Chapter 29

True-False Exchange
Topic: Exchange Diculty: 1
% Correct Responses: 62 Discrimination Index: 5
Correct Answer: False
29.1 Partial equilibrium analysis concerns only supply or only demand while general equilibrium
analysis deals with supply and demand at the same time.

Topic: Exchange Diculty: 1

% Correct Responses: 52 Discrimination Index: 31
Correct Answer: True
29.2 A pure exchange economy is an economy where goods are traded but there is no production.

Topic: Exchange Diculty: 1

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: False
29.3 In general equilibrium analysis, an allocation is a feasible allocation if every consumer is
consuming a bundle that costs no more than his or her income.

Topic: Exchange Diculty: 2

% Correct Responses: 53 Discrimination Index: 31
Correct Answer: True
29.4 From Walras' law it follows that in a market with two goods, if demand equals supply in
one market, then demand must equal supply in the other market.

Topic: Exchange Diculty: 1

% Correct Responses: 89 Discrimination Index: 14
Correct Answer: True
29.5 If the assumptions of the rst theorem of welfare economics apply, and if the economy is
in a competitive equilibrium, then any reallocation that benets someone must harm someone else.
 CHAPTER 29 Exchange 528

Topic: Exchange Diculty: 1

% Correct Responses: 95 Discrimination Index: 0
Correct Answer: True
29.6 If there are consumption externalities, then a competitive equilibrium is not necessarily
Pareto optimal.

Topic: Exchange Diculty: 1

% Correct Responses: 88 Discrimination Index: 0
Correct Answer: True
29.7 A competitive equilibrium allocation must be a feasible allocation.

Topic: Exchange Diculty: 2

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: True
29.8 The second welfare theorem states that if preferences are convex, then any Pareto optimal
allocation could be achieved as a competitive equilibrium after some reallocation of initial endow-
ments.

Topic: Exchange Diculty: 1

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: True
29.9 In a competitive pure exchange economy, if the total value of excess demand for all types
of food is zero, then the total value of excess demand for all nonfood commodities must be zero.

Topic: Exchange Diculty: 1

% Correct Responses: 84 Discrimination Index: 18
Correct Answer: True
29.10 Every allocation on the contract curve is Pareto optimal.

Topic: Exchange Diculty: 2

% Correct Responses: 75 Discrimination Index: 10
Correct Answer: True
29.11 In a pure exchange economy with two goods, if there is a competitive equilibrium with
prices p1 = 12; p2 = 27; then there must also be a competitive equilibrium with prices p1 = 24;
p2 = 54.
 TRUE-FALSE 529

Topic: Exchange Diculty: 2

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: True
29.12 If demand varies continuously with price, then even if there are thousands of goods there
will be at least one set of prices such that demand equals supply in every market.

Topic: Exchange Diculty: 3

% Correct Responses: 43 Discrimination Index: 23
Correct Answer: True
29.13 If allocation x is a competitive equilibrium at prices p and if everybody likes his bundle in
allocation y better than his bundle in allocation x; then the total value of allocation y at prices p
exceeds the total value of allocation x at prices p.

Topic: Exchange Diculty: 2

% Correct Responses: 58 Discrimination Index: 16
Correct Answer: True
29.14 If the initial endowment is on the contract curve, then there must always be a competitive
equilibrium in which no trade takes place.

Topic: Exchange Diculty: 2

% Correct Responses: 57 Discrimination Index: 40
Correct Answer: True
29.15 Jack Spratt's utility function is U(F; L) = L. His wife's utility function is U(F; L) = F . If
Jack's initial endowment is 70 units of F and 35 units of L and if Jack's wife's initial endowment
is 42 units of F and 70 units of L; then in an Edgeworth box for Jack and his wife, an allocation of
F and L will be Pareto optimal only if it is
at a corner of the box.

Topic: Exchange Diculty: 2

% Correct Responses: 57 Discrimination Index: 40
Correct Answer: True
29.16 Jack Spratt's utility function is U(F; L) = L. His wife's utility function is U(F; L) = F . If
Jack's initial endowment is 50 units of F and 25 units of L and if Jack's wife's initial endowment
is 30 units of F and 50 units of L; then in an Edgeworth box for Jack and his wife, an allocation of
F and L will be Pareto optimal only if it is
at a corner of the box.
 CHAPTER 29 Exchange 530

Topic: Exchange Diculty: 3

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: True
29.17 If two people have identical Cobb-Douglas utility functions, then in every Pareto optimal
allocation, they must consume all goods in the same proportions as each other.

