Click to see additional instructions 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=$100 (the same for all periods), and the value marginal product of the additional worker also the same in every period, VMP-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 an employment length of two periods (t=0 and t=1). For this firm the present value of the (marginal) costs of hiring an additional worker for two periods is $ The firm will make positive profit from this worker if VMP is above $ . If VMP=$110, is it worth it to hire an additional worker who will stay 3 periods? (Enter 1 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. The firm breaks even from hiring the additional worker for two periods if VMP is $ . In order for an additional worker to be worth hiring for 3 periods, VMP must be at least $ C. Consider how a signing bonus (as in part B) would compare with a wage raise instead. Suppose the union obtains a wage raise of $25 instead of a signing bonus of $100 and the employment length will be 3 periods. With the wage increase, the present value of the costs of an additional worker will be (Enter 1 for "higher", 0 for "the same" or "-1 for "lower") and the firm's willingness to hire will be (Enter 1 for "yes" or -1 for (Enter 1 for "greater", 0 for "the same" or "-1 for "less") than with the signing bonus. Is this the true for longer employment durations? "no".) D. Now suppose expected employment is 4 periods and the union raises wages by $25 in addition to introducing a signing bonus of $100. This is naturally expected to affect employment, but it is also possible that unionization has a positive influence on productivity. In order for the firm to maintain the same level of hiring under these circumstances as without a union, it would have to be the case that unionization also increases VMP by $ E. Recall that unionized workers often have lower turnover rates, and that in addition to increasing wages and/or affecting quasi-fixed costs of labour, unions may also influence productivity. Identify what changes to the values of variables in equation 6.1 relate to each of these factors.