Arturo and Belen consume only two goods, X and Y. They have strictly convex preferences and no kinks in their indifference curves. At the initial allocation, the ratio of Arturo's marginal utility of X to his marginal utility of Y is A and the ratio of Belen's marginal utility of X to his marginal utility of Y is B, where A

Question

Arturo and Belen consume only two goods, X and Y. They have strictly convex preferences and no kinks in their indifference curves. At the initial allocation, the ratio of Arturo's marginal utility of X to his marginal utility of Y is A and the ratio of Belen's marginal utility of X to his marginal utility of Y is B, where A < B. The competitive equilibrium price ratio is  = C.

Quizplus · Accepted Answer

Since Arturo's marginal utility ratio of X and Y is A and Belen's marginal utility ratio of X and Y is B, we know that Belen values good X more than Arturo does, i.e., Belen is relatively less satiated with good X compared to Arturo. Therefore, in the competitive equilibrium, the price of X will be higher, so that Belen will reduce his consumption of X and Arturo will increase his consumption of X until their marginal utilities of X and Y are equal and the market clears.

Since their preferences are strictly convex and there are no kinks, at the competitive equilibrium, the price ratio will be such that the marginal rate of substitution (MRS) of both consumers is equal to the price ratio.

Let pX and pY be the prices of goods X and Y, respectively. At the competitive equilibrium,

MRS_A = pX/pY = A

MRS_B = pX/pY = B

Since A < B, we know that the competitive equilibrium price ratio C = pX/pY will be between A and B. Therefore, the correct answer is E, A < C < B.

Arturo and Belen Consume Only Two Goods, X and Y