1. One question from the first question cluster and: (a) Let f($1, X2) = 2x9-5x23 + 0.0001efx? Find the short run average cost curve for each of r2 = 1, 1.5, 2, 2.5, 3 Find the long run average cost curve. You may have to assume equal prices to solve for the long run average cost curve, though a graph will do. (b) Let c(y1, y2) = y1 + 32 + (31y/2)3 Does this cost function have economies of scale for y1? What about economies of scope for any strictly positive y, and y2. Hint, economies of scale exist if for a positive set of y, and y2, c(y1, y2) > c(y1, 0) + c(0, y2) (c) Let y = Ar. Suppose that we see when p = 2,w = 1, r = 4 and y = 8 and when p = 1, w = 0.2, and x = 6. Can we identify the parameters of the production function from just this information? Suppose that we know nothing of the functional form and that in the second example y = 10. Graph what we know about the production function. (d) Suppose a Cobb Douglass production function with two inputs and exponents inside the production function y = 1 x,2 that are less than one. Derive the profit maximizing choices of $1, T2, andy for arbitrary prices. (e) Let AC(y) = 1/y+2+0.ly. Find the efficient point of production for this firm. Suppose every firm in the industry has access to the technology, find the region of economies of scope. Derive the long run average cost for this function. (f) Assume a market demand function of D(P) = 100 - P and a per firm cost function of C(q) or 20q. Find the competitive equilib rium. Assume that in order to boost wages, the local govt applies