Exam 30: Exchange

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(x_A, y_A) = 2x_A + 5y_A and Benito's utility function is given by U(x_B, y_B) . In the Edgeworth box constructed for Adelino and Benito, the set of Pareto optimal allocations is

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.

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,

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) = . If we let good 1 be the numeraire, so that p₁ = $1, then what will be the equilibrium price of good 2?

If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then

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?

Astrid's utility function is U(H_A, C_A) = H_AC_A. Birger's utility function is min{H_B, C_B}. 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

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