Exam 30: Exchange

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.

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 = C.

A small economy has only two consumers, Nick and Minnie. Nick's utility function is U(x, y) . 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?

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,

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 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,

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.

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,

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.

According to the first theorem of welfare economics:

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 situation is Pareto efficient if

A pure exchange economy is an economy where goods are traded but there is no production.

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.

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) = min{x^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.

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

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) = min{ 2x, 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.

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,

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.

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) = . If we let good 1 be the numeraire, so that p₁ = $1, then what will be the equilibrium price of good 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 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,