1. A consumer has a utility function given by U(x,y) = 4x + xy.

a) Describe in words what the marginal rate of substitution measures. For this utility function what is the marginal rate of substitution? Does the assumption of diminishing marginal rate of substitution hold? Why or why not?

b) Suppose the consumer has income of 80 and faces prices Px = 1 and Py = 4. Find the

market basket which maximizes the consumer's utility given their budget constraint. Carefully illustrate the situation on a well-labeled graph.

c) Find the consumer's demand function for good x (ie., find the consumer's optimal choice of x as a function of I, Px, and Py).