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Posted on Feb 20, 2024

2.) (20 points total) Suppose there are two consumers with different utility functions but the same initial endowments. Consumer 1: u (9,92) = 9192

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2.) (20 points total) Suppose there are two consumers with different utility functions but the same initial endowments. Consumer 1: u (9,92) = 9192 11 Consumer 2: u(q,92) = 99 Initial endowment for consumer 1 = (10,10) = initial endowment for consumer 2 a. (10 points) Given this information, draw the Edgeworth box with correct height and length, draw the initial endowment point E and accurate IC curves for both consumers that go through the initial endowment. Label everything! C. b. (5 points) Is the initial endowment Pareto efficient? Why or why not? Show your work. (5 points) What prices p and p2 would result in a competitive equilibrium at the initial endowment?

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a To draw the Edgeworth box we need to determine the height and length based on the provided utility functions The utility functions for both consumers are given as Consumer 1 u91 92 912 922 8281 8464 16745 Consumer 2 u91 92 912 922 8281 8464 16745 The height and length of the Edgeworth box should be determined by the maximum utility value which is 16745 in this case Next we draw the initial endowment point E which is given as 10 10 for both consumers Place this point in the Edgeworth box Finally we draw the indifference curves IC for both consumers that go through the initial endowment point E The shape of the IC curves will depend on the specific utility functions but they should intersect at the initial endowment point Label everything accordingly b To determine if the initial endowment is Pareto efficient we need to check if there is any possible reallocation of goods that can make both consumers better off without making any consumer worse off Since both consumers have the same initial endowment 10 10 any reallocation of goods within the Edgeworth box that lies on the contract curve the set of points where the ICs are tangential will make one consumer better off without making the other consumer worse off In this case since both consumers have different utility functions it is unlikely that the initial endowment point lies on the contract curve Therefore the initial endowment is not Pareto efficient c To find the prices p and p that would result in a competitive equilibrium at the initial endowment we need to find the prices at which the consumers marginal rates of substitution MRS are equal to the price ratio The MRS for consumer 1 is given by the ratio of the marginal utilities MRS MU2 MU1 The MRS for consumer 2 is given by the ratio of the marginal utilities MRS MU1 MU2 In a competitive equilibrium the price ratio equals the MRS for both consumers p p MRS MU2 MU1 p p MRS MU1 MU2 Since the utility functions are not provided we cannot calculate the exact values of MRS or the prices p and p However to find the competitive equilibrium you would need to calculate the MRS for each consumer ... blur-text-image