Topic: Exchange Diculty: 2

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: True
29.18 If two people have identical homothetic preferences and if their indierence curves have
diminishing marginal rate of substitution, then in an Edgeworth box, the locus of Pareto optimal
allocations between them is a diagonal straight line.

Topic: Exchange Diculty: 1

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: False
29.19 In a model with two consumers, two goods, and no production, the contract curve must
be a line going from one consumer's origin to the other consumer's origin.

Topic: Exchange Diculty: 2

% Correct Responses: 40 Discrimination Index: 20
Correct Answer: False
29.20 In a competitive pure exchange economy, if the initial endowment is on the diagonal line
between the two origins, then, according to the rst welfare theorem, there must always be a com-
petitive equilibrium in which no trade takes place.
Multiple Choice Exchange

Topic: Exchange Diculty: 2

% Correct Responses: 12 Discrimination Index: 8
Correct Answer: E
29.1 In a pure exchange economy with two persons and two goods, one person always prefers
more to less of both goods and one person likes one of the goods and hates the other so much that
she would have to be paid to consume it. Both are initially endowed with positive amounts of both
goods. The competitive equilibrium price of the good that one person hates must be:
(a) negative.
(b) smaller than the price of the good both people like.
(c) less than 1.
(d) could be positive or negative, depending on details of tastes and technology.
(e) positive.

Topic: Exchange Diculty: 2

% Correct Responses: 65 Discrimination Index: 35
Correct Answer: A
29.2 If an allocation is Pareto optimal and if indierence curves between the two goods have no
kinks, then it must be that:
(a) two consumers who consume both goods must have the same MRS between them but consumers may
consume the goods in dierent ratios.
(b) two consumers with the same income who consume both goods must have the same MRS, but if their
incomes dier their MRS's may dier.
(c) any two consumers who consume both goods must consume them in the same ratio.
(d) for any two consumers who consume both goods, neither will prefer the other consumer's bundle to his
own.
(e) all consumers receive the bundle that they prefer to any other bundle the economy could produce for
them.
 CHAPTER 29 Exchange 532

Topic: Exchange Diculty: 2

% Correct Responses: 55 Discrimination Index: 35
Correct Answer: E
29.3 According to the First Theorem of Welfare Economics:
(a) Every competitive equilibrium is fair.
(b) If the economy is in a competitive equilibrium, there is no way to make anyone better o.
(c) A competitive equilibrium always exists.
(d) At a Pareto optimum, all consumers must be equally wealthy.
(e) None of the above.

Topic: Exchange Diculty: 2

% Correct Responses: 76 Discrimination Index: 47
Correct Answer: A
29.4 A small economy
=
has only two consumers, Ben and Penelope. Ben's utility function is
U(x; y) = x + 84y1 2 . Penelope's utility function is U(x; y) = x + 7y. At a Pareto optimal allocation
in which both individuals consume some of each good, how much y does Ben consume?
(a) 36
(b) 6.50
(c) 12
(d) 13
(e) We can't tell without knowing the initial endowments.

Topic: Exchange Diculty: 2

% Correct Responses: 76 Discrimination Index: 47
Correct Answer: A
29.5 A small economy
=
has only two consumers, Leonard and Katerina. Leonard's utility function
is U(x; y) = x+144y1 2 . Katerina's utility function is U(x; y) = x+6y. At a Pareto optimal allocation
in which both individuals consume some of each good, how much y does Leonard consume?
(a) 144
(b) 9
(c) 24
(d) 18
(e) We can't tell without knowing the initial endowments.
 MULTIPLE CHOICE 533

Topic: Exchange Diculty: 2

% Correct Responses: 59 Discrimination Index: 37
Correct Answer: C
29.6 Eduardo and Francisca participate in an economy that is in competitive equilibrium. Al-
though they are unacquainted with each other, both purchase strawberries and champagne. Ed-
uardo's utility function is U(s; c) = 2s+c where s is the number of boxes of strawberries he consumes
per month and c is the number of bottles of champagne. Francisca's utility function is U(s; c) = sc.
From this information we can conclude that:
(a) Francisca consumes equal amounts of strawberries and champagne.
(b) Eduardo consumes more strawberries than champagne.
(c) Francisca consumes twice as many bottles of champagne as boxes of strawberries.
(d) Francisca consumes twice as many boxes of strawberries as bottles of champange.
(e) Eduardo consumes more champagne than strawberries.

