. The firm makes zero profit when price is $60. This price may or may not be a long-run equilibrium price. 8a. b. c. y = 2000 20p y = (p 5) / 2 y = 5p 25

d. The graph should have the demand curve going from p = 100 to y = 2000. The market supply curve has an intercept of 5 and a slope of 0.2. The equilibrium price is $79, and y* = 420. Each firm produces 42.

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9. This statement confuses change in demand with a change in the quantity demanded. When the demand for cigarettes falls, the quantity demanded also falls with the price. 10. If the Middle East supply is cut off this raises the cost of oil and reduces the LRS of gasoline. This reduces the quantity sold and raises the price. If in response to this a ceiling on gas prices is put in place then there will be a further reduction in the quantity supplied and a shortage will arise. A number of things might arise. Gasoline might be rationed by waiting, black markets may arise, and real resources will be devoted to acquiring the good. 11. Prices are determined by demand and supply. Demand is based on the budget constraint which in term is partly determined by ones income. Hence if the price rises to a certain level, someone must be able to afford it. 12. Yes it will be improving as long as the endowments are different. However, not everyone will be made better off. 13. Large fixed costs of production.

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14. Since cabs are regulated in numbers the elasticity of supply is zero. They are fixed in number. Umbrellas, on the other hand, are easily stored, and easily moved out to the street. The elasticity of supply is very large. The result is no increase in the price of umbrellas when it rains, but a large response in supply. 15. No he should shut down.

16. Sure. Long run and short run are related to expectations. If there has been some change in the economy that individuals take as permanent, then a long run adjustment is made. If the change is viewed as temporary, then even though it may last a long time, only a short run adjustment is made. 17a. Since every firm is identical, the LRS curve is flat at $30

. b. c. d. P = $30. Y = 1900. Each firm produces 20 units, so there are 95 firms. AC = y 20 + 400/y. MC = 2y 20. AC is at a minimum at y = 20.

y = p/2 + 10, The industry supply curve is y = 95p/2 + 950.

e. The price is still $30 because all firms are the same, including the potential entrants. Output is now 2400. 18a. b. MC = 6y +75, AC = 3y +75 +75/y. Price equals the minimum of AC which is $105.

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c. Quantity demanded is 4895 units, and each firm produces 5 units. Therefore there are 979 firms. 19a. b. c. d. 20a. b. c. d. 21. P* = 6, Q* = 240 The number of firms = 80 Qs = 40P PS = 1440; CS = 720 P = 10, Y = 280 The number of firms = 56, each produce 5, profits = 0 P = 4; Y = 252, y = 4.5 P = 10, Y = 210, the number of firms = 42 (a) Step functions of cumulative quantities demanded/supplied. (b) 3 < p < 3.5 (c) 2 tickets 22. (a) (y) = (p + 10)y y2 (b) 5 (c) SMC(y) = 2y 10 (d) 11/2 (e) 121/4 23. (a) DA+B(y) = 8 (2/3)y (b) SA+B(y) = (5/3) + (2/3)y (c) y* = 19/4 24. (a) Large numbers and product homogeneity (b) Perfect information (c) Independence 25. (a) from p=5 and Q=5/2 to p=5 and Q=7 (b) from p=10/3 and Q=10/3 to p=6 and Q=6 (c) from p=30/7 and Q=20/7 to p=8/3 and Q=28/3 (d) Yes, but would be very unusual.

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Chapter 9 Applications of the Competitive Model 1. 2. 3. The demand for heat in the night is different than the demand for heat in the day. They build cars and put them in a boat. The boat comes back filled with coal. False, the tax will be borne by the specific factor.

4. False, a subsidy creates a deadweight loss as well since it moves firms away from the efficient level of output. 5. Well, if the Japanese never did anything with the dollars, then yes, we should like the deficit. In other words, imports are not a bad thing. Eventually we pay for import through exports. Of course, the trade makes us better off.

6a.

Q 1 2 3 23 24

TC 110 119 127

MC 9 8 7

AC 110 59 42

AVC 10 9.5 9

366 388

22

15.9 16.2

11.5 12

b. Supply can be written as p = (1/1000)q 2, and the demand curve is p = 255 000/q. Solving we get q = 17 000 and p = $15. c. Each firm takes the price of $15 as given, and at this price the linear MC intersects it at a level of 17. This is also the minimum AC point. d. The supply curve is now p = (1/1000)q + 2. Solving we find the new equilibrium quantity is 15 000 with a price of $17. e. It is similar in shape to that of part c), but all cost curves shift up by $4. At the new equilibrium the firms are losing $2 per unit.

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7. If you are alone in experiencing this increase in theft, then there is nothing you can do about it. If all firms in the industry experience it, then there will be a rise in the price, and depending on the elasticity of demand, the price will rise to mitigate the increased cost. 8. They were in competition for citizens, especially women. To make the west more attractive for women, states offered them rights that they did not have in the Eastern states. 9. Equilibrium price will fall and quantity will increase. The quantity produced by each firm will decrease, and the number of firms will increase. Each firm will produce where [LAC(y) 100,000/y] is a minimum, and equilibrium price will be the value of [LAC(y) 100,000/y] at this minimum point. 10a. Consumers will prefer the lump-sum tax since it will cause price to rise by a smaller amount. b, The excise tax will lower output per firm while the lump-sum tax will result in no change in output per firm. 11a. It raises the price in both cases. If the demand for eggs becomes more elastic over time the price should drift down. b. The quota means that firms cannot produce more than 4000 eggs. As long as optimal number of eggs per farm exceeds this, the farms are constrained. c. They fall.

d. Assuming the farmers did not need to compete for the quota, then they benefit and consumers lose. Future farmers do not benefit because they will be required to pay for the quota. e. Every individual farmer would like to sell more eggs. The system will have to police this cheating. f. When it is inelastic. Under this condition the increase in revenue is greater.

12. The rep was just plotting a series of equilibrium points. That is, the points where a demand curve and supply curve intersected in a given year. There is no reason why this should pattern anything.
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13. Raspberry prices should be lowest at the time of harvest and then rise over the winter. Turnips should have the same general pattern, but with much less variance. 14. Those below 18 years of age face a lower set of punishments under the law. We dont know why males are more often engaged in crime. 15. Because people engage in protective activity that is costly.

16. No, it will depend on the relative elasticities of demand and supply. If secretaries are in more elastic supply then they will pay less of the tax. 17. There would be a large fall in the demand.

18. This lowers the cost of an abortion, increasing the number; it raises the cost of other medical services; and increases the price of adoption as the supply of babies falls. 19. The low male/female sex ratio for blacks means that men are relatively scarce and the terms of trade in sexual bargaining move in their favor. To compete for men, black women will be more willing to have sex out of marriage and the out of wedlock birthrate should be higher. 20a. b. 21. P = 180, Q = 440, Tex = 79 200, CS = 48 400, PS = 30 600. DWL = $6000. P = 200, Q = 500, CS = 62 500, PS = 40 000, DWL = $1500.

22. Auto thefts should fall, even if a car owner doesnt have the LoJack device. In other words, the device creates a positive externality for all car owners. It should also cause car thieves to substitute into other forms of burglary, including breaking into cars rather than stealing them. 23. This increases the incentive to own cars and reduces the incentive to take public transit. It reduces the number of vacant spots and increases the time spent looking. It reduces the density of cities. 24. (a) No, prices adjust so supply meets demand. (b) Condos are lower-cost substitutes for detached houses near city centers. 25.

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(a) MC(t) = 4 (b) 21 (c) Down. 26. (a) Q*=20 and p*=2 (b) p*=3 (c) 3750 (d) 15,000 27. (a) p*=1000 and Q*=500 (b) zero since time is needed for changes to begin (c) Q*=400 (d) 200 28. (a) p*=5 and Q*=100 (b) 100 (c) 40 (d) 20

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Chapter 10 - Monopoly 1a. The profit-maximizing price is $45 per book, 1250 books will be sold, profit will be $6250, and the author's royalty will be $37 500. b. The profit-maximizing price is $30 per book, 5000 books will be sold, profit will be $100 000, the author's share of the profit will be $75 000, and the publisher's share will be $25 000. Notice that the author, the publisher, and the student are all better off now then in part a. c. The problem with the original agreement is that the $30 royalty fee per book is not really a cost of production. It is just a way to compensate the author. As we have seen, profit sharing may be a better way to compensate the author. 2a. Marginal cost is $5, the profit-maximizing output is 20 units, the profit-maximizing price is $45, and profit is $800 F. b. Price is driven down to $45 when the monopolist produces 20 units, and price drops by $2 for every unit the entrant produces. c. The entrant would produce 10 units, price would be $25, and the entrant's profit would be $200 F. d. 3a. b. The market is a natural monopoly for any value of F greater than $200. In effect, the tax raises the monopolist's marginal cost by the amount of the tax, t. The following table gives the relevant information for various values of t:

t 0 6 12 18 4a.

output 29 28 27 26

price 93 96 99 102

profit 2523 2352 2187 2028

The profit-maximizing quantity and price are 40 and $120.

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b.

c. With a $105 price ceiling, the profit-maximizing price and quantity are $105 and 50. With a $130 price ceiling, the profit-maximizing quantity and price are 40 and $120 the price ceiling doesn't bind in this case.

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d. The efficient solution is price equal to $60 and quantity equal to 80 units. A price ceiling equal to $60.01 will get the monopolist to produce nearly 80 units at the price ceiling. If the price ceiling is exactly $60, however, the monopolist is content with any positive output, or no output at all.

5a.

