CHAPTER 32: Exchange
TRUE/FALSE
1. Partial equilibrium analysis concerns only supply or only demand while general equilibrium analysis
deals with supply and demand at the same time.
2. A pure exchange economy is an economy where goods are traded but there is no production.
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.
4. From Walras’s 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.
5. If the assumptions of the first theorem of welfare economics apply and if the economy is in a
competitive equilibrium, then any reallocation that benefits someone must harm someone else.
6. If there are consumption externalities, then a competitive equilibrium is not necessarily Pareto optimal.
7. A competitive equilibrium allocation must be a feasible allocation.
8. The second welfare theorem of economics states that if preferences are convex, then any Pareto
optimal allocation could be achieved as a competitive equilibrium after some reallocation of initial
endowments.
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.
10. Every allocation on the contract curve is Pareto optimal.
11. In a pure exchange economy with two goods, if there is a competitive equilibrium with prices p1
= $12 and p2 = $27, then there must also be a competitive equilibrium with prices p1 = $24 and p2 =
$54.
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.
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.
14. If the initial endowment is on the contract curve, then there must always be a competitive equilibrium
in which no trade takes place.
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 10 units of F and 5 units of L and if Jack’s wife’s initial endowment is 6 units of F and
10 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.
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 40 units of F and 20 units of L and if Jack’s wife’s initial endowment is 24 units of F
and 40 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.
17. 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 100 units of F and 50 units of L and if Jack’s wife’s initial endowment is 60 units of F
and 100 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.
18. 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.
19. If two people have identical homothetic preferences and if their indifference curves have a diminishing
marginal rate of substitution, then in an Edgeworth box, the locus of Pareto optimal allocations
between them is a diagonal straight line.
20. 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.
21. In a competitive pure exchange economy, if the initial endowment is on the diagonal line between the
two origins, then, according to the first welfare theorem of economics, there must always be a
competitive equilibrium in which no trade takes place.
MULTIPLE CHOICE
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
a.
must be negative.
b.
must be smaller than the price of the good both people like.
c.
must be less than 1.
d.
could be positive or negative, depending on details of tastes and technology.
e.
must be positive.
2. If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then
a.
two consumers who consume both goods must have the same MRS between them, but
consumers may consume the goods in different ratios.
b.
two consumers with the same income who consume both goods must have the same MRS,
but if their incomes differ, their MRSs may differ.
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.
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 off.
c.
a competitive equilibrium always exists.
d.
at a Pareto optimum, all consumers must be equally wealthy.
e.
None of the above.
4. A small economy has only two consumers, Charlie and Doreen. Charlie’s utility function is
U(x, y) = x + 154y1/2. Doreen’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 Charlie consume?
a.
121
b.
9
c.
22
d.
18
e.
We can’t tell without knowing the initial endowments.
5. A small economy has only two consumers, Nick and Minnie. Nick’s utility function is
U(x, y) = x + 154y1/2. Minnie’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 Nick consume?
a.
22
b.
18
c.
121
d.
9
e.
We can’t tell without knowing the initial endowments.
6. A small economy has only two consumers, Zeke and Maude. Zeke’s utility function is
U(x, y) = x + 48y1/2. Maude’s utility function is U(x, y) = x + 4y. At a Pareto optimal allocation in
which both individuals consume some of each good, how much y does Zeke consume?
a.
36
b.
12
c.
5
d.
10
e.
We can’t tell without knowing the initial endowments.
7. Eduardo and Francisca participate in an economy that is in competitive equilibrium. Although they are
unacquainted with each other, both purchase strawberries and champagne. Edouardo’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.
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 champagne.
e.
Eduardo consumes more champagne than strawberries.
8. Colette and Boris both consume the same goods in a pure exchange economy. Colette is originally
endowed with 9 units of good 1 and 6 units of good 2. Boris is originally endowed with 18 units of
good 1 and 3 units of good 2. They both have the utility function U(x1, x2) = x1/31x2/32. 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.
$12
c.
$1
d.
$6
e.
$3
9. Teresa and Jean-Pierre both consume the same goods in a pure exchange economy. Teresa is originally
endowed with 9 units of good 1 and 6 units of good 2. Jean-Pierre is originally endowed with 91 units
of good 1 and 14 units of good 2. They both have the utility function U(x1, x2) = x1/31x2/32. If we let
good 1 be the numeraire, so that p1 = $1, then what will be the equilibrium price of good 2?
a.
