Question

Description of the economy: For each of the following problems, consider a 2x2 Exchange Economy with two consumers A and B, and two goods X and Y . The preferences of consumer A can be represented by the utility function

uA(xA, yA) = xAyA , where xA is the amount of good A consumed by consumer A, and yA is the amount of good Y consumed by consumer A. The preferences of consumer B can be represented by the utility function

uB(xB, yB) = xB + yB , where xB is the amount of good B consumed by consumer B, and yB is the amount of good Y consumed by consumer B and the total endowment of good X in the economy is x¯ = 8 and the total endowment of good Y is y¯ = 4.

QUESTION 1 : Competitive equilibrium (a) Assume that consumer A’s initial endowments of good X and Y are (¯xA, y¯A) = (4, 2), and consumer B’s initial endowments of the two goods are (¯xB, y¯B) = (4, 2).

(i) Illustrate the initial endowments in the Edgeworth box, and draw an indifference curve for each consumer going through their endowment.

(ii) Illustrate the set of points in the Edgeworth box that are Pareto superior to the endowment. (iii) Illustrate the set of Pareto optimal allocations in the Edgeworth box that are Pareto superior to the endowment.

(iv) In this economy there is a unique competitive equilibrium. Normalizing the price of good Y to pY = 1, find the competitive equilibrium price of good X (i.e., pX) and the competitive equilibrium allocation (i.e., x ∗ A , y ∗ A , x ∗ B , and y ∗ B ). (v) Which consumer benefits most from trade in the competitive equilibrium?

(b) Assume, instead, that consumer A’s initial endowments of good X and Y are (x¯A, y¯A) = (6, 3), and consumer B’s initial endowments of the two goods are (x¯B, y¯B) = (2, 1). (Note that this means that the total endowments are still the same the total endowment of good X in the economy is x¯ = 8 and the total endowment of good Y is y¯ = 4.

(i) Illustrate the initial endowments in the Edgeworth box, and draw an indifference curve for each consumer going through their endowment.

(ii) Illustrate the set of points in the Edgeworth box that are Pareto superior to the endowment.

(iii) Illustrate the set of Pareto optimal allocations that Pareto superior to the endowment.

(iv) In this economy there is a unique competitive equilibrium. Normalizing the price of good Y to pY = 1, find the competitive equilibrium price of good X (i.e., pX) and the competitive equilibrium allocation (i.e., x ∗ A , y ∗ A , x ∗ B , and y ∗ B ). (v) Does consumer B benefit more from trade now than under the initial endowments from part (a)?

Answer 1

ANSWER 1 :

nitial enderoment S32 냉 3 (4,2) 2

ora P yx TD when 2- 2

Lon

Question 2 has to be done in the same way.