TR 0 9 16 21 24 25 24 21 16 9 0

MR 9 7 5 3 1 1 3 5 7 9

TC

MC 4

4 8 12 16 20 24 28 32 36 40

4 4 . . .

b. The key here is that the AC = MC and the line is flat at 4. P = 7, Q = 3, and profit equals 9. c. Consumers surplus equals 4.5.

d. P = 4, Q = 6. In doing this we are assuming that costs do not change with the change in market structure. e. f. Profit is zero, consumers surplus is 18. DWL = 4.5.

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g. Now the firm would still maximize profit at the original level, Q = 3, P = 7. The effective price paid is 4.03, the DWL is still 4.5, and the consumers surplus is 13.41. 6. It increases by $1.50.

7. No, not necessarily. For example, if we have an industry where each firm has different MC and different levels of AVC, then at some very low price only one firm will be in the industry, even though it is perfectly competitive. This firm still faces a horizontal demand curve and is not a monopoly. In other words, a perfectly competitive industry could be so small, one firm supplies the market. 8. If y 5, the possibility of import competition means that the Nickel Company

cannot charge a price higher than $85. Hence, its marginal revenue function is $85 for y 5. When y = 20, marginal revenue in the Canadian market is $50, the competitive price in the world market. For y > 20, the Nickel Company sells 20 units in the Canadian market at a price of $70 and y 20 in the world market at a price of $50. Its marginal revenue function is $50 for y > 20. If 5 < y 20, then the Nickel Company sells only in the Canadian market at a price equal to 90 - y, and its marginal revenue function is 90 2y. a. If a = 2, marginal revenue equals marginal cost when y = 25, and the company sells 20 units in Canada at a price of $70, and 5 units in the international market at a price of $50. Its revenue is $1650, and its costs (equal to the area under the marginal cost function and above the horizontal axis from 0 to 30 units) are $625. Its profit is then $1025.

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b. If a = 4, it sells 15 units in Canada at a price of $75, and it sells nothing in the international market. Its revenue is $1125, its costs are $450, and its profit is $675.

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c. If a = 34, it sells 2.5 units in Canada at a price of $85. Its revenue is $212.5, its costs are $106.25, and its profit is $106.25.

9. Total revenue is 200y y2/2, average revenue is 200 y/2, and marginal revenue is 200 y. 10. When a good is durable after individuals pay the high price, the monopolist can offer the good to other consumers at a lower price. In anticipation of this, the first customers offer the lower price to begin with. Disney was trying to convince people that it would not engage in this type of pricing. 11. Firms can become monopolies through producing good products at prices lower than competitors. It may be that monopoly pricing in these circumstances is better than competitive pricing at higher costs. 12. No. If increases in prices lead to increased revenue, then the tobacco market must be selling cigarettes in the inelastic region of the market demand curve. A monopoly firm would not do this. 13a. MC = 2y 4, MR = 80 2y, and AC is at a minimum when y = 25.

b. To set MC = MR. c.

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d. y* = 21, p* = $59, and the firm earns $257.

e. The firm will now sell 27 units at a price of $50, and the firm earns $104.

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14a. b. 15a. b. 16a. b.

pa = 33, ya = 27. Pb = 21 yb = 30 pa = 29, ya = 31. Pb = 23 yb = 26 p = 40, y = 30, profit = 800. p = 36, y = 32, profit = 780. Profit = py wL vK L = py wL vK + [py sK wL]

c. If we substitute the constraint in we see that profit equals K(s v). If s<v then clearly the firm will produce no output and set K = 0. d. If s = v the firm will produce the same cost minimizing output as it would if it was not regulated. e. 17a. b. c. If s > v then the firm increases the amount of capital and raises its average costs. p = 44, y = 36, profit = 1224. p = 8, y = 72. DWL = 648

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d. 18a. b. c.

AC would need to increase by $36. MC = AC = 10, MR = 24 y/2 y = 28, p = 17 profit = 196 (blue rectangle), CS = 98 (green triangle), DWL = 98 (red triangle)

d.

y0 = 56

e. CS = 0 (positive CS for first half of the quota is compensated by negative CS for second half), DWL = 0 (quantity is efficient), profit = 392 (black/yellow rectangle)

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19a.

Ym = 28, Pm = 114; Y* = 56, P* = 30; yes (MC and AC coincide)

b. Ym = 16.5, Pm = 148.5; Y* = 22, P* = 132; no yAC > y* (AC (green) always below MC (red))

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c.

Ym = 28, Pm = 114; Y* = 56, P* = 30; no y < y* (AC (green) always above MC (red))

20. (a) AC, MC, MR as given, AR is D(y) (b) 150 liters (c) p* = 8.5 (d) No, selling the extra milk would lower profit. 21. False. While it could be true in many cases, it is not universally true since while demand is always positive, it may be very small and shrink quickly with rising prices. 22. (a) AR(y) = 20 2y (b) TR(y) = 20y 2y2 (c) y=0 and y=10 (d) y=5 (e) MR(y) = 20 4y

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23. (a) MR(y) = 20 2y (b) y* = 5 (c) p* = 15 (d) 50 24. (a) MR(y) = 30 6y (b) Straightforward. (c) Area = 50/3 25. No, it makes no sense because there is no interior solution in this case. The firm should produce some trivial amount (or one unit if discrete units are only possible). This generates the same revenue, but minimizes costs. A tax extracts rents from the firm, but does not change the amount it produces (unless the firm goes out of business).

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Chapter 11 Input Markets and the Allocation of Resources 1. Salaries are determined by the supply and demand for labour in a given occupation. The demand for good college sports coaches is high because a good coach can generate millions of dollars for a university, and the supply of such people is limited because few have the talent. Although the supply of humanity professors is probably quite low, so is the demand. Hence salaries are not determined by how many hours one works, how many years it took to get an education, or how unpleasant the work is. However, these things do feed back into the supply of labour and therefore indirectly influence the wage rate. 2a. His marginal revenue function is 1.50 0.01y, the profit-maximizing output is 100 cans, the price is $1 per can, and his profit is $50 per ballgame.

b. The one costly input is the pop he buys. Letting z denote the quantity of pop, MRP(z) = 1.50 0.01z since the marginal product of this input is 1. This is, of course, Walley's input demand function, and he maximizes profit by choosing z so that MPP(z) is equal to the input price. If the input price is $.50 per can, he buys 100 cans, and if it is $0.70 per can, he buys 80 cans. 3. In equilibrium, z1 = 22, z2 = 18, w1 = 24, and w2 = 36.

4. Scarcity means that there are not enough schools, roads, cars, and other goods that we value. Since we always want more of these things, there must be too many jobs! The social problem is how do we allocate a scarce amount of labour to do the jobs

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that we value the most. With a price system, the quantity of labour demanded does depend on the wage rate. As a result, when people say there are not enough jobs, what they mean is that there are not enough jobs at a certain wage. 5a. b. c. Firm A will offer w = $30, and firm B will supply 60 units. Firm B will offer w = $72, and firm A will demand 48 units. Firm C would produce 80 units.

6. Suppose that the supply of labour to the labour broker is a + hz, where a and b are positive constants. The marginal factor cost to the labour broker is a + 2bz. Suppose that the demand for labour is c - dz, where c and d are positive constants and c > a. The broker will choose z so that marginal factor cost is equal to marginal revenue, employing z* = (c a)/(2(b + d)). Then, w1 = a + bz*, and w2 = c dz*. 7. As the wage increases workers substitute into more hours worked. However, if leisure is a normal good, then the income effect implies more leisure is desired. At high incomes, the level of hours worked might fall. 8a. Minimum wages tend to effect individuals with low levels of human capital. Teenagers, part-time workers, etc. b. Assuming that the wage is binding, then the minimum wage is above the equilibrium wage and as a result fewer workers are demanded. At the same time more workers supply their labour to the market and unemployment results. Workers will seek non-price forms of competition to get the high paying jobs. c. 9a. No, the increased min. wage reduces their competition. You get a straight line with slope 4.

b. Now the budget line has two kinks in it. At 24 hours of leisure the individual still can have $40 worth of consumption. Hence the budget line is vertical. When the individual starts working, the effective wage is only $1 per hour, so the slope of the budget line is reduced. This occurs until the welfare is paid back: After working 13 hours and 20 minutes. After this the wage is again $4 per hour. c. The effect will be to encourage individuals who are working to join the program.

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10. The demand for labour is based on the value of the marginal product. Sports stars would not earn the high salaries they do unless they could generate at least that much income to the team owner. 11a. The budget line, which is kinked at 40 hours of work, is illustrated in Figure S11.1. b. If indifference curves are smooth and convex, the individual will want to work overtime since MRS at 40 hours of work will be equal to w and for more than 40 hours of work the wage rate is 1.5w that is, the kinked budget line in Figure S11.1 will intersect the indifference curve at 40 hours of work. (This case is not shown in the figure.) c. The indifference curve in Figure S11.1 illustrates this case. Figure S11.1 Figure S11.2

12. Figure S11.2 is useful here. The initial equilibrium is at A, and the subsequent equilibrium is at B. Since Ralph works more than 40 hours in both the initial and the subsequent equilibrium, the wage increase for his primary job, where he can work just 40 hours, involves only an income effect. Hence, since leisure is a normal good, Ralph works less at B than at A. It is, of course, possible that Ralph chooses to work less than 40 hours after the wage increase. In this case, which we have not illustrated, Ralph reduces hours of work for his secondary job to zero. 13. Assuming that her indifference curves are smooth and convex, she would choose the 20% increase in her wage rate. See Figure S11.3. The key thing to notice in
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constructing Figure S11.3 is this: if Helga were to continue to work 10 hours, her income would increase by $100 under both options. If her indifference curves were kinky, it is possible that she would be indifferent between the two options. Figure S11.3

14a. There is a great deal of animosity and tension. Those in high demand fields want the salaries to be more flexible and the numbers of faculty in low demand fields to be limited. b. These problems will be more severe as the quality of university increases.

