A consumer has a utility function given by a) Derive an expression for the two marginal utilities: MU (1, ) and MU (1,202). Since MRS-MU, use these marginal utilities to derive a simple expression for the MRS (21,22). b) Optimal choice on the part of the consumer implies MRS-Suppose M = 20, P = P2 = 1. Show the optimal choice in this case on a well-labelled graph of the budget set. Include an indifference curve consistent with these preferences. c) Now keep income at 20, and p21, but set pi=2. Show the optimal choice in this case on a well-labelled graph of the budget set. Include an indifference curve consistent with these preferences. d) Now consider any set M.P.P. We have two equations that must hold: pi+p2t2 = M and MRS (,2)-2. Use these equations to solve for the consumer's demand function for good 1.