Suppose the production function is , and the price of y is p = 6. Assume x 1. (a) Find the firm?s marginal product MP(x) and average product AP(x). (b) Derive the firm?s value of marginal product VMP(x) and value of average product VAP(x). (c) What is the firm?s input demand curve x*(w)? 6. The inverse production function with one input and two outputs is . Assume the price of x is w=1. (a) Find the firm?s total cost curve C() and marginal cost curves and . (b) Find the firm?s supply curves and , subject to the nonnegative profit condition. (c) Suppose and . Calculate and . What is the firm?s profit? (d) Suppose rises to 2. Recalculate and . How has the firm?s profit changed? 4. A firm produces computers with two factors of production: labor L and capital K. Its production function is . Suppose the factor prices are and . (a) Graph the isoquants for y equal to 1, 2, and 3. Does this technology show increasing, constant, or decreasing returns to scale? Why? (b) Derive the conditional factor demands. (c) Derive the long-run cost function C(y). (d) If the firm wants to produce one computer, how many units of labor and how many units of capital should it use? How much will it cost? What if the firm wants to produce two computers? (e) Derive the firm?s long-run average cost function AC(y) and long-run marginal cost function MC(y). Graph AC(y) and MC(y). What is the firm?s long-run supply curve? 6. Consider the production function that uses three inputs: . Suppose the factor prices are . (a) What are the conditional factor demands , and ? (b) Find the long-run cost function C(y). (c) Find the long-run supply curve y*(p).