Topic: Exchange Diculty: 3

% Correct Responses: 75 Discrimination Index: 29
Correct Answer: D
29.7 Tomoko and Matt both consume the same goods in a pure exchange economy. Tomoko is
originally endowed with 16 units of good 1 and 14 units of good 2. Matt is originally endowed with
216 units of good 1 and 15 units of good 2. They both have the utility function U(x1; x2) = x11=3x22=3.
If we let good 1 be the numeraire, so that p1 = 1; then what will be the equilibrium price of good 2?
(a) 2
(b) 32
(c) 1
(d) 16
(e) 8
 CHAPTER 29 Exchange 534

Topic: Exchange Diculty: 3

% Correct Responses: 75 Discrimination Index: 29
Correct Answer: D
29.8 Holly and Steven both consume the same goods in a pure exchange economy. Holly is
originally endowed with 5 units of good 1 and 3 units of good 2. Steven is originally endowed with
5 units of good 1 and 2 units of good 2. They both have the utility function U(x1 ; x2) = x11=3x22=3.
If we let good 1 be the numeraire, so that p1 = 1; then what will be the equilibrium price of good 2?
(a) 2
(b) 8
(c) 1
(d) 4
(e) 2

Topic: Exchange Diculty: 2

% Correct Responses: 93 Discrimination Index: 32
Correct Answer: C
29.9 Pete and Dud live inD a Dtwo-commodity
D
world. Pete's utility function is U P (xP ; xP ) = xP xP .
D d
1 2 1 2
Dud's utility function is U (x1 ; x2 ) = minfx1 ; x2 g. Pete is initially endowed with 3 units of com-
modity 1 and 4 units of commodity 2. Dud is initially endowed with 7 units of commodity 1 and
6 units of commodity 2. Which of the following is true?
(a) Both consume 5 units of each good in competitive equilibrium.
(b) At competitive equilibrium, Dud consumes 6 units of each, since the 7th unit of his endowment of
commodity 1 gives him no added utility
(c) At a competitive equilibrium, Dud must consume equal amounts of both goods, so the price of good 1
must equal the price of good 2.
(d) The prices of the two goods cannot be equal in equilibrium since Pete and Dud do not have equal
endowments.
(e) All of the above statements are false.
 MULTIPLE CHOICE 535

Topic: Exchange Diculty: 1

% Correct Responses: 95 Discrimination Index: 17
Correct Answer: C
29.10 A situation is Pareto ecient if:
(a) there is no way to make everyone worse o without making someone better o.
(b) aggregate prots are maximized.
(c) there is no way to make someone better o without making someone else worse o.
(d) there is some way to make everyone better o.
(e) there is no way to make anyone better o.

Topic: Elasticity Diculty: 2

% Correct Responses: 46 Discrimination Index: 26
Correct Answer: E
29.11 Dan and Marilyn consume two goods, x and y. They have identical Cobb-Douglas utility
functions. Initially Dan owns 10 units of x and 10 units of y. Initially Marilyn owns 40 units of
x and 20 units of y. They make exchanges to reach a Pareto optimal allocation which is better
for both than the no-trade allocation. Which of the following is NOT necessarily true about the
allocation they trade to?
(a) Marilyn consumes 5 units of x for every 3 units of y that she consumes.
(b) The locus of Pareto optimal allocations is a diagonal straight line in the Edgeworth box.
(c) Dan's consumption of x is greater than his consumption of y.
(d) Dan consumes more than 10 units of x.
(e) Marilyn consumes at least 40 units of x.