$10
b.
$20
c.
$2
d.
$1
e.
$5
10. Colette and Hans both consume the same goods in a pure exchange economy. Colette is originally
endowed with 15 units of good 1 and 12 units of good 2. Hans is originally endowed with 97 units of
good 1 and 4 units of good 2. They both have the utility function U(x1, x2) = x1/31x2/32. If we let good 1
be the numeraire, so that p1 = $1, then what will be the equilibrium price of good 2?
a.
$14
b.
$28
c.
$2
d.
$1
e.
$7
11. Pete and Dud live in a two-commodity world. Pete’s utility function is U P(x P1, x P2) = x P1x P2. Dud’s
utility function is U D(x D1, x D2) = minx D1, x D2. Pete is initially endowed with 3 units of commodity
1 and 4 units of commodity 2. Dud is initially endowed with 7 units of commodity 1 and 6 units of
commodity 2.
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.
None of the above.
12. A situation is Pareto efficient if
a.
there is no way to make everyone worse off without making someone better off.
b.
aggregate profits are maximized.
c.
there is no way to make someone better off without making someone else worse off.
d.
there is some way to make everyone better off.
e.
there is no way to make anyone better off.
13. 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.
14. 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) = NxBx. Yvette’s utility function is U(Ny, By) = 2Ny + By.
Xavier is endowed with 3 units of berries and 8 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.
12.50
b.
19
c.
7.50
d.
9.50
e.
None of the above.
15. 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) = NxBx. Yvette’s utility function is U(Ny, By) = 2Ny + By.
Xavier is endowed with 5 units of berries and 13 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.
13.50
b.
18.50
c.
15.50
d.
31
e.
None of the above.
16. 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) = NxBx. Yvette’s utility function is U(Ny, By) = 5Ny + By.
Xavier is endowed with 4 units of berries and 13 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.
37.50
b.
69
c.
34.50
d.
32.50
e.
None of the above.
17. Irene and Orville live in an isolated valley and trade with no one but each other. They consume only
cantaloupes and grapefruits. Irene has an initial endowment of 5 cantaloupes and 12 grapefruits.
Orville has an initial endowment of 19 cantaloupes and 25 grapefruits. For Irene, the two goods are
perfect substitutes, one for one. For Orville, they are perfect complements, one for one. At all Pareto
efficient allocations,
a.
Irene must consume at least 17 grapefruits.
b.
Irene must consume at least 13 grapefruits.
c.
Orville must consume 21.50 cantaloupes.
d.
the slopes of the two traders’ indifference curves are the same.
e.
Orville must consume all of the cantaloupes.
18. Sheila and Ivan live in an isolated valley and trade with no one but each other. They consume only
apples and oranges. Sheila has an initial endowment of 6 apples and 19 oranges. Ivan has an initial
endowment of 18 apples and 20 oranges. For Sheila, the two goods are perfect substitutes, one for one.
For Ivan, they are perfect complements, one for one. At all Pareto efficient allocations,
a.
Sheila must consume at least 25 oranges.
b.
the slopes of the two traders’ indifference curves are the same.
c.
Ivan must consume 17.50 apples.
d.
Sheila must consume at least 15 oranges.
e.
Ivan must consume all of the apples.
19. Marilyn and Chen live in an isolated valley and trade with no one but each other. They consume only
bananas and tomatoes. Marilyn has an initial endowment of 4 bananas and 11 tomatoes. Chen has an
initial endowment of 20 bananas and 27 tomatoes. For Marilyn, the two goods are perfect substitutes,
one for one. For Chen, they are perfect complements, one for one. At all Pareto efficient allocations,
a.
Marilyn must consume at least 15 tomatoes.
b.
the slopes of the two traders’ indifference curves are the same.
c.
Marilyn must consume at least 14 tomatoes.
d.
Chen must consume 22.50 bananas.
e.
Chen must consume all of the bananas.
20. 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) = minxA, yA and Bartolo’s utility function is
U(xB, yB) = maxxB, yB. 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.
21. 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.
22. 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.
23. Arturo and Belen consume only two goods, X and Y. They have strictly convex preferences and no
kinks in their indifference 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.
a.
C B.
b.
C A.
c.
C = A.
d.
C = B.
e.
A C B.
