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l) A consumer has expenditure function 2 P1332 e ,u = v. . (p ) [P1 + P2] (a) Find the Hicksian demand functions 311(3), a) and hp, u). (b) At initial prices p0 = (1,1) and income I = 8, the consumer gets a level of utility on = 4. When prices increase to p1 = (2,1) the agent gets a level of utility cl = v12. What is the compensating variation associated with this price change? (c) Invert the expenditure function to nd the indirect utility function V(p, I) (recall tthe woodchuck iden- tities). (d) Use Roy's identity to construct the Marshallian demand function D(p, I). 2) (a) A rm has production function f(k,) = [\\/k + \\/]' for some parameter a > 0. For what value of 0: does the function f have constant returns to scale? Provide an argument to support your answer. (13) Another rm has cost function C(wk, mg, q) = 10+ (to;c +21/wkwg+wg)q3/2 if q > 0 and C(wk, mg, 0) = 0. Find the conditional input demand functions Mack, mg, q) and ick, tug, q). Draw the MC and AC functions. 3) A rm has SC and LC functions graphed below. In a new gure plot the corresponding SMC, SAC, LMC and LAC functions. Be precise