Question 1. Consider a firm that can use three inputs (z1, Z2, and z3) to produce its output a according to a technology that can be summarized by a Cobb-Douglas production function q = f(Z1, Z2 Z3) = 2142,14z,V2zzV2 a) Relabel y = -21 y2 = -22; y3 = -2; and y4 = q and write the expression of the firm's production set Y. b) Compute the expressions for the firm's marginal product of the three net inputs. Does the firm's technology exhibit diminishing marginal returns to input 1, 2, and/or 3? c) Check if the firm's technology is characterized by increasing, decreasing, or constant returns to scale. The firm wishes to produce 32 units of output. The input prices are wi = 1, W2 = 1, and w3 = 1. d) Write the firm's cost minimization problem. e) Write the Kuhn Tucker conditions for the firm's cost minimization problem f) Solve the Kuhn Tucker conditions and show that the firm minimizes its cost of production when it employs the three inputs in the following proportions: Z2 = Z3 = 27 g) Show that the firm's total cost of producing the 32 units is C = 40. h) Now, consider any production function f.):R! +R+ (the firm uses n inputs to produce one output) that satisfies increasing returns to scale. Currently the firm is producing a units at a total cost of Cand an average cost of C/q. Suppose the firms wishes to double its output. Will the firm's average cost double? Less than double? Or more than double? Clearly, support your argument