24. 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.
25. A small economy has only two consumers, Harold and Irene. Harold’s utility function is
U(x, y) = x + 50y1/2. Irene’s utility function is U(x, y) = x + 5y. Harold is endowed with 500 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 Harold consume?
a.
50 units
b.
25 units
c.
28 units
d.
23 units
e.
There is not enough information to determine how much y he will consume.
26. A small economy has only two consumers, Ivan and Marilyn. Ivan’s utility function is
U(x, y) = x + 18y1/2. Marilyn’s utility function is U(x, y) = x + 3y. Ivan is endowed with 135 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 Ivan consume?
a.
7 units
b.
12 units
c.
9 units
d.
18 units
e.
There is not enough information to determine how much y he will consume.
27. A small economy has only two consumers, Boris and Vanessa. Boris’s utility function is
U(x, y) = x + 16y1/2. Vanessa’s utility function is U(x, y) = x + 2y. Boris is endowed with 160 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 Boris consume?
a.
32 units
b.
19 units
c.
14 units
d.
16 units
e.
There is not enough information to determine how much y he will consume.
28. Abduls utility is U(X A, Y A) = minX A, Y A, where X A, and Y A are his consumptions of goods X
and Y respectively. Babettes utility function is U(X B, Y B) = X B Y B, where X B and Y B are her
consumptions of goods X and Y. Abduls initial endowment is no units of Y and 6 units of X. Babettes
initial endowment is no units of X and 10 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
a.
6/(p + 1) + 5 = 10.
b.
10/6 = p.
c.
10/(p + 1) + 3 = 10.
d.
min6, 10 + 6/2p = 10.
e.
min6, 10 + 10/2p = 10.
29. Abduls utility is U(X A, Y A) = minX A, Y A, where X A and Y A are his consumptions of goods X
and Y respectively. Babettes utility function is U(X B, Y B) = X B Y B, where X B and Y B are her
consumptions of goods X and Y. Abduls initial endowment is no units of Y and 5 units of X. Babettes
initial endowment is no units of X and 11 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
a.
11/(p + 1) + 2.50 = 11.
b.
5/(p + 1) + 5.50 = 11.
c.
11/5 = p.
d.
min5, 11 + 5/2p = 11.
e.
min5, 11 + 11/2p = 11.
30. Abduls utility is U(X A, Y A) = minX A, Y A, where X A and Y A are his consumptions of goods X
and Y respectively. Babettes utility function is U(X B, Y B) = X B Y B, where X B and Y B are her
consumptions of goods X and Y. Abduls initial endowment is no units of Y and 7 units of X. Babettes
initial endowment is no units of X and 6 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
a.
min7, 6 + 7/2p = 6.
b.
7/(p + 1) + 3 = 6.
c.
6/7 = p.
d.
6/(p + 1) + 3.50 = 6.
e.
min7, 6 + 6/2p = 6.
31. Professor Nightsoils utility function is U N (B N, P N) = BN + 4P1/2N and Dean Interfaces utility
function is U I (B I, P I) = BI + 2P1/2I, where B N and B I are the number of bromides and P N and P I
are the number of platitudes consumed by Nightsoil and Interface respectively. If Nightsoils initial
endowment is 5 bromides and 20 platitudes and if Interfaces initial endowment is 3 bromides and 20
platitudes, then at any Pareto efficient allocation in which both consume positive amounts of both
goods,
a.
Nightsoil consumes the same ratio of bromides to platitudes as Interface.
b.
Interface consumes 8 platitudes.
c.
Interface consumes 4 bromides.
d.
Interface consumes 4 bromides.
e.
Interface consumes 4 bromides.
32. Professor Nightsoils utility function is U N (B N, P N) = BN + 4P1/2N and Dean Interfaces utility
function is U I (B I, P I) = BI + 2P1/2I, where B N and B I are the number of bromides and P N and P I
are the number of platitudes consumed by Nightsoil and Interface respectively. If Nightsoils initial
endowment is 4 bromides and 10 platitudes and if Interfaces initial endowment is 3 bromides and 15
platitudes, then at any Pareto efficient allocation in which both consume positive amounts of both
goods,
a.
Interface consumes 3.50 bromides.
b.
Nightsoil consumes the same ratio of bromides to platitudes as Interface.
c.
Interface consumes 2 bromides.
d.
