CHAPTER 32: Exchange
MULTIPLE CHOICE
1. An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has
an initial endowment of 6 apples and 4 bananas. Doris has an initial endowment of 12 apples and 2
bananas. Charlie’s utility function is U(AC, BC) = ACBC, where AC is his apple consumption and BC is
his banana consumption. Doris’s utility function is U(AD, BD) = ADBD, 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 18 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 12 apples for every 2 bananas that she consumes.
2. An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has
an initial endowment of 3 apples and 4 bananas. Doris has an initial endowment of 6 apples and 2
bananas. Charlie’s utility function is U(AC, BC) = ACBC, where AC is his apple consumption and BC is
his banana consumption. Doris’s utility function is U(AD, BD) = ADBD, 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 more bananas per apple than Doris does.
c.
Doris consumes equal numbers of apples and bananas.
d.
Charlie consumes 9 apples for every 6 bananas that he consumes.
e.
Doris consumes 6 apples for every 2 bananas that she consumes.
3. An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has
an initial endowment of 3 apples and 8 bananas. Doris has an initial endowment of 6 apples and 4
bananas. Charlie’s utility function is U(AC, BC) = ACBC, where AC is his apple consumption and BC is
his banana consumption. Doris’s utility function is U(AD, BD) = ADBD, where AD and BD are her apple
and banana consumptions. At every Pareto optimal allocation,
a.
Charlie consumes 9 apples for every 12 bananas that he consumes.
b.
Charlie consumes more bananas per apple than Doris does.
c.
Doris consumes equal numbers of apples and bananas.
d.
Charlie consumes the same number of apples as Doris.
e.
Doris consumes 6 apples for every 4 bananas that she consumes.
4. 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) = ACBC, where AC is his apple consumption and BC is
his banana consumption. Doris’s utility function is U(AD, BD) = ADBD, 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 6 apples for every 6 bananas that she consumes.
5. An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has
an initial endowment of 5 apples and 10 bananas. Doris has an initial endowment of 10 apples and 5
bananas. Charlie’s utility function is U(AC, BC) = ACBC, where AC is his apple consumption and BC is
his banana consumption. Doris’s utility function is U(AD, BD) = ADBD, 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 more bananas per apple than Doris does.
c.
Doris consumes equal numbers of apples and bananas.
d.
Charlie consumes 15 apples for every 15 bananas that he consumes.
e.
Doris consumes 10 apples for every 5 bananas that she consumes.
6. In Problem 4, Ken’s utility function is U(QK, WK) = QKWK and Barbie’s utility function is
U(QB, WB) = QBWB. If Ken’s initial endowment were 4 units of quiche and 6 units of wine and Barbie’s
endowment were 8 units of quiche and 6 units of wine, then at any Pareto optimal allocation where
both persons consume some of each good,
a.
Ken would consume 4 units of quiche for every 6 units of wine.
b.
Barbie would consume twice as much quiche as Ken.
c.
Ken would consume 12 units of quiche for every 12 units of wine that he consumes.
d.
Barbie would consume 8 units of quiche for every 6 units of wine that she consumes.
e.
None of the above.
7. In Problem 4, Ken’s utility function is U(QK, WK) = QKWK and Barbie’s utility function is
U(QB, WB) = QBWB. If Ken’s initial endowment were 6 units of quiche and 9 units of wine and Barbie’s
endowment were 12 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 18 units of quiche for every 18 units of wine that he consumes.
b.
Barbie would consume 12 units of quiche for every 9 units of wine that she consumes.
c.
Ken would consume 6 units of quiche for every 9 units of wine.
d.
Barbie would consume twice as much quiche as Ken.
e.
None of the above.
8. In Problem 4, Ken’s utility function is U(QK, WK) = QKWK and Barbie’s utility function is
U(QB, WB) = QBWB. If Ken’s initial endowment were 4 units of quiche and 10 units of wine and
Barbie’s endowment were 8 units of quiche and 10 units of wine, then at any Pareto optimal allocation
where both persons consume some of each good,
a.
Ken would consume 4 units of quiche for every 10 units of wine.
b.
Ken would consume 12 units of quiche for every 20 units of wine that he consumes.
c.
Barbie would consume 8 units of quiche for every 10 units of wine that she consumes.
d.
Barbie would consume twice as much quiche as Ken.
e.
None of the above.
9. In Problem 4, Ken’s utility function is U(QK, WK) = QKWK and Barbie’s utility function is
U(QB, WB) = QBWB. If Ken’s initial endowment were 8 units of quiche and 11 units of wine and
Barbie’s endowment were 16 units of quiche and 11 units of wine, then at any Pareto optimal
allocation where both persons consume some of each good,
a.
