Exam 30: Exchange

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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.

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Professor Nightsoils utility function is U N (B N, P N ) = Professor Nightsoils utility function is U N (B N, P N ) =   and Dean Interfaces utility function is U I (B I, P I ) =   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, and Dean Interfaces utility function is U I (B I, P I ) = Professor Nightsoils utility function is U N (B N, P N ) =   and Dean Interfaces utility function is U I (B I, P I ) =   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, 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,

(Multiple Choice)
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Mutt's utility function is U(m, j) = max{ 3m, 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

(Multiple Choice)
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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,

(Multiple Choice)
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A small economy has only two consumers, Zeke and Maude. Zeke's utility function is U(x, y) A small economy has only two consumers, Zeke and Maude. Zeke's utility function is U(x, y)   . 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? . 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?

(Multiple Choice)
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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.

(Multiple Choice)
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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.

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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.

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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.

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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?

(Multiple Choice)
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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) = min{xA, yA} and Bartolo's utility function is U(xB, yB) = max{xB, yB}. In an Edgeworth box for Amaranda and Bartolo, the set of Pareto optimal allocations is

(Multiple Choice)
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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.

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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.

(Essay)
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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) = 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(x<sub>1</sub>, x<sub>2</sub>) =   . If we let good 1 be the numeraire, so that p<sub>1</sub> = $1, then what will be the equilibrium price of good 2? . If we let good 1 be the numeraire, so that p1 = $1, then what will be the equilibrium price of good 2?

(Multiple Choice)
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Professor Nightsoils utility function is U N (B N, P N ) = Professor Nightsoils utility function is U N (B N, P N ) =   and Dean Interfaces utility function is U I (B I, P I ) =   , 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, and Dean Interfaces utility function is U I (B I, P I ) = Professor Nightsoils utility function is U N (B N, P N ) =   and Dean Interfaces utility function is U I (B I, P I ) =   , 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, , 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,

(Multiple Choice)
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A small economy has only two consumers, Harold and Irene. Harold's utility function is U(x, y) A small economy has only two consumers, Harold and Irene. Harold's utility function is U(x, y)   . 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? . 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?

(Multiple Choice)
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If there are consumption externalities, then a competitive equilibrium is not necessarily Pareto optimal.

(True/False)
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Mutt's utility function is U(m, j) = max{ 3m, 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

(Multiple Choice)
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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.

(Essay)
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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.

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