Topic: Exchange Diculty: 3

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: D
29.12 Xavier and Yvette are the only two persons on a desert island. There are only two
goods, nuts and berries. Xavier's utility function is U(Nx ; Bx ) = Nx Bx . Yvette's utility function is
U(Ny ; By ) = 6Ny + By . Xavier is endowed with 4 units of berries and 10 units of nuts. Yvette is
endowed with 6 units of berries and 8 units of nuts. In a competitive equilibrium for this economy,
how many units of berries does Xavier consume?
(a) 35
(b) 64
(c) 30
(d) 32
(e) None of the above.
 CHAPTER 29 Exchange 536

Topic: Exchange Diculty: 3

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: D
29.13 Xavier and Yvette are the only two persons on a desert island. There are only two
goods, nuts and berries. Xavier's utility function is U(Nx ; Bx ) = Nx Bx . Yvette's utility function is
U(Ny ; By ) = 3Ny + By . Xavier is endowed with 3 units of berries and 10 units of nuts. Yvette is
endowed with 6 units of berries and 8 units of nuts. In a competitive equilibrium for this economy,
how many units of berries does Xavier consume?
(a) 19.50
(b) 33
(c) 14.50
(d) 16.50
(e) None of the above.

Topic: Exchange Diculty: 2

% Correct Responses: 57 Discrimination Index: 9
Correct Answer: B
29.14 Eva and Ollie live in an isolated valley and trade with no one but each other. They con-
sume only grapefruits and lemons. Eva has an initial endowment of 10 grapefruits and 15 lemons.
Ollie has an initial endowment of 14 grapefruits and 26 lemons. For Eva, the two goods are per-
fect substitutes, one-for-one. For Ollie, they are perfect complements, one-for-one. At all Pareto
ecient allocations:
(a) Eva must consume at least 25 lemons.
(b) Eva must consume at least 17 lemons.
(c) Ollie must consume 17.50 grapefruits.
(d) the slopes of the two traders' indierence curves are the same.
(e) Ollie must consume all of the grapefruits.
 MULTIPLE CHOICE 537

Topic: Exchange Diculty: 2

% Correct Responses: 57 Discrimination Index: 9
Correct Answer: B
29.15 Isabella and Horace live in an isolated valley and trade with no one but each other. They
consume only tomatoes and grapes. Isabella has an initial endowment of 20 tomatoes and 2 grapes.
Horace has an initial endowment of 4 tomatoes and 38 grapes. For Isabella, the two goods are per-
fect substitutes, one-for-one. For Horace, they are perfect complements, one-for-one. At all Pareto
ecient allocations:
(a) Isabella must consume at least 22 grapes.
(b) Isabella must consume at least 16 grapes.
(c) Horace must consume 19 tomatoes.
(d) the slopes of the two traders' indierence curves are the same.
(e) Horace must consume all of the tomatoes.

Topic: Exchange Diculty: 3

% Correct Responses: 11 Discrimination Index: 35
Correct Answer: C
29.16 Amaranda and Bartolo consume only two goods, X and Y . They can trade only with each
other and there is no production. The total endowment of Good X equals the total endowment
of Good Y . Amaranda's utility function is U(xA ; yA) = minfxA ; yA g and Bartolo's utility function
is U(xB ; yB ) = maxfxA ; yB g. In an Edgeworth box for Amaranda and Bartolo, the set of Pareto
optimal allocations is:
(a) the main diagonal.
(b) both diagonals.
(c) the whole Edgeworth box.
(d) the edges of the box and the main diagonal.
(e) the edges of the box.
 CHAPTER 29 Exchange 538

Topic: Exchange Diculty: 3

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: C
29.17 Adelino and Benito consume only two goods X and Y . They trade only with each other
and there is no production. Adelino's utility function is given by U(xA; yA ) = 2xA +5yA and Benito's
utility function is given by U(xB ; yB ) = 2(6xB + 15yB )1=2. In the Edgeworth box constructed for
Adelino and Benito, the set of Pareto optimal allocations is:
(a) the main diagonal.
(b) both diagonals.
(c) the entire contents of the Edgeworth box.
(d) the right and left edges of the box.
(e) the upper and lower edges of the box.