15. It hurts them because it lowers the rate of return on capital they invest and raises the cost of capital that they borrow. 16. The demand for CAD technicians is much higher than the demand for English professors. 17. Adults who deliver papers, pick berries, and generally do low-skill jobs that children can compete for. 18. Because workers here have more human capital and are more productive. The higher wages reflect this higher level of productivity. 19. Wages in Canada will fall in those markets where the Sri Lankans work. The rental rate in Sri Lanka will fall. The wages in Sri Lanka will rise.

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20. No, this is a good discussion question to get students to think about the limits of the neoclassical model of labour markets. 21a. b. It would look like Figure 11.13 It would increase.

22a. MRP(z) = 2400 40z, and ARP(z) = 1600 20z. MRP(z) is the firm's demand function. The firm will use 59 units when the input price is $40, and it will use 58 units when it is $80. The profit-maximizing rule for this input market is to choose z so that w is equal to MRP: w = p(120 2z) where p is price of the firm's output. b. Marginal cost is just input price divided by marginal product. Hence, setting marginal cost equal to price, we get w/(120 2z) = p as the profit-maximizing rule, which is equivalent to the profit-maximizing rule in the input market. c. Again, the firm will choose z so that w = p(120 2z). The firm will use 59.3 units when the input price is $40, and it will use 58.7 units when it is $80. 23a. The necessary condition is to set the MRTS equal to the relative price. That is, K/L=1/4.

b.

L = (Q/2)(r/w)1/2, K = (Q/2)(w/r)1/2

c. Initially the demand for labour was L = y. With the minimum wage, the demand is L = .71y, which is lower.

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24a. L*= (9+8w)/w and C* = (18+16w)/p. Therefore, the optimal bundles are L* = 11 and C* = 33. b. The supply of labour is 24-L*. Therefore the supply of labour is (16w 9)/w. c) If the individual works 8 hours he can consume 25.5 units of C and 16 units of leisure, which gives a utility level of 21.8. If the individual does not work he can only purchase 13.5 units of C and 24 hours of leisure for a utility level of 16.4. Hence he would work the 8 hours because it improves his level of utility. 25a. z1* = y(w2/w1)1/2, and z2* = y(w1/w2)1/2. This means the cost function is C* = 2y(w1w2)1/2, implying that in equilibrium the price of the output is P = 2(w 1w2)1/2. b. The equilibrium conditions are w1* = y(w2/w1)1/2, and w2* = y(w1/w2)1/2/4.

c. If we solve y in (b) in terms of prices, we get y= (w1w2)1/2/2, and substitute into the price equation in a), we get: P = y.

26. (a) 8hrs (b) 5hrs (c) Firm A (d) Firm B

27. If $12 is less than the max AP, then choose the level with the downward-sloping MP, else choose 0 hours. 28. (a) $20,661 (b) Fall. (c) Fall.

30. Create a new processing plant jointly owned by the farmers. Or try a cartel (problem with the prisoners dilemma, though it would be a repeated game). Or designate a single seller to negotiate all sales.

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31. (a) $141.41 (b) The new production function.

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Chapter 12 Labour Market Applications 1. New competition breaks the monopsonist power in the market, and forces the owners to pay salaries that are closer to the marginal products. Thus, salaries should rise, and prices should come down! 2a. Hilary will hire 48 workers at a wage rate of $26.

b. Given Hilary's demand for labour, if the wage rate is less than $60, an increase in the wage rate will cause Hilary to hire more workers. c. The highest wage rate consistent with not reducing employment is $42.

3a. The equilibrium wage rate is 68, 102 workers are allocated to sector 1, and 48 workers are allocated to sector 2. b. The wage rate in sector 2 will be 44, and 96 workers will be in this sector.

c. There will be approximately 88 workers chasing 54 .jobs in sector 1, in any one period, there will therefore be about 34 unemployed workers, or an unemployment rate of 23%. The expected wage in sector 1 in any period will be 61.2, equal to the certain wage in sector 2.

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4(i) Lump-sum transfers are consistent with Pareto-optimality because they do not distort market prices. (ii) They are impractical as a means of redistributing income, or wealth, because for any practical set of guidelines determining who is to receive a transferthere are actions which some people can take that would qualify them for the transfer. This means, of course, that for these individuals, the transfers are conditional, that is, they are not lump-sum transfers. (iii) In the presence or a conditional transfer, the price of leisure to individuals is not equal to the price of labour to firms, which distorts the allocation of time to leisure and work. 5. If the demand for services is price-inelastic, then an increase in the price of professional services increases the total income that members of the profession can earn and decreases the quantity of services demanded. Thus, immediately after the price increase, existing professionals will earn more and work less. But this makes the profession more attractive, and more people will enter it, reducing the average income

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and average hours worked by each professional. If existing professionals and new professionals have identical preferences, the entry of new professionals will cease only when the profession is as attractive as it was before the price increase. In this case, in the long run professionals are no better off, and society is worse off because each professional is underemployed. If existing professionals do not have to meet higher entry standards, they have a clear private incentive to increase entry standards. The increase in standards will make the profession less attractive to new entrants, and the supply of professional services will shift leftward, increasing the price of professional services. 6. The $50/day is essentially an income effect, which lowers the amount of work by increasing the amount of leisure demanded. The wage subsidy has a small income effect, but has a substitution effect towards more work. 7. The problem was that when you double low wages, you still end up with low wages. Women working for $7/hour were not much enticed to work at $14/hour, given that they were single parents who had to worry about things like daycare, school, etc. The one thing that mattered most to the women was part-time versus full time work. If the program could be applied to part time work, then it would probably have a bigger effect. 8. In the closed shop the workers are earning a premium which no doubt leads to excess supply. Given that there will be no wage competition here, the firm is likely to engage in other forms of discrimination. 9. The fundamental problem with comparable worth is that it confuses total and marginal value. 10. Women have to take time off to have children. During this time they may find it hard to keep up their human capital. The cost of having children is higher for women in science than for women in the humanities. 11. Wages are not determined by total productivity. The marginal product of one more ambulance driver is what determines the wage, and this is usually much lower than other occupations. 12a. b. UR = 20 and UD = 40. Ransom should get 160 and Divine should get 40.
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c. d.

Ransom should get 40 and Divine should get 160. They should now split the food 50-50.

13. The logic behind this is that once information is discovered, it costs nothing to disseminate it. Therefore, the government should pay the inventor for the effort, and place the information in the public domain for all to use. If the value of the innovation is known, this will improve welfare. There is still an incentive to invent, and the idea is used optimally. In practice, it may be impossible to determine the true value of the idea. In fact, the state may end up purchasing many innovations that are of no value at all. 14a. X1*=12 ,X2*=60

b.

X1*=14 ,X2*=70

c.

X1*= 24 ,X2*=40

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d.

X1*=15 ,X2*=50

15a.

Z = 30, W = $8

b. Unexploited gains from trade: If monopsonist could hire additional workers without raising the overall wage level...... c. Efficiency improving if: $8 < W* < $13. A minimum wage within this range would result in an increase in employment. d. W* = $9 (Z*=36)

16. Men would be unable to compete with women for the jobs, and the industries would become dominated by women.

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17. It seems difficult to support this information with a simple discrimination argument. If discrimination is against homosexuals, then why do lesbians earn more than straight women? Lesbians are about as likely to be mothers than marriage heterosexual women. This difference in fertility likely explains differences in human capital accumulation. Likewise, in gay relationships, some males may make human capital decisions that encourage household rather than market production, and their market wages reflect this. 18. If an occupation, prize, or activity requires extreme levels of IQ, then females will be drastically under-represented. Likewise, if low IQ individuals are more likely to get caught in crime, males will be over represented in prison. This is not discrimination, but a reflection of the pool available. 19. Absolutely. Consider strong hockey or football players. Females are unable to compete with men in the NFL (as are most men), and these players earn substantial wages for being so exceptional. This is not a matter of discrimination. 20. People will engage in costly discrimination if they do not have to bear the costs of the discrimination. Hence, it is more likely in non-profit firms, government agencies, and firms where managers (not owners) make the decisions. 21a. They likely have chronic low enrollments and be in low demand by students. b. By offering high grades, these departments encourage students to enroll in courses they otherwise would not take. 22. (a) Minimum wage will have no impact since it is below the competitive equilibrium wage of $10. (b) Minimum wages greater than $10 will cause inefficiencies. (c) The monopsonist will hire 6 workers at $6. (d) At a minimum wage of $10 the monopsonist will hire the most workers. (e) The minimum wage level of $12 will maximize the wages.

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Chapter 13 Competitive General Equilibrium 1. When good 1 is monopolized, efficiency in product mix is violated because the common value of MRS exceeds MRT. Hence, too little of good 1 is produced. By subsidizing the production of good 1 or by taxing the production of good 2, we can cause the production of good 1 to increase and the production of good 2 to decrease. By choosing the value of the subsidy or tax appropriately, we can establish equality of MRS and MRT in general equilibrium. 2. Producers in the region where input 1 is taxed will use an input bundle where MRTS = (w1 + t)/w2; producers in the other region will use a bundle where MRTS = w1/w2. Hence, the condition for efficiency in production is not satisfied. Notice that the economy is inside its production possibilities frontier in this case. 3. Unless the degree of monopsony power is identical for all firms, MRTS will not be identical for all firms. Hence, the economy will not be efficient in production: it will be inside its production possibilities frontier. Wages and capital costs would have to be subsidized. 4. It is not Pareto optimal. The tax creates a deadweight loss due to the reduction in consumption of cereal. This would not depend on the distribution of tastes. 5. No, a number of individuals are made worse off by NAFTA. However, NAFTA clearly raised the wealth levels of all countries involved. 6. No.