Interface consumes 5 platitudes.
e.
Interface consumes 3 bromides.
33. Professor Nightsoils utility function is U N (B N, P N) = BN + 4P1/2N and Dean Interfaces utility
function is U I (B I, P I) = BI + 2P1/2I where B N and B I are the number of bromides and P N and P I
are the number of platitudes consumed by Nightsoil and Interface respectively. If Nightsoils initial
endowment is 4 bromides and 25 platitudes and if Interfaces initial endowment is 2 bromides and 20
platitudes, then at any Pareto efficient allocation in which both consume positive amounts of both
goods,
a.
Nightsoil consumes the same ratio of bromides to platitudes as Interface.
b.
Interface consumes 9 platitudes.
c.
Interface consumes 5 bromides.
d.
Interface consumes 3 bromides.
e.
Interface consumes 4 bromides.
34. An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has
an initial endowment of 3 apples and 10 bananas. Doris has an initial endowment of 6 apples and 5
bananas. Charlie’s utility function is U(A C, B C) = A C B C, where A C is his apple consumption and
B C is his banana consumption. Doris’s utility function is U(A D, B D) = A D B D, where A D and B D
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 15 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 6 apples for every 5 bananas that she consumes.
35. An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has
an initial endowment of 6 apples and 6 bananas. Doris has an initial endowment of 12 apples and 3
bananas. Charlie’s utility function is U(A C, B C) = A C B C, where A C is his apple consumption and
B C is his banana consumption. Doris’s utility function is U(A D, B D) = A D B D, where A D and B D
are her apple and banana consumptions. At every Pareto optimal allocation,
a.
Charlie consumes more bananas per apple than Doris does.
b.
Charlie consumes the same number of apples as Doris.
c.
Charlie consumes 18 apples for every 9 bananas that he consumes.
d.
Doris consumes equal numbers of apples and bananas.
e.
Doris consumes 12 apples for every 3 bananas that she consumes.
36. An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has
an initial endowment of 6 apples and 6 bananas. Doris has an initial endowment of 12 apples and 3
bananas. Charlie’s utility function is U(A C, B C) = A C B C, where A C is his apple consumption and
B C is his banana consumption. Doris’s utility function is U(A D, B D) = A D B D, where A D and B D
are her apple and banana consumptions. At every Pareto optimal allocation,
a.
Charlie consumes more bananas per apple than Doris does.
b.
Doris consumes equal numbers of apples and bananas.
c.
Charlie consumes the same number of apples as Doris.
d.
Charlie consumes 18 apples for every 9 bananas that he consumes.
e.
Doris consumes 12 apples for every 3 bananas that she consumes.
37. Kens utility function is U(Q K, W K) = Q K W K and Barbies utility function is U(Q B, W B) = Q B W
B. If Kens initial endowment were 3 units of quiche and 11 units of wine and Barbies endowment were
6 units of quiche and 11 units of wine, then at any Pareto optimal allocation where both persons
consumed some of each good,
a.
Ken would consume 3 units of quiche for every 11 units of wine that he consumed.
b.
Barbie would consume twice as much quiche as Ken.
c.
Ken would consume 9 units of quiche for every 22 units of wine that he consumed.
d.
Barbie would consume 6 units of quiche for every 11 units of wine that she consumed.
e.
None of the above.
38. Kens utility function is U(Q K, W K) = Q K W K and Barbies utility function is U(Q B, W B) = Q B W
B. If Kens initial endowment were 5 units of quiche and 9 units of wine and Barbies endowment were
10 units of quiche and 9 units of wine, then at any Pareto optimal allocation where both persons
consumed some of each good,
a.
Ken would consume 15 units of quiche for every 18 units of wine that he consumed.
b.
Barbie would consume twice as much quiche as Ken.
c.
Ken would consume 5 units of quiche for every 9 units of wine that he consumed.
d.
Barbie would consume 10 units of quiche for every 9 units of wine that she consumed.
e.
None of the above.
39. Kens utility function is U(Q K, W K) = Q K W K and Barbies utility function is U(Q B, W B) = Q B W
B. If Kens initial endowment were 5 units of quiche and 7 units of wine and Barbies endowment were
10 units of quiche and 7 units of wine and Barbie’s endowment were 10 units of quiche and 7 units of
wine, then at any Pareto optimal allocation where both persons consumed some of each good,
a.