Topic: Exchange Diculty: 2

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: D
29.18 Tamara and Julio consume only bread and wine. They trade only with each other and
there is no production. They both have strictly convex preferences. Tamara's initial endowment of
bread and wine is the same as Julio's.
(a) At the initial endowment their marginal rates of substitution must be the same.
(b) In a competitive equilibrium, the ratio of the two prices must be 1.
(c) In a competitive equilibrium, they must consume identical consumption bundles.
(d) If they have identical utility functions, then the initial allocation is Pareto optimal.
(e) None of the above.
 MULTIPLE CHOICE 539

Topic: Exchange Diculty: 2

% Correct Responses: 53 Discrimination Index: 49
Correct Answer: E
29.19 Arturo and Belen consume only two goods, X and Y . They have strictly convex preferences
and no kinks in their indierence curves. At the initial allocation, the ratio of Arturo's marginal
utility of X to his marginal utility of Y is A and the ratio of Belen's marginal utility of X to his
marginal utility of Y is B; where A < B . The competitive equilibrium price ratio is px=py = C .
Then:
(a) C > B.
(b) C < A.
(c) C = A.
(d) C = B.
(e) A < C < B.

Topic: Exchange Diculty: 2

% Correct Responses: 30 Discrimination Index: 20
Correct Answer: B
29.20 In a two-person, two-good, exchange economy, both consumers have quasilinear utility
functions, linear in Good 2. If quantities of Good 1 are measured horizontally and quantities of
Good 2 are measured vertically in the Edgeworth box, the set of Pareto optimal allocations includes
(a) a horizontal line through the interior of the box.
(b) a vertical line.
(c) a straight line from the lower left to the upper right corner of the box.
(d) a curved line from the lower left to the upper right corner of the box.
(e) all four edges of the box.
 CHAPTER 29 Exchange 540

Topic: Exchange Diculty: 0

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: B
29.21 A small =economy has only two consumers, Roger and Heidi. Roger's utility function is
U(x; y) = x + 50y1 2. Heidi's utility function is U(x; y) = x + 5y. Roger is endowed with 625 units of
x and 60 units of y. They make trades to reach a Pareto optimal allocation of resources in which
both persons consume positive amounts. How much y does Roger consume?
(a) 50
(b) 25
(c) 28
(d) 23
(e) There is not enough information to determine how much y he will consume.

Topic: Exchange Diculty: 0

% Correct Responses: 0 Discrimination Index: 0
Correct Answer: B
29.22 A small economy
=
has only two consumers, George and Penelope. George's utility function
is U(x; y) = x + 16y1 2. Penelope's utility function is U(x; y) = x + 4y. George is endowed with 64
units of x and 60 units of y. They make trades to reach a Pareto optimal allocation of resources in
which both persons consume positive amounts. How much y does George consume?
(a) 8
(b) 4
(c) 7
(d) 2
(e) There is not enough information to determine how much y he will consume.
 MULTIPLE CHOICE 541

Topic: Exchange Diculty: 2

% Correct Responses: 20 Discrimination Index: 37
Correct Answer: A
29.23 Abdul's utility is U(XA ; YA) = minfXA ; YAg where XA and YA are his consumptions of goods
X and Y respectively. Babette's utility function is U(XB ; YB ) = XB YB where XB and YB are her
consumptions of goods X and Y . Abdul's initial endowment is no units of Y and 10 units of X .
Babette's initial endowment is no units of X and 12 units of Y . If X is the numeraire good and p
is the price of good Y; then supply will equal demand in the market for Y if the following equation
is satised.
(a) 10=(p + 1) + 6 = 12
(b) 12=10 = p
(c) 12=(p + 1) + 5 = 12
(d) Minf10; 12g + 10=(2p) = 12
(e) Minf10; 12g + 12=2p = 12

Topic: Exchange Diculty: 2

% Correct Responses: 20 Discrimination Index: 37
Correct Answer: A
29.24 Abdul's utility is U(XA; YA) = minfXA ; YAg where XA and YA are his consumptions of
goods X and Y respectively. Babette's utility function is U(XB ; YB ) = XB YB where XB and YB are
her consumptions of goods X and Y . Abdul's initial endowment is no units of Y and 4 units of X .
Babette's initial endowment is no units of X and 14 units of Y . If X is the numeraire good and p
is the price of good Y; then supply will equal demand in the market for Y if the following equation
is satised.
(a) 4=(p + 1) + 7 = 14
(b) 14=4 = p
(c) 14=(p + 1) + 2 = 14
(d) Minf4; 14g + 4=(2p) = 14
(e) Minf4; 14g + 14=2p = 14
 CHAPTER 29 Exchange 542