7. It would mean that all inputs were the same, and that there were no diminishing marginal products. 8. In reading A Modest Proposal one is impressed at Swifts attempt to make it seem as if the scheme would be Pareto Optimal. It would solve a hunger problem, incomes would be higher, etc. This blatant abuse of the concept, by not counting the welfare of those eaten, is in fact, the source of the humor. 9a. MRSa = 2/3, MRSb = 1/3.

b. Yes, they would like to trade. Avi would offer to give Y for X because he has a higher marginal value for X than Bindi.
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c.

P = 1, XA* = 12, YA* = 4, XB* = 8, YB* = 8 (They swap their endowments)

d. Yes. This price is determined where the excess demand is zero, and as a result the gains from trade are maximized. No other allocation can improve total welfare. At this allocation the MRS for each are equal to the relative price. 10a. For country A we have Y = (300 x3)1/3. For country B the PPC is Y = (37.5 x3)1/3. b. In each country the MRTS must equal the relative input prices.

c. Labour will be allocated such that the MRTS is equal across the two countries. The new PPC is X = 1.5[600 (Y/1.5)3]1/3, so if Y = 5, then X approximately equals 12. 11a. MRS1 = 1/x1, MRS2 = 2y2/x2, both are diminishing in x.

b. The box will have dimensions 170 by 30, with the endowment point at (130,10). The plot shows the initial indifference curves for the 2 individuals.

b) y2=px2/2, where p=px/py.

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c. The MRS of each individual must be equal and must equal the price. The offer curves of the two individuals intersect at the equilibrium, indifference curves are tangent to each other.

12a.

px/py = 1/2

b. If we check for good x, we see that A demands 40, and B demands 80, which adds up to the endowment of 120. Same for y. c. The gain in terms of y is 0. They trade at the competitive equilibrium price. Thus they retain the same quantity of goods, evaluated in terms of good Y. d. 13a. b. c. 14a. Mr. A. increases his utility from 1200 to 1600. PPC: 2X1 + X22/625 = 120 Production = Consumption. X1 = 40.00; X2 = 158.11 Production: X1 = 47.5, X2 = 125; Consumption: X1 = 36.25; X2 = 181.25 Produce: X1 = 100, X2 = 40; Consume: X1 = 30, X2 = 180

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b. Produce and consume: X1 = 44.72, X2 = 120. So, produce less X1 and more X2; consume more X1 and less X2.

15. (a) Straightforward. Contract curve follows the fixed proportions. (b) 1 to 2 (c) 2 to 1 (d) Yes. (e) No.

16. (a) Straightforward. (b) Sue's is 24 and Joe's is 26 (c) Straightforward. (d) Sue gets (24/5, 24/5) and Joe gets (26/5, 26/5)

17. Joe's favour. p1 must become 5/3. 18. Yes.

19. The coercer would take the other's endowment. No, it doesn't hold.

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Chapter 14 Price Discrimination and Monopoly Practices 1. Coupons take time to cut out, remember, and use. As a result, only the low time cost customers use the coupons and receive the lower price. These are also the customers who have time to shop around and therefore, have the higher demand elasticities. 2. It is an attempt to enforce resale price maintenance.

3. It prevents the alcohol from being sold as a beverage. This separates the market and allows for price discrimination. 4. It is a form of block booking that allows Rogers to extract more total revenue from its customers. 5. They are not credible because children are ultimately interested in their own welfare, and are unlikely to do damage to themselves. However, children may attempt to foster a reputation of rash abandon and irrationality that makes them appear credible. Teenagers may also take actions that commit them to certain behaviors which make their threats more credible. 6. Consider the Expo strategy. The $100 ticket enables the holder to avoid time spent in line, while the $20 ticket entails a time price time spent in line multiplied by the value that the individual places on his or her time. People who place a high value on their time will buy the $100 ticket, and those who place a low value on their time will buy the $20 ticket. For this to be a profitable strategy, it is necessary but not sufficient that the demand for tickets of the former group be less price-elastic than the demand of the latter group. 7. Suppose that there are two types of readers (or film buffs). One type is impatient and wants to reader the very latest books while the other type is patient and willing to wait a few months before reading a newly-released book. If demand for the impatient group is more price-inelastic than demand for the patient group, then this may be a profitable way to price discriminate. Market segmentation is achieved by self-selection. 8. Probably not. It is probably more of an example of efficient bundling. When you buy a shirt, it always comes with the buttons sewed on because it is cheaper for the manufacturer to do this than the customer.

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9. This is an example like the popcorn in the movie theatre. Suppose there are two types of customers, those that really like the night club scene, and those less interested. If those that really like the club also have a high demand for drinks, then the club will do better to raise the price of drinks and extract surplus that way, while still allowing the low demanders in. 10. First, the clientele is more homogeneous when there is dancing. Second, there is nothing to tie-in in the latter case. People go to the pub to drink, and this determines the amount they are willing to pay. 11a. The profit-maximizing prices are $60 and $35, and maximized profit is $906.25.

b. There are many such schemes, so the following is just one of many correct answers. The two prices are $60 and $35, and the higher price applies to the first 4.5 units. Relative to a), the increase in profit is 112.5 (4.5 multiplied by $25). c. p = 120 6y and and MR = 120 12y MR = 90 24y/5 if y <= 25/3 if y > 25/3

p = 90 12y/5

p* = $45 and maximized profit = $843.75

12. Let w1 and w2 be the discriminatory rates, with w1 > w2. In the model of monopsony discrimination, effective equal-pay-for-equal-work legislation will eliminate the employer's ability to discriminate. Hence, all wages will be equal in the monopsony equilibrium. The equilibrium wage will be larger than w2 and smaller than w1,

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employment of group 2 will increase, and employment of group 1 will decrease. The real difficulty is making this legislation effective since the employer has a profit incentive to disguise discrimination, for example, by labeling the same job done by men and women in different ways. The primary problem with equal-pay-for-work-of-equal-value legislation is that an external enforcer would have difficulty in observing "value." The appropriate concept of value would seem to be marginal revenue product. How could an external enforcer accurately observe marginal revenue product? In practice, two jobs are often deemed to produce equal value if they require roughly equivalent training and education. Of course, this does not mean that the marginal revenue products of the two jobs are equal. Neither kind of legislation is necessary when all labour markets are competitive since equal pay for equal work and equal pay for work of equal value are properties of the competitive equilibrium. 13. Consider the choice of a member of group A (or B) between one firm in which all other employees are members of group A (or B), and another in which some employees are members of group B (or A), and let w1 and w2 be the corresponding reservation wages. The preferences outlined in the exercise imply that w1 < w2 - that is, a wage premium is needed to induce the individual to work with employees who are members of the other group. Hence, any firm which is integrated will have to pay more for its labour than one which is segregated. If the industry is competitive, only segregated firms will survive. However, if employers are not bigoted, there will be no wage differential between the groups in the segregated equilibrium. For example, if the wage for group A exceeded the wage for group B, employers' demand for group B would rise and their demand for group A would fall until wage equality was established. 14. It prevents the garments from being resold, and undercutting their price discrimination over time through the sale. 15. 16. Who knows why they ask. It is unlikely to work. The marginal cost of the kids is practically zero.

17. General Motors would say that it is an issue of quality. If you fix the car yourself, do a bad job, and the car breaks down, then you tend to blame GM and not your own poor workmanship.

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18. A person can go into Chapters, look at a book, and if they like it, go purchase at Amazon.com. Many thought this practice would drive the full service bookstores out of business, but the two seem to exist together. If it did drive Chapters out of business that would not be efficient. Their services are valuable, it is just that Amazon allows customers to steal the service. Im not sure what Chapters is doing. One thing is clear, however, after shipping and waiting, the cost difference between the two types of stores is not that great. 19. 20a. b. No, because it costs more to serve them. The figure would be like Figure 14.4. See figure S14.1.

Figure S14.1

If the MC curve is below the intersection of the two marginal revenue curves, then the capacity constraint is binding. The total number of seats needed to set marginal revenue equal to marginal cost in the two markets exceeds the total number of seats available. Hence, the seats are allocated at the intersection of the two marginal revenue curves. c. They will fly with empty seats if the intersection of the marginal revenue curves is below the marginal costs. d. Youd want a plane just big enough that the marginal revenue curves intersect just at the marginal costs.

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21a.

If the firm just adds up all of the demands, then profit is $11 520 and price is $9.

b. With simple price discrimination the prices are $11.5, and $7.5 and total profit is $12 720. c. 22a. b. c. With separate two part pricing the profits are $25 440 and the price is $3. Set p = k for the popcorn, and charge 0.5[a/b k] to get in. Now the firm will sell y = (a bk) / (2 q) units of popcorn. If q = 0, then we get the monopoly solution to the popcorn problem.

23a. The prices are p1 = 56, p2 = 122. The quantities are y1 = 8, y2 = 6. The profit equals $707. b. c. 24a. E1 = 7/3 (= 2.33), E2= 61/45 (= 1.36) The market with the lower elasticity has the higher price. The first demand is more likely the evening one.

b. With price discrimination we have: pA = $4.5, pB = 2.5, qA = 10, qB = 10, and profit = $60. Without price discrimination we have: p = 3.167, q = 20.0, and profit = $33.33. 25. (a) y*=3/2 and p* = 8.5 (b) 9/4 (c) 27/8 26.

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(a) MR1(y1) = 10 - 2y and MR2(y2) = 20 - 4y2. (b) Segment 1 gets 5/3 and segment 2 gets 10/3. 27. (a) y*=5/3 and p*=25/3 and fee=25/18 (b) 275/18 28. It could. 29. It could. 30. This indicates a lack of competition.

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Chapter 15 Introduction to Game Theory 1. Yes it is a Nash equilibrium. In fact, it is a dominant strategy Nash equilibrium.

