There is a firm with technology that can be described by the production function y = 4z1^1/2 + 2z2^1/2 with output price p = 6 and input prices w1 = 2 and w2 = 6. Now assume that the firm is making long-run decisions and can choose input 1 (z1) and input 2 (z2).
(a) Use the expressions w1 = pMP1 and w2 = pMP2 to solve for optimal z1 and z2.
(b) What is the firm’s profit-maximizing quantity of output y?
(c) Do the values for z1 and z2 satisfy the cost minimization condition MRT S = −w1/w2?
(d) Sketch the isoquant and isocost lines associated with this problem.
(e) What type of returns to scale are associated with this kind of production function?