Question

Suppose a firm 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 W_t=$100 (the same for all periods), and the value marginal product of a worker is also the same in every period, VMP_t=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. How productive must a worker be each period in order for the firm to hire a worker expected to work 2 periods: VMP = . If VMP=110 is it worth it to hire a worker for 3 periods? (yes/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. How productive must a worker be each period in order for the firm to hire a worker expected to work 2 periods: VMP = . In order for the firm to hire a worker for 3 periods, a worker's productivity in each period must be VMP = .

C. Explain how this might relate to the observation that unionized workers have lower turnover rates.

Answer 1

Total cost of hiring periods in ! a employee for n { We & Training cost tul = Now training cost = 50, We 100 #t. [ 100 + 50 a loont so tal 10 on t50 Then at equilibrium ; VMP = . For 125 no 2 - 2) VMP 11666 not worth For n 3, VMP Then if ump to hire labor. =llo it is B. with with spring E 100 + 150 spring bonus total cost nises to 100n + 150 HET

1oon +150 Therefore at equilibrium: VMP = For 2; VMP- IT 5 - 150 For n = 3 VMP c. VMP = competitive the As in market wage union workers getting paid higher wage effective wage than the union Therefore, union labor. non labor has lower twin over rate than non union labors.