Every firm is better off producing where price equals marginal cost, regardless of the actions of other firms. 2a. b. 3. (A, A) is the NE. To play (A,A) in each round. If she thinks the bids are too low, then she should bid $1 above the highest bid. If

she thinks the bids are too high, then she should bid $1. 4. There are 8 strategy combinations, laid out in the table below. Jays Payoff 18 28 19 29 19 29 20 30 Jills Payoff 18 28 19 29 19 29 20 30 Mos Payoff 9 5 14 10 14 10 19 15

Strategy (Jay, Jill, Mo) KKK KKP KPK KPP PKK PKP PPK PPP c.

P is the dominant strategy for Jay and Jill, and K is the dominant strategy for Mo.

Therefore, PPK is the dominant strategy equilibrium. 5. Lets suppose that the 1 point conversion is a sure thing, and that the two point conversion is successful with probability p. Lets also assume that the Huskies actually get the last two touchdowns in the game. Let W be the utility associated with winning, T the utility associated with a tie, and L the utility associated with losing. Assume that W > T > L.

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Consider first the coachs strategy of going for 1 point on the first touchdown and 2 points on the second. By assumption, they get the 1 point on the first touchdown (with probability 1). They will get 2 points and a win on the second with probability p, and 0 points and a loss with probability (1 p). Hence, the expected utility associated with the coachs strategy is pW + (1 p)L. Now consider the alternative strategy of going for 2 points on the first touchdown. They will actually get the 2 points with probability p, and if they do get 2 they will go for 1 point on the second since that assures the win, which contributes pW to their expected utility. On the other hand, they will get 0 points of the first touchdown with probability (1 p), and if they do they will go for 2 points on the second (since they lose for sure if thy get only 1 point); they will get the 2 points and a tie with probability p, and they will get 0 points and a loss with probability (1 p); the contribution to expected utility is (1 p)[pT + (1 p)L]. Adding, we see that going for 2 on the first touchdown yields an expected utility equal to pW + (1 p)[pT + (1 p)L]. Since pW + (1 p)[pT + (1 p)L] exceeds pW+ (1 p)L, this line of argument suggests that the coach had the wrong strategy. 6a. b. That is up to the student. The NE is for each to buy 5 tickets. If Anoop buys 1, then Beatrice should buy 2,

but then Anoop would want to buy 3, etc. c. The Pareto optimal solution is for each to buy one ticket. This gives the same

probability of winning, but with the lowest cost. d. Anoop buys three, and Beatrice buys 4. It would be Pareto optimal for Anoop to

buy nothing and Beatrice to buy 1. 7. Using her budget constraint to eliminate y1 as a choice variable, we get the following payoff function for Linda in this game is
1

(x1,x2)

U1(x1,100 x1,x2)

Similarly, Rosas payoff function in this game is

(x1,x2)

U2(x2,100 x2,x1)

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Clearly, this is a game of plain substitutes, since 1(x1,x2) is a decreasing function of x2 and 2(x1,x2) a decreasing function of x1. Hence, Proposition 15.1 is applicable. 8. Let p1 be the probability that One chooses Rock, and p 2 the probability that One chooses Paper; then 1 p1 p2 is the probability that One chooses Scissors. Similarly, let q1 be the probability that Two chooses Rock, and q2 the probability that Two chooses Paper; then 1 q1 q2 is the probability that Two chooses Scissors. Then the set of pairs (p1,p2) such that 1 p1 0, 1 p2 0, and p1 + p2 1 is the set of mixed strategies for One. Twos strategy set is exactly parallel. To form a payoff function we need to pick utilities for outcomes. In this game a player can win (if her choice is rock and her opponents is scissors, or if her choice is paper and her opponents is rock, or if her choice is scissors and her opponents is paper), lose (if her choice is rock and her opponents is paper, if her choice is paper and her opponents is scissors, or if her choice is scissors and her opponents is rock), or draw (if both choose the same action). Let 1 be the utility of winning, 0 the utility of a draw, and -1 the utility of lose. There is no best way to assign these utility numbers. The important thing is that we assign the largest utility to winning and the smallest to losing. With these utility numbers, Ones payoff function is: 1 = p1[(1 q1 q2) q2] + p2[q1 (1 q1 q2)] + (1 p1 p2)[q2 q1]

Collecting terms, 1 = p1(1 3q2) + p2(3q1 1) + (q2 q1) Now lets use the payoff function to find Ones best response function. Notice that if (1 3q2) > (3q1 1) or equivalently, if 2/3 > q1 + q2, then Ones payoff is maximized by choosing (p1,p2) = (1,0) since the rate at which Ones payoff changes as p 1 is increased (1 3q2) exceeds the rate at which it changes as p2 is increased (3q1 1). Hence, Ones best response to any (q1,q2) such that 2/3 > q1 + q2 is (p1,p2) = (1,0). Conversely, Ones best response to any (q1,q2) such that 2/3 < q1 + q2 is (p1,p2) = (0,1). Finally, if 2/3 = q1 + q2, then Ones best response is any (p1,p2), including (p1,p2) = (1/3,1/3). As you can easily verify, Twos payoff function is

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2 = q1(1 3p2) + q2(3p1 1) + (p2 p1) Twos best response to any (p1,p2) such that 2/3 > p1 + p2 is (q1,q2) = (1,0), and her best response to any (p1,p2) such that 2/3 < p1 + p2 is (q1,q2) = (0,1), and if 2/3 = p1 + p2, then her best response is any (q1,q2), including (q1,q2) = (1/3,1/3). Looking at the best response functions, it is clear that in the Nash equilibrium is (p1,p2) = (1/3,1/3) and (q1,q2) = (1/3,1/3). 9a. b. c. 10. The graph is in the text. The subgame perfect NE is for Bart to cut the cake into equal sizes. No. The best response functions are R1(y2) = (A By2)/2B And the Nash equilibrium is y1* = y2* = A/3B As A increases, bribes received in equilibrium increase, because an increase in A shifts the demand curve for bribes upward. A B increases, bribes received in equilibrium decrease because an increase shifts the demand curve for bribes downward. 11. The general result for Nim is the following: when a player is making a move, if the piles are unbalanced, meaning that one pile has more matches than the other, then the subgame perfect equilibrium strategy for the player is to balance the pilesthat is, to remove enough matches from the larger pile so that the piles have the same number of matches; if the piles are unbalanced, any move is subgame perfect. Applying these strategies to different situations, we get the following result: if the piles are initially unbalanced, One wins, if they are initially balanced, Two wins. 12. The best response functions are: R1(y2) = (A+By2)/2N R2(y1) = (A+By1)/2N R2(y1) = (A By1)/2B

And the Nash equilibrium is

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y1* = y2* = A/(2N-B) This solution makes sense only if 2N B > 0, and if this condition is not satisfied the best response functions do not intersect in the strategy space of the game (the set of (y1,y2) such that y1 0 and y2 0).

Equilibrium effort levels decrease as N increases (because the marginal cost of effort increases as N increases), they decrease as A decreases (because the marginal benefit of effort decreases as A decreases), and they decrease as B decreases (because the marginal benefit of effort decreases as A decreases). 13. Supposedly the purpose of tipping is to improve service, but of course a patron can stiff a server by leaving no tip. This problem is partially solved by repeated interactions. If you leave no tip this meal, youll get poor service at the next meal. This still seems to fail to explain why many people leave tips. On occasion a waiter might confront a patron who leaves a poor tip, and this small threat might induce payment. 14. If they have =1 then there is no prisoners dilemma element to this game at all.

15. Since captains were the ones most likely to die in battle, they had little incentive to engage the enemy. The British Navy rules forced them to fight. Given that they had to fight, they spent a lot of time training the men to fight. Interestingly, the British Navy was not well known for its sailing ability. It took Nelson almost a year to catch the French and Spanish fleet at Trafalgar. But once he caught them, it was no contest. 16. This is a generalized Put-Keep game.

a. A player motivated only by private gain would reason as follows. There is nothing I can do to influence the actions of the other N 1 players in this game, so I will concentrate on the implications of my own actions. On the one hand, if I keep the keep the $X, I am richer by $X. On the other hand, if I put the $X in the envelope, there will be $(X + Y) additional dollars in the common pool (the $X I put in the envelope and the $Y the host will add to it), of which I will get $(X + Y)/N. b. Clearly, I am better of to keep the $X if X > (X Y)/N, or if N > 1 + Y/X. But if N < 1 + Y/X, I am better off to put the $X in the envelope.

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c. The larger is N or X, and the smaller is Y, the more likely it is that the player will keep $X. Conversely, the smaller is N or X, and the larger is Y, the more likely it is that the player will put the $X in the envelope. d. A player motivated by self interest will now want to know whether he or she is richer if all players keep $X or all put $X in their envelopes. If all players keep the $ X, each is richer by $X. In contrast, if all players put their $X in their envelopes, there will be $N(X + Y) in the common pool, and each will be richer by $(X + Y). Hence, each player will vote to require all players to put their $X in their envelopes.

17.

Take Alderall Take Alderall Dont Take Alderall 2,2 1,4

Dont Take Alderall 4,1 3,3

This game is a basic Prisoners Dilemma, and both students end up taking the drug.

18. (a) Quick Wait & Copy Wait & Copy 0,0 Do The Assign 8,8 (b) Quick has the dominant strategy to do the assignment. (c) Quick will do the assignment and Slow will copy. Slow Do The Assign 5,5 8,5

19. (a) a 3 (b) b<3

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(c) a>3 and b>3 (d) None.

20(a) (b) Adam wins.

