Suppose there are only two goods x, x2, with the price of the second good normalized (P, 1). For each of the following utility functions, sketch the graph of the indifference curve corresponding to u(x) = 1, and sketch the expenditure function corresponding to the constraint u(x) 1. Next, verify Shepard's Lemma for where the expenditure function is differentiable. What is true when the expenditure function is not differentiable? (a) (Perfect complements) u(x) = min{ax, bx2} where a, b > 0 (b) (Perfect substitutes) u(x) = ax + bx2 where a, b>0