Exam 30: Exchange

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(N_x, B_x) = N_xB_x. Yvette's utility function is U(N_y, B_y) = 2N_y + B_y. 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?

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 small economy has only two consumers, Charlie and Doreen. Charlie's utility function is U(x, y) . 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 competitive equilibrium allocation must be a feasible allocation.

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

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(N_x, B_x) = N_xB_x. Yvette's utility function is U(N_y, B_y) = 2N_y + B_y. 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?

If the initial endowment is on the contract curve, then there must always be a competitive equilibrium in which no trade takes place.

Abduls utility is U(X A, Y A ) = min{X 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

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,

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.

Every allocation on the contract curve is Pareto optimal.

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.

Mutt's utility function is U(m, j) = max{ 3m, 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 small economy has only two consumers, Ivan and Marilyn. Ivan's utility function is U(x, y) . 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?

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.

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,

Partial equilibrium analysis concerns only supply or only demand while general equilibrium analysis deals with supply and demand at the same time.

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.

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