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Suppose a firm is considering hiring an additional worker. The firm's initial costs when hiring a worker include hiring and training costs of $50. The wage rate for each period of employment is W1=$1 00 (the same for all periods), and the value marginal product of the additional worker is also the same in every period, VMPt=VMP (a constant). Assume the interest rate is zero (the firm has no discounting factor over time). A. Write out this firm's profit maximizing employment rule for two periods. If an additional worker is expected to work 2 periods, the VMP of the additional worker must be above in order for the firm to gain from the additional worker. If VMP=110 is it worth it to hire the additional worker if they will stay 3 periods? (Enter1 for "yes" or -1 for "no". B. Now suppose that the union negotiates a signing bonus of $100 which the firm must pay initially (in addition to the hiring and training costs) when it hires a worker. Write out the new profit maximizing employment rule for two periods. Now the firm gains from hiring the additional worker for two periods if VMP is at least . In order for the additional worker to be worth hiring for 3 periods, VMP must be at least 0. Compared to negotiating a signing bonus of $100, negotiating a wage raise of $25 will lead to employment levels when expected employment length is 4 periods. (Enter 1 for "higher", 0 for "the same" or "-1 for "lower) D. Suppose expected employment is 4 periods and the union raises wages by $25 as well as introducing a signing bonus of $100. In order for the firm to maintain the same level of hiring, it would have to be the case that union influence increased productivity by E. Recall that unionized workers often have lower turnover rates, and that in addition to increasing wages and/or quasi-fixed costs of labour, unions may also influence worker productivity. Identify how each of these variables can relate to this model