Barbie would consume twice as much quiche as Ken.
b.
Ken would consume 8 units of quiche for every 11 units of wine.
c.
Ken would consume 24 units of quiche for every 22 units of wine that he consumes.
d.
Barbie would consume 16 units of quiche for every 11 units of wine that she consumes.
e.
None of the above.
10. In Problem 4, Ken’s utility function is U(QK, WK) = QKWK and Barbie’s utility function is
U(QB, WB) = QBWB. If Ken’s initial endowment were 3 units of quiche and 7 units of wine and Barbie’s
endowment were 6 units of quiche and 7 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 7 units of wine.
b.
Ken would consume 9 units of quiche for every 14 units of wine that he consumes.
c.
Barbie would consume twice as much quiche as Ken.
d.
Barbie would consume 6 units of quiche for every 7 units of wine that she consumes.
e.
None of the above.
11. In Problem 1, suppose that Morris has the utility function U(b, w) = 4b + 12w and Philip has the utility
function U(b, w) = bw. 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 1/3 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 flatter as you move from left to right.
12. In Problem 1, suppose that Morris has the utility function U(b, w) = 6b + 6w and Philip has the utility
function U(b, w) = bw. 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 1/1 passing through the upper right corner of the box.
b.
a curve that gets steeper as you move from left to right.
c.
a straight line running from the upper right corner of the box to the lower left.
d.
a straight line with slope 1/1 passing through the lower left corner of the box.
e.
a curve that gets flatter as you move from left to right.
13. In Problem 1, suppose that Morris has the utility function U(b, w) = 4b + 4w and Philip has the utility
function U(b, w) = bw. 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.
14. In Problem 1, suppose that Morris has the utility function U(b, w) = 5b + 15w and Philip has the utility
function U(b, w) = bw. 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 1/3 passing through the lower left corner of the box.
b.
a straight line with slope 1/3 passing through the upper right corner of the box.
c.
a straight line running from the upper right corner of the box to the lower left.
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.
15. In Problem 1, suppose that Morris has the utility function U(b, w) = 7b + 21w and Philip has the utility
function U(b, w) = bw. 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 1/3 passing through the lower left corner of the box.
b.
a straight line with slope 1/3 passing through the upper right corner of the box.
c.
a curve that gets steeper as you move from left to right.
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.
16. In Problem 2, 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
12 units of cheese and no herring, then where p is a competitive equilibrium price of herring and
cheese is the numeraire, demand equals supply in the herring market. This implies that
a.
12/(p + 1) + 6.50 = 13.
b.
12/13 = p.
c.
13/12 = p.
d.
12/p + 13/2p = 13.
e.
min13, 12 = p.
17. In Problem 2, 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 3 units of herring and if Birger’s initial endowments are
13 units of cheese and no herring, then where p is a competitive equilibrium price of herring and
cheese is the numeraire, demand equals supply in the herring market. This implies that
a.
13/3 = p.
b.
3/13 = p.
c.
13/p + 3/2p = 3.
d.
13/(p + 1) + 1.50 = 3.
e.
min3, 13 = p.
18. In Problem 2, 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 8 units of herring and if Birger’s initial endowments are 7
units of cheese and no herring, then where p is a competitive equilibrium price of herring and cheese is
the numeraire, demand equals supply in the herring market. This implies that
a.
7/p + 8 / 2p = 8.
b.
7/(p + 1) + 4 = 8.
c.
8/7 = p.
d.
7/8 = p.
e.
min8, 7 = p.
19. In Problem 2, 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 20 units of herring and if Birger’s 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, demand equals supply in the herring market. This implies that
a.
4/(p + 1) + 10 = 20.
b.
20/4 = p.
c.
4/20 = p.
d.
4/p + 20/2p = 20.
e.
min20, 4 = p.
20. In Problem 2, 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 20 units of herring and if Birger’s initial endowments are
9 units of cheese and no herring, then where p is a competitive equilibrium price of herring and cheese
is the numeraire, demand equals supply in the herring market. This implies that
a.
9/p + 20/2p = 20.
b.
9/20 = p.
c.
20/9 = p.
d.
9/(p + 1) + 10 = 20.
e.
min20, 9) = p.
21. Suppose that in Problem 8, Mutt’s utility function is U(m, j) = max2m, 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.
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.