Topic: Exchange Diculty: 2

% Correct Responses: 63 Discrimination Index: 38
Correct Answer: B
29.25 Professor Nightsoil's utility function is UN (BN ; PM ) = BN + 4PN= and Dean Interface's
1 2

=
utility function is UI (BI ; PI ) = BI +2PI where BN and BI are the number of bromides and PN and
1 2

PI are the number of platitudes consumed by Nightsoil and Interface respectively . If Nightsoil's
initial endowment is 4 bromides and 15 platitudes and if Interface's initial endowment is 5 bromides
and 20 platitudes, then at any Pareto ecient allocation in which both persons consume positive
amounts of both goods, it must be that:
(a) Nightsoil consumes the same ratio of bromides to platitudes as Interface.
(b) Interface consumes 7 platitudes.
(c) Interface consumes 4.50 bromides.
(d) Interface consumes 3 bromides.
(e) Interface consumes 4 bromides.

Topic: Exchange Diculty: 2

% Correct Responses: 63 Discrimination Index: 38
Correct Answer: B
29.26 Professor Nightsoil's utility function is UN (BN ; PM ) = BN + 4PN= and Dean Interface's
1 2

=
utility function is UI (BI ; PI ) = BI +2PI where BN and BI are the number of bromides and PN and
1 2

PI are the number of platitudes consumed by Nightsoil and Interface respectively . If Nightsoil's
initial endowment is 2 bromides and 10 platitudes and if Interface's initial endowment is 3 bromides
and 25 platitudes, then at any Pareto ecient allocation in which both persons consume positive
amounts of both goods, it must be that:
(a) Nightsoil consumes the same ratio of bromides to platitudes as Interface.
(b) Interface consumes 7 platitudes.
(c) Interface consumes 2.50 bromides.
(d) Interface consumes 2 bromides.
(e) Interface consumes 5 bromides.
 MULTIPLE CHOICE 543

Topic: Exchange Diculty: 2

% Correct Responses: 61 Discrimination Index: 58
Correct Answer: B
29.27 An economy has two people Charlie and Doris. There are two goods, apples and bananas.
Charlie has an initial endowment of 5 apples and 4 bananas. Doris has an initial endowment of
10 apples and 2 bananas. Charlie's utility function is U(AC ; BC ) = AC BC where AC is his apple
consumption and BC is his banana consumption. Doris's utility function is U(AD ; BD ) = AD BD
where AD and BD are her apple and banana consumptions. At every Pareto optimal allocation:
(a) Charlie consumes the same number of apples as Doris.
(b) Charlie consumes 15 apples for every 6 bananas that he consumes.
(c) Doris consumes equal numbers of apples and bananas.
(d) Charlie consumes more bananas per apple than Doris does.
(e) Doris consumes apples and bananas in the ratio of 10 apples for every 2 bananas that she consumes.

Topic: Exchange Diculty: 2

% Correct Responses: 61 Discrimination Index: 58
Correct Answer: B
29.28 An economy has two people Charlie and Doris. There are two goods, apples and bananas.
Charlie has an initial endowment of 3 apples and 12 bananas. Doris has an initial endowment of
6 apples and 6 bananas. Charlie's utility function is U(AC ; BC ) = AC BC where AC is his apple
consumption and BC is his banana consumption. Doris's utility function is U(AD ; BD ) = AD BD
where AD and BD are her apple and banana consumptions. At every Pareto optimal allocation:
(a) Charlie consumes the same number of apples as Doris.
(b) Charlie consumes 9 apples for every 18 bananas that he consumes.
(c) Doris consumes equal numbers of apples and bananas.
(d) Charlie consumes more bananas per apple than Doris does.
(e) Doris consumes apples and bananas in the ratio of 6 apples for every 6 bananas that she consumes.
 CHAPTER 29 Exchange 544

Topic: Exchange Diculty: 2

% Correct Responses: 55 Discrimination Index: 41
Correct Answer: C
29.29 Ken's utility function is U(QK ; WK ) = QK WK and Barbie's utility function is U(QB ; WB ) =
QB WB . If Ken's initial endowment were 3 units of quiche and 9 units of wine and Barbie's endow-
ment were 6 units of quiche and 9 units of wine, then at any Pareto optimal allocation where both
persons consume some of each good:
(a) Ken would consume 3 units of quiche for every 9 units of wine.
(b) Barbie would consume twice as much quiche as Ken.
(c) Ken would consume 9 units of quiche for every 18 units of wine that he consumes.
(d) Barbie would consume 6 units of quiche for every 9 units of wine that she consumes.
(e) None of the above.