21. (a) B of S (b) PD (c) PD (d) G of D

22. (a) EPO(p,q) = p(3q-1) - q + 2 (b) q>1/3

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Chapter 16 Game Theory and Oligopoly 1a. Output, price, and profit are 180 units, $150, and $16 200.

b. Given n firms, output of a representative firm, equilibrium price, and profit of a representative firm are 360/(n + 1), $60(n + 4)/(n + 1), and $64 800/(n + 1)2.

n y* p* Profit

2 120 120 7200

3 90 105 4050

4 72 96 2592

5 60 90 1800

c. In the symmetric collusive equilibrium, each firm produces 90 units and earns a profit of $8100. The violator should produce 135 units, and the inducement to violate an agreement is then $1012.5. d. The limit output is 240 units, the limit price is $120, and the monopolist's profit is $16 200 $1800. e. Three firms will enter since the profit of a forth would be negative ($408). Each firm will earn a profit equal to $28 800 $20 000 = $8800. f. Five firms will enter, and each will earn a profit equal to $240.

g. Just one firm will enter, as every additional firm will drive operational profits to zero and none of the participants can cover the fixed cost anymore. The profit of the one firm will be the monopoly profit of $16 200 $3000 = $13 200. 2. Under the common property institution, we have the following payoff matrix:

R R E (180/180) (210/90)

E (90/210) (120/120)

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And under the private property institution, we have the following payoff matrix: R R E (180/180) (120/180) E (180/120) (120/120)

In the first game, the dominant strategy is E, and in the second game, it is R. 3. The profit-maximizing price and quantity are $500 and 250, a combination that generates revenue of $125 000. When K is 100 000, there will be one firm operating at capacity; when K is 50 000, there will be two firms operating at 1/2 capacity; and when K is 25 000, there will be five firms operating at 1/5 capacity. 4. Let A be the amount spent by the incumbent firm on advertising prior to entry. If quantity demanded from an entrant given its price and the incumbent's price is negatively related to A, then advertising is a barrier to entry. 5. An infinite inventory would mean a zero marginal cost of production, and a finite inventory would mean a zero marginal cost for the amount held in Inventory. If, in the post-entry equilibrium, the entrant's profit is negatively related to the incumbent's marginal cost, then inventories are a barrier to entry. 6. First, learning by doing can constitute a barrier to entry for the reason outlined in exercise 5: the lower is an incumbent firm's marginal cost, the more aggressive it may be toward new entrants. Second, firms may have an incentive to produce abnormally large quantities early on in order to get down the learning curve, thereby realizing lower marginal costs and hence making it more difficult for other firms to enter. 7. Suppose both firms produce a positive output in the Nash equilibrium, and that their strategies are quantities of output. Let y1' and y2' denote the Nash equilibrium quantifies of firms one and two. First we want to argue that the isoprofit curve of firm one through the Nash equilibrium is U-shaped. Beginning at the Nash equilibrium, suppose we increase (or decrease) y1 by a small amount. As a result, the profit of firm one will fall. To get back to the isoprofit curve, we would have to increase y2 since firm one's profit increases as Y2 increases. Hence, the isoprofit curve for firm one through the Nash equilibrium is U shaped. Further, strategy combinations above this isoprofit curve give rise to a larger profit for firm one. A similar argument shows that the isoprofit

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curve for firm two through the Nash equilibrium is C-shaped, and that strategy combinations to the right of this curve give rise to a larger profit for firm two. It then follows that, beginning at the Nash equilibrium, if the output of both firms is increased by a small amount, the profit of both firms increases. Hence, joint profit is not maximized in the Nash equilibrium because the firms produce too little. It may useful to produce a figure in which you draw the two isoprofit curves through the Nash equilibrium. 8. Spending money to simply reshuffle the existing numbers of smokers is not profit enhancing. 9. Yes it would. At a maximum price of $400, the revenue to the entrant would only be 20 million, not enough to cover the cost of entry. Therefore, the incumbent would get the entire 40 million. 10. As was argued in the chapter, the merger of two firms producing complements will result in an increase in output and total surplus. Other things constant, this type of merger should be allowed. 11a. C1 = C2. Each puts in effort.

b. Now the optimal effort is each, and C = 1. If Milt thinks that Michelle is doing the first best level of cleaning, he cuts back. c. Error in question, it should tell you what the cost of babysitting is.

d. It will not be cleaned at the optimal level. M&M will revert back to the Nash solution. 12a. b. c. Total output = 60, p = 40, profits = 1050 Total output = 37.5, p = 62.5, profits = 1725, DWL = 421.88 Total output = 50, y1 = y2 = 16.67, p = 50, profits = 1516.67, DWL = 83.33

d) Recursively, solve for y3 in terms of y1 and y2 first, plug in, solve for y2 in terms of y1 and finally for y1: y1 = 18.54, y2 = 17.46, y3 = 16.00, total output = 52.00, p = 48.00, profits = 1441.56. There is advantage of playing sequentially for firm 1 here, as its profit was bigger by 9.31 in the Cournot case (an implication of the quadratic cost function).

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13a. Assuming y2 = 20, the residual demand, MR and the MC curves are shown in the plot below (the original demand curve is given as the dotted line).

The best response functions are y1 = (120 3y2)/7 and y2 = (120 3y1)/7.

b. Each firm will produce 12 units in equilibrium, price will be $48, and each firm's profit will be $504. 14a. The best response functions are y1 = (21 y2)/2 and y2 = (27 y1)/2. Equilibrium quantities are y1 = 5 and y2 = 11. Equilibrium price is $42.

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b. The equilibrium price is $26.99. The second firm makes all the sales. It sells 21 units and its profit per unit sold is $17.99, in total $377.85. The first firm does not sell anything as its MC is above equilibrium price. 15a. y1 = 30 y2/2, y2 = 30 y1/2. The equilibrium is yi = y2 = 30, p = 50, profit = 800 for both. b. Now firm 1 produces 30 units (profit = 900) and firm 2 produces 15 (profit = 450).

c. The figure should look like 16.5, with the new equilibrium (solid lines) lying southeast of the Cournot equilibrium (dotted lines). Firm 2 is on a lower isoprofit line, while firm 1 is on a higher isoprofit line.

d. 16.

He chooses first (there is a first mover advantage of 900 800 = 100). The Cournot-Nash equilibrium quantities are both equal to /(2 ). If is

positive this is a game of plain complements, and if it is negative it is a game of plain substitutes. If the set up is interpreted as a game involving two firms that choose quantities, when is positive the goods produced by the firms are complements. When

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it is negative they are substitutes. The set up can, however, be interpreted in a variety of ways. To get another interpretation of this model when is negative, suppose that = 120 and = = 2; then we have the model of inefficient bribe taking discussed in Chapter 15. In fact, any version of the model laid out in this problem in which is negative can be interpreted as a model of inefficient bribe taking. To get another interpretation of this model when is positive, consider a situation involving two roommates who help each other with their homework. Interpret x1 and x2 as the time they spend on homework. Assume that the cost of time spent studying is (x1)2 for roommate 1, and (x2)2 for roommate 2. Assume too that the more time one roommate spends on homework the better able she is to help the other student with homework. This is the key assumption in this application. Specifically, assume that the benefit to roommate 1 of an hour spent studying by roommate 1 is + x 2, and that the benefit to roommate 2 of an hour spent studying by roommate 2 is + x 1. Then the gross benefits are x1( + x2) for roommate 1, and x2( + x1), for roommate 2. Finally, subtracting costs from benefits, we get the payoff functions for this game: 1(x1,x2) = x1( + x2) (x1)2 2(x1,x2) = x2( + x1) (x2)2

17. Yes, if there's a good chance that it could form a monopoly.

18. y*=15.

19. (a) y1* = 25 - y2/2 (b) y2* = 25 - y1/2 (c) 50/3 (d) 80/3

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20. Yes, merging could solve the prisoner's dilemma. Yes, consumers would fair worse under a monopoly. 21. It allows them to compete on things other than price.

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Chapter 17 Choice Making Under Uncertainty 1. The expected monetary value of this game is 1 + 1 + 1 + 1 + 1 + ..., the sum of an infinite string of 1s, or infinity, yet most people are unwilling to pay even $10 for the right to play this game. 2. The individual is risk-neutral, then utility is a linear function of wealth, and the individual always chooses the prospect with the highest expected monetary value. 3. The card on top the deck is either a club, or it is not, so no risk is involved. But, since the individual doesn't know whether the card is or is not a heart, imperfect information is involved. Knowing only the original five-card hand, it is sensible for the individual to behave as if the probability that the top card is a heart is 9/47, or to have a subjective probability equal to 9/47. 4a. Guy is indifferent between $12 and a gamble that pays $20 with probability 0.7 and $0 with probability 0.3. b. U(20) = l, U(12) = 0.7, U(0) = 0

c) Guy is indifferent between the riskless prospect that pays $12 with probability 1 and the risky prospect that pays $20 with probability 0.7 and $0 with probability 0.3. The expected monetary value of the riskless prospect is $12, which is less than the $14 expected monetary value of the risky prospect. Hence, Guy is risk-averse. d. e. 0.6, 0.54, 0.7, 0.58, 0.64 C, E, A, D, B

5. The following is a utility function for Kunuk: U(100) = 1, U(50) = 1/2, U(10) = 0. Calculating expected utilities reveals that Kunuk is indifferent between the prospects in part a, prefers the first prospect in part b, and the second in part c. 6. When the probability of rain is 1/20, Ingrid's expected profit is $10.80 if she fertilizes, and it is $10.80 if she does not. Hence, she will be indifferent between fertilizing or not if she is risk-neutral (if U(w) = w); she will fertilize if she is risk-inclined (if U(w) = w3); and she will not fertilize if she is risk-averse (if U(w) = w 1/3).

