(b) Show that if r* E R., and at - 0, then Mus P2 2) In class we solved for the Marshallian demand and indirect utility function for a consumer with a Cobb-Douglas utility function. Suppose the utility function is U($1, 12) = mix, Note that here we have specialized to the case 3 - 1 - a. Let x* = (x], r,) be a solution to the consumer's problem for a price vector p and income I. Suppose the price of good 1 increases to pi > p1. Find the substitution and income effects. Hint: you already have the demand functions so you know the solution at a given pa- rameter (p, /). Find the bundle B - (bi, by) and income /' such that the consumer has the same utility from B as a*, and B is an optimal bundle for a consumer facing prices (P1, P2) with income I'. 3) In class we solved for the Marshallian demand and indirect utility function for a consumer with a Cobb-Douglas utility function. (a) What is the price elasticity of good 1 (with respect to its own price)? What is the income elasticity of good 1? Suppose at current prices and income, the consumer buys 500 units of good 1. Approximately, what would be the consumption of good 1 if the price of good 1 increased by 1% while income increased by 2%? (b) Is good 2 a gross substitute for good 1? (c) Verify that Roy's identity is satisfied in this case