Topic: Exchange Diculty: 2

% Correct Responses: 55 Discrimination Index: 41
Correct Answer: C
29.30 Ken's utility function is U(QK ; WK ) = QK WK and Barbie's utility function is U(QB ; WB ) =
QB WB . If Ken's initial endowment were 3 units of quiche and 12 units of wine and Barbie's en-
dowment were 6 units of quiche and 12 units of wine, then at any Pareto optimal allocation where
both persons consume some of each good:
(a) Ken would consume 3 units of quiche for every 12 units of wine.
(b) Barbie would consume twice as much quiche as Ken.
(c) Ken would consume 9 units of quiche for every 24 units of wine that he consumes.
(d) Barbie would consume 6 units of quiche for every 12 units of wine that she consumes.
(e) None of the above.
 MULTIPLE CHOICE 545

Topic: Exchange Diculty: 3

% Correct Responses: 20 Discrimination Index: 12
Correct Answer: D
29.31 Morris has the utility function U(b; w) = 3b + 12w and Philip has the utility function
U(b; w) = bw; where b is the number of books consumed per month and w is bottles of wine con-
sumed per month. If we draw an Edgeworth box with books on the horizontal axis and wine on the
vertical axis and if we measure Morris' consumptions from the lower left corner of the box, then
the contract curve contains:
(a) a straight line running from the upper right corner of the box to the lower left.
(b) a curve that gets steeper as you move from left to right.
(c) a straight line with slope 1=4 passing through the lower left corner of the box.
(d) a straight line with slope 1=4 passing through the upper right corner of the box.
(e) a curve that gets atter as you move from left to right.

Topic: Exchange Diculty: 3

% Correct Responses: 20 Discrimination Index: 12
Correct Answer: D
29.32 Morris has the utility function U(b; w) = 4b + 12w and Philip has the utility function
U(b; w) = bw; where b is the number of books consumed per month and w is bottles of wine con-
sumed per month. If we draw an Edgeworth box with books on the horizontal axis and wine on the
vertical axis and if we measure Morris' consumptions from the lower left corner of the box, then
the contract curve contains:
(a) a straight line running from the upper right corner of the box to the lower left.
(b) a curve that gets steeper as you move from left to right.
(c) a straight line with slope 1=3 passing through the lower left corner of the box.
(d) a straight line with slope 1=3 passing through the upper right corner of the box.
(e) a curve that gets atter as you move from left to right.
 CHAPTER 29 Exchange 546

Topic: Exchange Diculty: 2

% Correct Responses: 62 Discrimination Index: 39
Correct Answer: A
29.33 Astrid's utility function is U(HA; CA) = HACA. Birger's utility function is minfHB ; CBg. If
Astrid's initial endowment is no cheese and 8 units of herring and if Birger's initial endowments
are 8 units of cheese and no herring, then where p is a competitive equilibrium price of herring and
cheese is the numeraire, it must be that demand equals supply in the herring market. This implies
that:
(a) 8=(p + 1) + 4 = 8
(b) 8=8 = p
(c) 8=8 = p
(d) 8=p + 8=2p = 8
(e) Minf8; 8g = p

Topic: Exchange Diculty: 2

% Correct Responses: 62 Discrimination Index: 39
Correct Answer: A
29.34 Astrid's utility function is U(HA; CA) = HACA. Birger's utility function is minfHB ; CBg. If
Astrid's initial endowment is no cheese and 12 units of herring and if Birger's initial endowments
are 8 units of cheese and no herring, then where p is a competitive equilibrium price of herring and
cheese is the numeraire, it must be that demand equals supply in the herring market. This implies
that:
(a) 8=(p + 1) + 6 = 12
(b) 8=12 = p
(c) 12=8 = p
(d) 8=p + 12=2p = 12
(e) Minf12; 8g = p
 MULTIPLE CHOICE 547

