40 points) Consider a consumer with the following utility function: U(X, Y ) X3/4Y1/4 (a) (5 oints) Derive the consumer's marginal rate of substitution (U) MUx MUy (b) (3 points) How oes the MRS depend on X and Y? (c) (2 points) Does this consumer have convex or concave references? (d) (5 points) Write this consumer's budget constraint. (e) (5 points) State the ptimality condition that relates the marginal rate of subst tution to the prices. f) (10 points) Use the optimality condition from part (e) and the budget constraint from part (d) o solve for this consumer's demand functions X* and Y. Fod by the function ybr arhet su Sun g) (5 points) Now suppose there are 100 consumers with this utility function and each consumer as I = $4. Denote the market quantity demanded for good Y as QY. Find Qy de doen the To po h) (5 points) Suppose the market supply for good Y is given by the function: QY 4Py Solve for he equilibrium price and quantity in the market for good Y