Roberto works in a factory making electric cars. Currently, his firm pays him $35 per hour and he works 35 hours per week. Each hour he works he experiences disutility of effort from working valued at $5 per hour. In addition, should Roberto lose his job the government will pay him an unemployment benefit of $15 per hour, for each hour he would otherwise work each week, for a maximum of 20 weeks. Prior to the coronavirus pandemic if Roberto lost his job the expected duration of unemployment before he would find another job is 10 weeks.

(a) Calculate Roberto's

(i) Employment rent per hour

(ii) Total employment rent

(b) With the advent of the coronavirus pandemic the economy has gone into recession causing Roberto's expected duration of unemployment to increase to 30 weeks.

Furthermore, the dramatic increase in the expected duration of unemployment has resulted in psychological stress from unemployment valued at $3 per hour.

In the light of these developments re-calculate Roberto's:

(i) Employment rent per hour

(ii) Total employment rent

(Hint: It will be necessary to base the calculations on two periods, the first, covering weeks 1-20, when the unemployment benefit is available and the second, covering weeks 21-30, when the unemployment benefit is not available)

(c) Describe the relationship between the size of the employment rent and:

(i) the expected duration of unemployment

(ii) the size of the unemployment benefit per hour

(iii) the size of the psychological cost of unemployment per hour.