Topic: Exchange Diculty: 2

% Correct Responses: 29 Discrimination Index: 27
Correct Answer: B
29.35 Mutt's utility function is U(m; j) = maxf4m; jg and Je's utility function is U(m; j) = 2m+j.
Mutt is initially endowed with 3 units of milk and 2 units of juice and Je is initially endowed with
5 units of milk and 6 units of juice.If we draw an Edgeworth box with milk on the horizontal axis
and juice on the vertical axis and if we measure goods for Mutt by the distance from the lower left
corner of the box, then the set of Pareto optimal allocations includes the:
(a) left edge of the Edgeworth box, but no other edges.
(b) bottom edge of the Edgeworth box, but no other edges.
(c) left edge and bottom edge of the Edgeworth box.
(d) right edge of the Edgeworth box, but no other edges.
(e) right edge and top edge of the Edgeworth box.

Topic: Exchange Diculty: 2

% Correct Responses: 29 Discrimination Index: 27
Correct Answer: B
29.36 Mutt's utility function is U(m; j) = maxf4m; jg and Je's utility function is U(m; j) = 3m+j.
Mutt is initially endowed with 3 units of milk and 2 units of juice and Je is initially endowed with
5 units of milk and 6 units of juice.If we draw an Edgeworth box with milk on the horizontal axis
and juice on the vertical axis and if we measure goods for Mutt by the distance from the lower left
corner of the box, then the set of Pareto optimal allocations includes the:
(a) left edge of the Edgeworth box, but no other edges.
(b) bottom edge of the Edgeworth box, but no other edges.
(c) left edge and bottom edge of the Edgeworth box.
(d) right edge of the Edgeworth box, but no other edges.
(e) right edge and top edge of the Edgeworth box.
Essay Exchange
Topic: Exchange Diculty: 2
% Correct Responses: 0 Discrimination Index: 0
29.1 In a pure exchange economy, Ollie's utility function is 0 U(x; y) = 3x + y and Fawn's utility0
function is U(x; y) = xy. Ollie's initial allocation is 1 x and no y s. Fawn's initial allocation is no x s
and 2 y0 s. Draw an Edgeworth box for Fawn and Ollie. Put x0s on the horizontal axis and y0 s on
the vertical axis. Measure goods for Ollie from the lower left and goods for Fawn from the upper
right. Mark the initial allocation with the letter W . The locus of Pareto optimal points consists of
two line segments. Describe these line segments in words or formulas and show them on your graph.
Answer: The Edgeworth box is 1 unit wide and 2 units high. Along the contract curve, Fawn
consumes 3 times as much y as x. The contract curve consists of a line running from the upper
right corner of the box to the point on the bottom of the box where Fawn consumes all of the y
and 2=3 units of x and a line from this point to the lower left of the box.

Topic: Exchange Diculty: 3

% Correct Responses: 0 Discrimination Index: 0
29.2 An economy has 2000 people. 1000 of them have utility functions U(x; y) = x+y and 1000 of
them have utility functions U(x; y) = minf2x; yg. Everybody has an initial allocation of 1 unit of x
and 1 unit of y. Find the competitive equilibrium prices and consumptions for each type of person.
Answer: Prices are 1 and 1. The rst type of person will consume 2=3 units of y and 4=3 units of
x and the second type of person will consume 4=3 units of y and 2=3 units of x.

Topic: Exchange Diculty: 2

% Correct Responses: 0 Discrimination Index: 0
29.3 Will likes apples and hates bananas. Wanda likes both apples and bananas. Both of them
have convex preferences. Will's initial endowment is 10 apples and 5 bananas. Wanda's initial
endowment is 5 bananas and 10 apples. a) Draw an Edgeworth box with apples on the horizontal
axis. Label the initial endowment point, W . b) Show two indierence curves for each person. c)
Show where on your diagram the Pareto optimal allocations are.
Answer: The Pareto optimal allocations include all of the allocations where Will has no bananas.
If stu for Will is measured from the lower left corner, then these allocations are all along the
bottom of the box.