Part I: Multiple choice
1. As the interest rate rises, does the intertemporal budget constraint become steeper. True or
false?
2. In a production process is it possible to have decreasing marginal product in an input and yet
increasing returns to scale. True or false?
3. Which of the following are true?
(3a) Average fixed costs never decrease with output;
(3b) Average total costs are always greater than or equal to average variable costs;
(3c) Average cost can never rise while marginal costs are declining.
4. Some individual cannot be made better off if we are at a Pareto efficient allocation. This
statement is true or false?
5. Some individual can be made better off if we are at a Pareto efficient allocation. This
statement is true or false?
6. In the short run, if the price of the fixed factor is increased, profits will increase. This is true or
false?
7. If the law of diminishing marginal product did not hold, the world's food supply could be
grown in a flowerpot. True or false?
8. True or false? If we know the contract curve, then we know the outcome of any trading.
9. If the preferences are concave will the consumer ever consume both of the goods together?
10. Average fixed costs never increase with output;
11. Average total cost is always greater than average variable cost by a constant amount;
12. In the short run, a perfectly competitive firm always maximises profit when average total
cost is at minimum
13. If a firm shuts down in the short run, its profits will equal zero
14. In a factory setting, if the number of workers is increased while keeping other inputs constant
(e.g., machinery), production will likely be an initial boost. However, as more workers are hired,
they may get in each other's way, leading to inefficiencies, and the additional output per new
worker may decrease. This is an example of the law of diminishing marginal product.
15. Consider a fixed-sized field with a fixed amount of fertilizer. As more fertilizer is added to
the field, there will be an initial increase in crop yield. However, beyond a certain point, adding
more fertilizer may lead to diminishing returns, as the soil becomes saturated and excessive
fertilizer becomes wasteful or even harmful. This is an example of the law of diminishing
marginal product.
16. In a production process is it possible to have decreasing marginal product in an input and yet
decreasing returns to scale
17. The marginal rate of substitution measures the slope of the indifference curve. This can be
interpreted as how much the consumer is willing to give up good 2 to acquire more of good 1
18. Financial institutions such as insurance markets and the stock market provide ways for
consumers to diversify and spread risks
19. In the long run a firm always operates at the minimum level of average costs for the
optimally sized plant to produce a given amount of output.
20. A Cournot equilibrium in which each firm has a small market share implies that price will be
very close to marginal cost-that is, the industry will be nearly competitive, true or false
Part II: Calculating exercise
1. How much is $1 million to be delivered 20 years in the future worth today if the interest rate is
20 percent?
2. A firm has a cost function given by c(y) = 10y2 + 1000. What is its supply curve? At what
output is average cost minimized?
3. The monopolist faces a demand curve given by D(p) = 10p-3. Its cost function is c(y)=2y.
What is its optimal level of output and price?
4. What is the present value of $100 one year from now if the interest rate is 10%? What is the
present value if the interest rate is 5%?
5. A firm has a cost function given by c(y) = 10y2+ 1000. What is its supply curve? At what
output is average cost minimized?
6. If D(p) = 100/p and c(y) = y2, what is the optimal level of output of the monopolist?
7. If a consumer has a utility function u(x1, x2) = x1x24, what fraction of her income will she
spend on good 2?
8. The monopolist faces a demand curve given by D(p) = 100−2p. Its cost function is c(y)=2y.
What is its optimal level of output and price?
9. Company Traki is considering an investment project. This project can bring in a profit of $50
billion with a 50% probability of success and can fail with a 50% probability. This failure would
mean a loss of $10 billion in costs.
a. Calculate the expected profit for the project.
b. Assuming the manager is risk averse, can this project be done? Explain?
10. If a consumer has a utility function: U = 52X-2X2+116Y-5Y2
a. Show the law of diminishing marginal utility in that function.
b. This customer's income is 350, price X is 5, price Y is 2. Write the budget constraint equation
for this consumer.
11. A monopolist has the demand function P = 30 -1/2Q and average total cost is 14
a. Calculate the monopolist's profit.
b. Calculate deadweight loss.
c. If the ceiling price is 18, what is the decision (on price, quantity) of this firm?
12. If the cost function is TC = Q2 +1, what is the supply curve of the firm?
Part III: Short answers
1. Consider a cartel in which each firm has identical and constant marginal costs. If the cartel
maximizes total industry profits, what does this imply about the division of output between the
firms.
2. What happens to the budget line if the price of good 2 increases, but the price of good 1 and
income remain constant? Illustrate it by graph.
3. Suppose that indifference curves are described by straight lines with a slope of -b. Given
arbitrary prices and money income p1, p2, and m, what will the consumer's optimal choices look
like? Illustrate it by graph.
4. Consider a cartel in which each firm has identical and constant marginal costs. If the cartel
maximizes total industry profits, what does this imply about the division of output between the
firms.
5. What happens to the budget line if the price of good 2 increases, but the price of good 1 and
income remain constant? Illustrate it by graph.
6. If Robinson's marginal rate of substitution between coconuts and fish is -2 and the marginal
rate of transformation between the two goods is -1, what should he do if he wants to increase his
utility?
7. Originally the consumer faces the budget line p1x1 + p2x2 = m. Then the price of good 1
doubles, the price of good 2 becomes 8 times larger, and income becomes 4 times larger. Write
down an equation for the new budget line in terms of the original prices and income.
8. Which of the following are monotonic transformations?
(1) u = 2v − 13; (2) u = −1/v2; (3) u = 1/v2; (4) u = ln v; (5) u = −e−v; (6) u = v2; (7) u = v2
for v > 0; (8) u = v2 for v < 0
9. The Cobb-Douglas production function is given by f(x, y) = Axayb . It turns out that the type
of returns to scale of this function will depend on the magnitude of a + b. Which values of a + b
will be associated with the different kinds of returns to scale?
10. We saw that a monopolist never produced where the demand for output was inelastic. Will a
monopsonist produce where a factor is inelastically supplied?
11. Is it ever better for a perfectly competitive firm to produce output even though it is losing
money? If so, when?
12. The Cobb-Douglas utility function has the property that:
U(tx1, tx2) = (tx1)a (tx2)1-a = ta t1-a x1ax21-a = t x1a xx1-a = tu(x1, x2).
Prove that Cobb-Douglas preferences are indeed homothetic.
13. Can an economy that is in competitive equilibrium be Pareto efficient
14. Compare and contrast the characteristics of perfect competition and monopoly.
15. How does the concept of deadweight loss relate to market inefficiencies?
16. Consider a cartel in which each firm has identical and constant marginal costs. If the cartel
maximizes total industry profits, what does this imply about the division of output between the
firms?
17. What is the difference between total utility and marginal utility?
18. In the case a firm pollutes the environment, use knowledge about externalities and
government intervention to solve this problem.
19. Suppose a consumer has preferences between two goods that are perfect substitutes. Can you
change prices in such a way that the entire demand response is due to the income effect?