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7. This is good advice. Once we introduce a transactions cost, the competitive equilibrium price of insurance (with risk-neutral firms) rises by the amount of the transactions cost. If that cost is large enough relative to the expected loss, it is no longer sensible to buy insurance. Let c denote the transaction cost, and consider full coverage against a loss L that occurs with probability p. The competitive equilibrium price of insurance is then pL + c. From Figure 5.4 (Microeconomics, p. 155), we see that the reservation price for a policy offering full coverage is Ir = w0 wce. For a risk-averse person, Ir necessarily exceeds pL, so it is a good idea to buy insurance when there is no transactions cost. However, if c is large enough, the price of insurance, pL + c, will exceed Ir, and the individual is better off without the insurance. 8a. 9. 29; b. no, maybe, yes; c. $59; d. $50 From the purchase Ms Q will get an expected utility of

EUBuy = Papproval ln(2 500 000) + (1 Papproval) ln(350 781.06) For the threshold probability of approval EU Buy has to equal the utility Ms Q derives from her initial wealth of 1 Million. Solving this EU Buy = U(1 Million) gives the result of Papproval = 1/2. 10. We want to show that

pU(0) + (1 p)U(W) < p2U(0) + 2p(1 p)U(W/2) + (l p)2U(W) which can be reduced to (l/2)U(0) + (1/2)U(W) < U(W/2) This last inequality is clearly satisfied if Lucky Pierre is risk-averse. 11. Clearly GM doesnt buy insurance to diversify risk. GM is most likely buying information, and the insurance contract is a way for those selling the information to guarantee its quality. For example, experts in how to prevent fires sell this information, and insure against fire as a promise that the information is good. 12. Simply draw a picture like 17.6, except where the indifference curves are convex to the origin. The certainty equivalent wealth level lies to the right of w 0 (1 q)L, and so a risk neutral firm would not insure this type of individual.

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13a. The expected utility of the gamble is $6. Therefore, she would be indifferent between $36 and this gamble. This is her certainty equivalent. b. The risk premium is $3.

c. No, she will not accept this. The utility derived from the certain income of $35 in the insured case is smaller than her certainty equivalent. 14. False. Since these utility functions are not ordinal, they are no longer invariant to monotonic transformations. For example, if U(w) = w, U represents risk-neutral preferences while V represents risk-loving preferences. 15a. b. c. Expected Value = $860, Expected Utility = 29 Max. Profit = Max Rev. Exp. Cost = EV CE = $860 $841 = $19 Max Willing. to Pay = Max. Rev. = w(good) CE = $900 $841 = $59

16. (a) $192.50 (b) B=$100 17. (a) Indifferent. (b) Two. (c) Single. (d) for (b) she'd use all available baskets, for (c) no change. (e) risk spreading for risk averse individuals. 18. (a) No. There could be costs (e.g. embarrassment) and he's likely risk averse.

19. (a) Reject. (b) Pay 7.481 to avoid. 20. Yes. Sell insurance to you risk averse friend and buy it from your risk seeking friend. There will be a spread that you can keep.

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Chapter 18 Asymmetric Information, the Rules of the Game, and Externalities 1. These interpretations are straightforward.

2a. Type 1 firms emit 120 units of gunk, and type 2 firms emit 180 units. In total, the 10 firms emit 1500 units of gunk. b. A tax equal to $100 per unit of gunk will do the job. Type 1 firms emit 20 units of gunk, and type 2 firms emit 80 units now. Assuming that all firms are perfect competitors in their output markets, the 500 units of gunk are efficiently allocated since the value of the marginal product of gunk is identical in all firms. c. The aggregate supply is 500 units, and the aggregate demand is 1500 10 w, where w is the price of the right to emit 1 unit of gunk. Equilibrium price is $100, and the allocation of the 500 units to the 10 firms is identical to the allocation in part b. d. In this case, the gunk emission rights are inefficiently allocated, since the emission rights are not allocated to their most productive uses. Both type 1 and type 2 firms emit 50 units of gunk, 3a. b. 40 units Given y1, individual 2 will choose y2 to satisfy the following equation:

50 y1 y2* = 20, or y2* = 30 y1 Similarly, individual 1 will choose y1* = 30 y2* Adding y1* and y2, we get 30 units supplied. Hence, if 30 units are supplied, neither individual will want to supply more or less mosquito control, and we therefore have a Nash equilibrium. Notice that the Nash equilibrium is not unique, any combination of supply adding up to 30 is a NE. c. The socially optimal quantity satisfies the following equation:

300(50 y) = 20

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Thus, 749/15 (approx. 49.93) units of mosquito control is socially optimal. Let S denote the quantity supplied by all individuals other than individual i. Then individual i will supply yi* = 30 S Hence, given the quantity supplied by all other individuals, each individual will supply just enough so that the aggregate supply is 30 units. Thus, any situation in which aggregate supply is 30 units is a Nash equilibrium. d. Begin by supposing that one naive individual will supply 30 units. What will all the others do? Free ride by supplying nothing. 4. In the first case, we need BA + BB + BC < K, and BA and BB greater than K/3. Observe that BB + BC < 2K/3; otherwise, BA + BB + BC would exceed K since BA necessarily exceeds K/3. We must find a bribe S such that S > BB K/3 and S < K/3 BC, which requires only that K/3 - BC > BB K/3, or that BB + BC < 2K/3. Hence, there is a bribe that C would offer to B to vote against the project and that B would accept. Now, suppose that BA + BB + BC > K, and that only A and B would vote for the project. This does not rule out the possibility that BB + BC < K/3; hence, C might be able to bribe B to vote against the project. But A would be willing to offer an even larger bribe, T. The largest bribe that C would offer B is K/3 BC, in which case B's net benefit is K/3 - BC. If A offers B a bribe T to vote for the project, then B's net benefit is BB - K/3 + T. Hence, T must be larger than 2K/3 - BB BC for B to prefer A's bribe to C's maximum bribe. The largest bribe A would be willing to offer is T = BA K/3. We must then show that BA K/3 exceeds 2K/3 BB BC, which requires only that BA + BB + BC > K. Such bribes ensure that cost-benefit-efficient solutions are implemented. 5. Yes it would be. The fence is a cost used to establish and protect property rights. In this case the iso-profit lines for the rancher would be vertical lines, and horizontal lines for the farmer. 6(i) This is the nature of competition. Wealth was created in this case for consumers and other producers, even though you are hurt. (ii) One explanation might be the cost of preventing a crime. I can prevent my house from the burglar by installing costly locks, guard dogs, and a large fence. However, when I do this I impose a cost on my neighbors, since they must now protect their

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property. In the case of burglars, it might be cheaper to put a fence around them (jail) than putting a fence around each individual house. (iii) Presumably because the property rights are not assigned. Therefore transaction costs are not zero, and the Coase Theorem does not apply. 7. The necklace is a likely candidate for ransom because its value in resale is so low. When others know the item is stolen, they know their property rights to the good are never going to be well defined. As a result, they offer a low price. The wine could be easily resold. 8a. With private property the owner will hire 5 workers. At this level the value of the marginal product just equals the wage. b. With open access 8 workers will enter until their average product equals their alternative wages. c. With common property the workers will maximize the average product and restrict their numbers to 4 workers. 9. There are more problems in life than trespassing trees and cows. A well defined property line stops neighbors from infringing on one another in a host of areas. Respecting all the rights of your neighbor is the secret to getting along with them. 10a. TP = 100z, MP = AP = 100.

b. On the lake the 16 fishers catch 1600 fish. The 84 on the ocean catch 8400, for a total of 10 000. At this allocation each fisher has an average product of 100. c. If they were all on the ocean the total catch would still be 10 000, meaning that the net value of the lake is zero. d. The marginal products should be equal, therefore z = 4, and 96 should be on the ocean. e. The new total is 10 400, leaving a net value of the lake at 400. f. If the enforcement of property rights was costless, then ownership of the lake should be made private, and the fisher in possession of the lake should hire 3 additional fisher at the reservation wage of 100.

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11a.

x = (1000y).5 y (and y = (1000x).5 x).

b. The easiest way to solve this is to set y = x, since the game is symmetric, and solve either function in a or b. y = x = 250. c. Each athlete exerts a negative externality on the other. In equilibrium the probability of winning is still 0.5. The net gain to the race, though is only 25 000 each instead of 50 000. d. Each would be better off if steroids could be eliminated from competition.

e. With cost = 1000, doping will continue, just with less steroids in equilibrium (x = y = 25). Expected gain will still be 25 000. f. With n = 10, expected gain with steroids is 1000 for each runner, compared to 10 000 without doping. In general, the ratio of gain without/gain with steroids is n. However, consumption of steroids falls with rising n (x = y = 9 for n = 10).

12a.

Optimal effort E*= (100p w)/200p.

b. V* = (100p w)2/400p c. The Nash Equilibrium of one firm is E = (100p w)/100p(N + 1). The aggregate NE is NE*=[(100p w)/100p](N/(N + 1)). The aggregate value in Nash Equilibrium is V* = [(100p w)2/100p][N/(N + 1)2] 13. a. Gleaning was common in environments where monitoring was simply too costly given the small value of the scraps being taken. Rather than police what was left over from production, owners allowed workers to take. b. When goods were unique it was difficult for the worker to take too much. The owner would identify the large amount of his goods taken. Once goods become standard, a worker could embezzle goods and then sell them on the black market. The original
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owner could not tell what was his, and had a hard time policing the behavior. One solution was to simply say workers are no longer to have any goods in their pockets when they leave the factory floor. 14. (a) Bees help pollinate the fruit trees. Positive. (b) Noise and possible old gum stuck under the desks. Negative. (c) Other do relatively worse. Negative. (d) Causes office to smell. Negative. 15. (a) nonrivalrous and nonexcludable. (b) nonrivalrous and nonexcludable. (c) rivalrous and nonexcludable. (d) rivalrous and excludable. (e) nonrivalrous and excludable. 16. (a) Yes. (b) $200 (c) Yes. $25 (d) $300 17. (a) Straightforward. (b) Horizontal summation of DA and DB. (c) x*=16/5 (d) Vertical summation of DA and DB. (e) x*=12/5 18. Transactions costs such as enforcement coercion.

