1. (20 points) Let ($1, 12) be some interior bundle on the budget constraint, and suppose p1 = 4 and p2 = 2. If the marginal rate of substitution at (21, 12) is -3, then is (21, 12) optimal? Explain why or why not, and justify your answer with economic intuition. (Partial credit for a purely graphical argument.) 2. (20 points) When prices were (p1, p2) = (5,2), Tim chose the bundle ($1, 12) = (3,4). Now at the new prices (pj, p, ), he chooses the bun- dle (x1, x2) = (1,7). For what prices (p,, p,) is Tim's behavior consistent with the weak axiom of revealed preferences? 3. (20 points) Amy has utility function u(r1, 12) = min (21 12, mix;}. De- rive Amy's demand function for a, and :2. For what values (if any) of m. pi, and pa are the goods gross complements or gross substitutes of each other? Part