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Assume that a rm has a two-period planning horizon and operates in perfectly competitive output and labour markets. Suppose that the expected output price is P0 = P1 = $20, where the subscripts 0 and 1 refer to the time period (ie, 0 refers to the current period and 1 refers to the next period). The market interest rate is r. Suppose the rm's production function is Q = 10W where N is the number of workers employed by the rm in each period. Note that the marginal product of labour is MPP = 5 * (N) '0'5. a. Assume that there are no hiring costs. Calculate VMPo and VMP; and then write down the relationship between VMPg, VMP; and W0 and W; in this two-period model. (4 marks) b. Suppose that the interest rate is ve percent (ie, r = 0.05) and that the market wage is W0 = W1 = $10 per worker. Calculate the optimal employment level in both periods. (2 marks) 0. Without any calculation, briey discuss how each of the following changes affects the employment level (both existing employees and hiring new workers) in each period. (6 marks) i. The output price is lower than expected in the next period (ie. t=1). ii. There is an unexpected training cost at the beginning of next period for new workers. iii. At the beginning of current period, the government informs rms that there will be a layoff tax in both periods, paid by the rms when they layoff a worker. For simplicity in this part, assume that the only time period is the current time. Suppose that N = N1.- + NM where N1: and NM are female and male workers, respectively. Suppose that the market wage per female and male worker is W1: = WM = $10 but there is discrimination against males with a discrimination coefcient of 20 percent on their wage. Note that the marginal products are MPF = MPM = 5 * (NF + NMTO'5 (Hint: note that workers are equally productive.) (1. Calculate a male's wage after discrimination. Then, calculate the number of each type of workers (ie, NF and NM) that the rm hires. e. Briey suggest two things that male workers can do to improve their employment opportunities