Question

Ethel has preferences over amounts of goods 1 and 2 represented by the utility function u(x1, x2) = (x1)^2 + x2, where x1 denotes how much of good 1 she has and x2 denotes how much of good 2 she has. Write an expression for Ethel’s marginal utility for good 1. Does she like good 1? Explain your answer. Write an expression for Ethel’s marginal rate of substitution at any point. Do Ethel’s preferences exhibit diminishing marginal rate of substitution? Suppose Ethel was at the point (x1, x2) = (10,10) , and Pete offered to give her 2 units of good 2 in exchange for 2 units of good 1. Would Ethel be willing to accept this trade? Explain your answer. On a graph with good 1 on the horizontal axis, sketch Ethel’s indifference curves through the points (1, 0), (2, 0), (3, 0) and (4, 0). Does Ethel have convex preferences?

Answer 1