22. Suppose that in Problem 8, Mutt’s utility function is U(m, j) = max4m, 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.
right edge of the Edgeworth box but no other edges.
b.
left edge of the Edgeworth box but no other edges.
c.
bottom 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.
23. Suppose that in Problem 8, Mutt’s utility function is U(m, j) = max2m, 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.
right edge of the Edgeworth box but no other edges.
b.
bottom edge of the Edgeworth box but no other edges.
c.
left 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.
24. Suppose that in Problem 8, Mutt’s utility function is U(m, j) = max4m, j and Jeff’s utility function is
U(m, j) = 2m + j. Mutt is initially endowed with 2 units of milk and 2 units of juice, and Jeff is initially
endowed with 6 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.
right edge of the Edgeworth box but no other edges.
c.
left edge and bottom edge of the Edgeworth box.
d.
bottom edge of the Edgeworth box but no other edges.
e.
right edge and top edge of the Edgeworth box.
25. Suppose that in Problem 8, 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 2 units of milk and 2 units of juice, and Jeff is initially
endowed with 6 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.
left edge of the Edgeworth box but no other edges.
d.
bottom edge of the Edgeworth box but no other edges.
e.
right edge and top edge of the Edgeworth box.
26. In Problem 3, Professor Nightsoil’s utility function is UN(BN, PN) = BN + 4p1/2N and Dean Interface’s
utility function is UI(BI, PI) = BI + 2p1/2I. If Nightsoil’s initial endowment is 6 bromides and 20
platitudes and if Interface’s initial endowment is 2 bromides and 10 platitudes, then at any Pareto
efficient allocation where both persons consume positive amounts of both goods,
a.
Nightsoil consumes the same ratio of bromides to platitudes as Interface.
b.
Interface consumes 6 platitudes.
c.
Interface consumes 4 bromides.
d.
Interface consumes 4 bromides.
e.
Interface consumes 2 platitudes.
27. In Problem 3, Professor Nightsoil’s utility function is UN(BN, PN) = BN + 4p1/2N and Dean Interface’s
utility function is UI(BI, PI) = BI + p1/2I. If Nightsoil’s initial endowment is 5 bromides and 10
platitudes and if Interface’s initial endowment is 2 bromides and 10 platitudes, then at any Pareto
efficient allocation where both persons consume positive amounts of both goods,
a.
Interface consumes 4 platitudes.
b.
Nightsoil consumes the same ratio of bromides to platitudes as Interface.
c.
Interface consumes 3.50 bromides.
d.
Interface consumes 2 bromides.
e.
Interface consumes 2 platitudes.
28. In Problem 3, Professor Nightsoil’s utility function is UN(BN, PN) = BN + 4p1/2N and Dean Interface’s
utility function is UI(BI, PI) = BI + 2p1/2I. If Nightsoil’s initial endowment is 4 bromides and 15
platitudes and if Interface’s initial endowment is 7 bromides and 15 platitudes, then at any Pareto
efficient allocation where both persons consume positive amounts of both goods,
a.
Interface consumes 3 bromides.
b.
Interface consumes 5.50 bromides.
c.
Nightsoil consumes the same ratio of bromides to platitudes as Interface.
d.
Interface consumes 6 platitudes.
e.
Interface consumes 3 platitudes.
29. In Problem 3, Professor Nightsoil’s utility function is UN(BN, PN) = BN + 4p1/2N and Dean Interface’s
utility function is UI(BI, PI) = BI + 2p1/2I. If Nightsoil’s initial endowment is 7 bromides and 5
platitudes and if Interface’s initial endowment is 8 bromides and 10 platitudes, then at any Pareto
efficient allocation where both persons consume positive amounts of both goods,
a.
Interface consumes 1 bromide.
b.
Interface consumes 3 platitudes.
c.
Nightsoil consumes the same ratio of bromides to platitudes as Interface.
d.
Interface consumes 7.50 bromides.
e.
Interface consumes 2 platitudes.
30. In Problem 3, Professor Nightsoil’s utility function is UN(BN, PN) = BN + 4p1/2N and Dean Interface’s
utility function is UI(BI, PI) = BI + 2p1/2I. If Nightsoil’s initial endowment is 3 bromides and 20
platitudes and if Interface’s initial endowment is 5 bromides and 15 platitudes, then at any Pareto
efficient allocation where both persons consume positive amounts of both goods,
a.
Interface consumes 7 platitudes.
b.
Nightsoil consumes the same ratio of bromides to platitudes as Interface.
c.
Interface consumes 4 bromides.
d.
Interface consumes 4 bromides.
e.
Interface consumes 3 platitudes.