Ken would consume 15 units of quiche for every 14 units of wine that he consumed.
b.
Barbie would consume 10 units of quiche for every 7 units of wine that she consumed.
c.
Ken would consume 5 units of quiche for every 7 units of wine that he consumed.
d.
Barbie would consume twice as much quiche as Ken.
e.
None of the above.
40. Morris has the utility function U(b, w) = 3b + 3w 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 consumed 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’s 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 1/1 passing through the lower left corner of the box.
d.
a straight line with slope 1/1 passing through the upper right corner of the box.
e.
a curve that gets flatter as you move from left to right.
41. Morris has the utility function U(b, w) = 4b + 4w 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 consumed 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’s consumptions from the lower left corner of the box, then the contract curve contains
a.
a curve that gets steeper as you move from left to right.
b.
a straight line with slope 1/1 passing through the upper right corner of the box.
c.
a straight line with slope 1/1 passing through the lower left corner of the box.
d.
a straight line running from the upper right corner of the box to the lower left.
e.
a curve that gets flatter as you move from left to right.
42. Morris has the utility function U(b, w) = 4b + 16w 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 consumed 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’s consumptions from the lower left corner of the box, then the contract curve contains
a.
a straight line with slope 1/4 passing through the lower left corner of the box.
b.
a straight line running from the upper right corner of the box to the lower left.
c.
a straight line with slope 1/4 passing through the upper right corner of the box.
d.
a curve that gets steeper as you move from left to right.
e.
a curve that gets flatter as you move from left to right.
43. Astrids utility function is U(H A, C A) = H A C A. Birgers utility function is minH B, C B. If Astrids
initial endowment is no cheese and 11 units of herring and if Birgers initial endowments are 4 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.
4/(p + 1) + 6 = 12.
b.
4/12 = p.
c.
412/4 = p.
d.
4/p + 12/2p = 12.
e.
min12, 4 = p.
44. Astrids utility function is U(H A, C A) = H A C A. Birgers utility function is minH B, C B. If Astrids
initial endowment is no cheese and 5 units of herring and if Birgers initial endowments are 6 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.
6/(p + 1) + 2.50 = 5.
b.
5/6 = p.
c.
6/p + 5/2p = 5.
d.
6/5 = p.
e.
min5, 6 = p.
45. Astrid’s utility function is U(HA, CA) = HACA. Birger’s utility function is minHB, CB. If Astrid’s
initial endowment is no cheese and 13 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.
13/8 = p.
b.
8/p + 13/2p = 13.
c.
8/13 = p.
d.
8/(p + 1)+ 6.50 = 13.
e.
min13, 8 = p.
46. Mutt’s utility function is U(m, j) = max3m, j and Jeff’s utility function is U(m, j) = 2m + j. Mutt is
initially endowed with 3 units of milk and 2 units of juice and Jeff 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.
47. Mutt’s utility function is U(m, j) = max3m, j and Jeff’s utility function is U(m, j) = 3m + j. Mutt is
initially endowed with 6 units of milk and 2 units of juice and Jeff is initially endowed with 2 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.
bottom edge of the Edgeworth box but no other edges.
b.
left edge of the Edgeworth box but no other edges.
c.
right edge of the Edgeworth box but no other edges.
d.
left edge and bottom edge of the Edgeworth box.
e.
right edge and top edge of the Edgeworth box.
48. Mutt’s utility function is U(m, j) = max3m, j and Jeff’s utility function is U(m, j) = 4m + j. Mutt is
initially endowed with 4 units of milk and 2 units of juice and Jeff is initially endowed with 4 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 and bottom edge of the Edgeworth box.
b.
right edge of the Edgeworth box but no other edges.
c.
bottom edge of the Edgeworth box but no other edges.
d.
left edge of the Edgeworth box but no other edges.
e.
right edge and top edge of the Edgeworth box.
PROBLEM
1. In a pure exchange economy, Ollie’s utility function is U(x, y) = 3x + y and Fawn’s utility 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 y’s.
Draw an Edgeworth box for Fawn and Ollie. Put x on the horizontal axis and y 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.
2. An economy has 2,000 people. 1,000 of them have utility functions U(x, y) = x + y and 1,000 of them
have utility functions U(x, y) = min2x, y. 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.
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 indifference curves for each person.
c. Show where on your diagram the Pareto optimal allocations are.