Producer theory

(40 points) Acme Corporation uses two inputs, 21 and 22, to produce two outputs, ql and (12. The inputs are available at prices ml and wz, respectively, while it sells the outputs at prices p1 and 192, respectively. Its production set is described by the transformation function 1:011, 612,21IZz) = max{q;', 013'} Zizg where 1x, 5 E (0, 1) and 7 > 1. (Note that this transformation function is written in terms of outputs q and inputs 2, not net outputs y if we did that it would be Hy) = max{yry'2'} (-ys)\"(y4)5-) (a) (10 points) If the firm's optimal production level of on is c7, what is its opti- mal production level of 12, r1207)? Reformulate the firm's prot maximization problem as a choice of q, 21, and 22 by replacing an with q and on with (1207). (b) (10 points) What must be true about 04 + for Acme's prot maximization prob- lem to have a solution for all prices 191, p2, w1, w2? Give a condition involving 7. (c) (20 points) Assuming your condition from part (b) holds, solve for Acme's sup- ply correspondence (including unconditional factor demands)