Suppose two individuals in an exchange economy have identical utility functions given by Person A has an endowment of x = 9 y = 8,person B has one of x = 16 y = 2.The price ratio that will prevail in equilibrium is: A)p_x / p_y= 2.5. B)p_x / p_y = 1.0. C)p_x / p_y= 0.4. D)p_x / p_y = 0.125.

Question

Quizplus · Accepted Answer

In equilibrium, individuals will equate their marginal rate of substitution to the price ratio. The marginal rate of substitution for both individuals is given by MRS = -2x/y. Therefore, for person A, MRS = -2(9)/8 = -2.25 and for person B, MRS = -2(16)/2 = -16. They will trade until the price ratio is equal to the ratio of their marginal rates of substitution. Thus, (p_x / p_y) = 2.25/16 = 0.14. Therefore, the closest answer choice is C with p_x / p_y = 0.4.

Suppose Two Individuals in an Exchange Economy Have Identical Utility