(40%) Suppose a competitive firm may manufacture electronics using machinery and labor. Let z] and 22 denote the quantity of machinery and labor respectively. The firm may use one of the two production technology. . Under Technology A, the machinery will be manually operated by workers, so that both factors are needed for production. The production function is given by FA(21, 22) = 4(2122)+ . Technology B leads to full automation. The production function is given by F(21, 22) = (21)#. The firm uses no workers. Suppose the factor prices are given by un = 1 and w2 = 4. We are interested in how the profit-maximizing input bundle changes with good price p. We break down the analysis into two steps. We first find out the profit-maximizing bundle under each technology. Then we work out the firm's choice of technology, and hence the corresponding input bundle. (a) First suppose that the firm is using technology B given w = 1 and un = 4. i. Under technology B, find out the firm's quantity demanded for machinery in term of the good price p. ii. Show that the maximal profit " under technology B is given by (b) Now suppose that the firm is using technology A given w = 1 and wy = 4. i. Show that under technology A, the profit-maximizing input bundle is given by ii. Show that the maximal profit under technology A is given by (c) We now study the firm's choice of technology. Explain why the firm will use technology B if the good price above p and technology A if the good price is below p. Find out the cut-off value of good price p. Hint: What is a firm's objective? (d) We now study the firm's JOINT choice of technology and input bundle. Let good price be the horizontal axis and quantity demanded for labor be the vertical axis be . Plot how the firm's quantity demanded for labor $2 varies with the good price. Indicate p in your graph. Hint: The firm may use different technology at different prices. Make sure you account for the choice of the technology. (e) We fix the good price p > 0. Let labor be the horizontal axis and its marginal revenue product be the vertical axis. Depict the marginal revenue product curves p - MP and p - MP, for technology A and B in the same graph. (f) With the aid of the diagram below, Bobby argues that "The curve for p - MP is downward sloping due to diminishing marginal product of labor. Suppose the good price increases, the curve for p - MP, will shift up. The firm keeps hiring more labor until p . MPy falls back to the same level as the wage rate. So the quantity demanded for labor ALWAYS increases with the good price." - PMP Do you agree with Bobby's conclusion? Do you agree with Bobby's explanation? Explain your answer in details. Hint: Your answer in part (d) and (e) should provide you some inspiration