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Chapter 19 The Theory of the Firm 1a. Indifference curves are shown for U = 200 and U = 400.

b, c and d are all straightforward calculations. The next figure illustrates solution b

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e.

2.

Race the horses with Bart riding Brews horse and Brett riding Barr's horse.

3. What are the club's incentives? Suppose a tradesperson does an unsatisfactory job. It is reasonable to assume that the homeowner will leave the club, and the club's future revenue will decline by $50. Hence, in the future, the club would refuse to refer club members to this particular tradesperson. But the tradesperson, anticipating this result, has a clear incentive to do satisfactory work in the first place. Hence, the club solves the asymmetric information problem. 4. Why does the parent company choose to sell franchises instead of hamburgers? Imagine the organizational difficulties that the firm would encounter if it attempted to manage literally thousands of restaurants. By selling franchises, the firm puts these managerial problems in the hands of thousands of independent business people. Why does the parent firm insist on exclusive ownership? Apparently, to avoid the kind of problem we encountered in our model of partnerships. Why does the parent company inspect the operations of its franchisees? The company is selling, and franchisees are

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buying, an image uniform quality products in clean and healthy surroundings. The only way to produce such an image is to ensure that franchisees do produce a uniform quality product in clean and healthy surroundings. The assurance that all restaurants will be inspected and that licenses will be revoked if the restaurant is not up to standard is the primary assurance that franchisees have that the McDonald's image will be worth something. Why does one franchisee care about how others run their restaurants? Because the McDonald's image is produced collectively by all the restaurants in the chain. Why does the parent firm agree to the restriction that it cannot sell other franchises within a specified radius? In the absence of such a restriction, the value of a franchise would be small, perhaps zero. 5. Designers are paid a salary because it is relatively easy to monitor them. All the publisher needs to do is to look carefully at the books under a particular designer's control. Authors are not paid by salary because it is very difficult to monitor their work to discover if a particular text is properly done would require significant effort from a number of other experts and because it is ordinarily the author and not the publisher who knows what kind of book the market demands. Commissions are common is sales work because monitoring the effort of salespersons is often very costly. By tying the salesperson's compensation to sales made, the firm avoids the need to monitor extensively the salesperson's effort. 6. The key here is that the specialized equipment produced by firm O is a specific input, while the chip, produced by many firms, is a generic input. Hence, one would expect firm O to buy the generic input and then assemble and sell lemon computers. Any other arrangement involves the tricky contractual problems raised by specific inputs. 7. By insisting on multiple sources for specific inputs, firms reduce the holdup problems that specific inputs create. In effect, IBM improves its bargaining position with respect to its suppliers of specific inputs by insisting on multiple sources. Of course, security of supply is another advantage of multiple sourcing. 8. The compensation arrangements outlined in this problem are examples of deferred-compensation schemes. They are designed to reduce turnover by employees with firm-specific human capital. Such schemes, if successful, allow a firm to economize on its investment in firm-specific human capital by reducing the number of employees it must train.

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9. By choosing w1 < w' and w2 > w', the firm can be certain that a trained employee would never quit to take another job in period 2, and it can be sure that college-bound potential employees will not accept jobs in period 1 only to quit and go to college in period 2. Hence, this is the preferred wage profile. 10. See the answer to question 17.13

11. The gains from specializing in farming are quite limited due to its seasonal nature. One cannot specialize in planting wheat and remain employed for more than a couple of months a year. Thus farmers are forced to be jack of all trades. On the other hand, due to the large role of nature, there are ample opportunities to cheat in standard labour contracts. Hence farming is dominated by families because they have minimal transaction costs, and do not forgo large gains from specialization. 12. The different attributes of the building are easy to identify and measure their use. There is often little interaction between the uses of the different attributes. For example, the use of space on one floor (the color of the walls, the line of business) has no impact on the use of space on other floors. Hence, the different attributes are easily owned by separate individuals. On the other hand, a machines value critically depends on how everyone uses it. Multiple users increase the amount of depreciation on the equipment. Hence there tends to be a single owner. 13. The problem is that increased specialization isolates knowledge, and this allows for greater transaction costs. Hence the division of labour is not just limited by the extent of the market, but by the nature and level of transaction costs as well.

14. Risky. The shareholders face an option-like payoff, so taking large risks allow large possible gains with limited down-side risk. Salaried employees would rather those risks that minimized the chance that the firm closes down.

15. (a) e*=1/2 and y*=1 (b) u* = (c) No.

16.

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Yes, marriage partnerships can lead to reduced efforts. However, marriage likely solves other problems in the production of children. Also, the costs of hiring a spouse by a wage are not zero either.

17. (a) e*=1/2 and y*=1/2 and u*=1/4 (b) e*=1/6 and y*=1/3 (c) u*=11/36. Yes. (d) u*=1/12. No.

18. (a) e*=5 and y*=48. (b) e* remains the same. (c) e* increases. (d) y* decreases. (e) y* increases.

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Chapter 20 Asymmetric Information and Market Behaviour 1. The store must engage in some form of reputation investment. Most jewellery stores spend a great deal on advertising and other forms of sunk investments to ensure quality. In addition to this many of these stores post a bond that the stone is genuine. 2. Yes this is a shortage. The price does not rise because we make it illegal to trade babies for money. In the black market, the price for a baby is high. Babies are mostly rationed on a first-come, first-served basis, with qualifiers for types of parents, etc. One reason for not selling babies is that it reduces (almost eliminates) baby thefts. If there was a market for babies, it would be easier to steal babies and resell them. This would imply huge costs of protecting children. A similar argument holds for why we dont allow the sale of wild meat, it cuts down on poaching. 3. Legally Carla does, but apparently the economic right belongs to the little girl.

4. In the case of the employee and the firm, bargaining over the gains from trade is allowed because they are dealing with wealth that they both created. We want firms and employees to get together and generate wealth, even if it means some costs of negotiating. With the case of child ransom, the gain from trade results from an initial theft. This theft is wealth dissipating, and so we would want to discourage this type of behavior. 5. With civil law you always know who the other party is, so you take them directly to court. Police are only necessary when violence is involved or the instigator is not known. 6. It could be brand identification. We can identify the manufacturer of a car by its shape and the name on the side, same with street bikes. However, for tractors and offroad vehicles that must be viewed at a distance, the identification must be cruder. 7a. Five workers where marginal product is equal to 4, the opportunity cost.

b. The commune wants to maximize the average product, which in this case involves 1 worker per farm. c. With open access people enter the farm until the average product equals 4, which is 10 workers.

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d. If it is still under open access, then more people would move on to the land and the rent would still be completely dissipated. e. If the farmer must share his output, then he decides to put labour on the field until the share of the marginal product equals the outside opportunity. This reduces labour effort. Because there is less effort, the return to the land is also lower. f. No they wouldnt, which is why a share contract is not just like a tax.

g. The problem with wage contracts is that you have to monitor the farmer. Given the large role of nature in farming this is extremely difficult. In fact, there really is no such thing as a wage farmer. There have been many attempts to explain the pattern of contracting for rent versus share contracts. Some explain it using concepts of risk aversion, though this turns out to be inconsistent with the facts. For example, sugarcane is one of the least risky crops to grow, and yet is completely grown under share contracting. Another reason is that rent contracts cause the farmer to mine the soil and hence a share contract slows the farmer down. The problem with share contracting though is that the output can be underreported. 8. The federal government provided insurance which encouraged the banks to make riskier loans given that they were protected from the downside risk. 9. We will develop an argument based on adverse selection. The key thing to note is that under the group plan, all individuals in the group must buy the insurance, whereas in the open market, individuals are free to buy insurance or not. Hence, adverse selection is a possibility in the open market, if there is adverse selection, only individuals who have relatively poor health will buy insurance and the price will be correspondingly higher than it is for the group. At best, this is only part of the real story. Transactions costs are likely be lower for group plans, leading to a lower price. And to the extent that the insurance market is not competitive, large groups will be able to get a lower price than will individuals. 10. The problem with buying blood is that self-interested sellers have no incentive to reveal the diseases they carry or the dangerous social practices in which they engage. Indeed, if they anticipate that they cannot sell their blood if they do reveal their hidden characteristic, they have a positive, and socially perverse, incentive to keep it hidden. This socially-perverse incentive is absent when blood is raised by charitable donation. This is another source of market failure driven by asymmetric information.

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11. Yes, if some age/sex groups have significantly worse accident probabilities than others. 12. It is probably both. Bad drivers might buy the car because they know they will be in an accident (adverse selection), but good drivers might drive more poorly because they know they are in a safe car (moral hazard). 13. No doubt Franklin was exaggerating at his savings, but there was probably some truth to what he was saying. An apprentice would work under a craftsman for his food and lodging. They were infamous for not working too hard and eating too much. Once Franklin began paying the marginal cost of his eating expenses, he cut down his consumption and his expenses fell accordingly. This is moral hazard. 14. Absolutely. The screen was whether or not your social capital was sufficient. By entering a duel you demonstrated you had enough social capital to be trusted. Therefore, you maintained the social relationship. It was only when someone failed to carry out a duel that they revealed themselves to be untrustworthy. 15. (a) Lower. (b) Worse. (c) Worse. (d) Worse. 16. (a) Yes. (b) They could receive a percent of the selling price. 17. (a) $185 (b) With the warranty, both have expected utility of 8. Without the warranty, careful peoples expected utility of 8.4. The EU of those who are not careful is 5.2. (c) Only those who are not careful. (d) They would expect to lose $85 per warranty. 18. (a) Adverse Selection. (b) Moral Hazard. (c) Adverse Selection. (d) Moral Hazard. 19.
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More since there would be a longer time to extract the excess profit available from cheating. Risk aversion.

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