Topic 9: Unemployment : Search and Efficiency Wages

1. Topic 9: Unemployment : Search and Efficiency Wages

2. Out previous models all assume that consumer divide his time between leisure and market work • In this topic we will consider another usage of consumer’s time, that is unemployment • Two key features of unemployment are; • Involves searching for work • The unemployed is worse off than the employed

3. We will discuss two models on the determinants of the unemployment rate. • the search model • The efficiency wage model

4. The search model • The first search model was developed in the late 1960’s • The model looks at the factors that motivate the search behavior of unemployed workers • We have U = the fraction of workers who are unemployed and • (1-U) = the fraction of workers who are employed

5. The welfare of an employed worker • The jobs of the employed differ according to the wage they pay • The real wage associated with a particular job is w • The value of being employed can be written as Ve(w) • This is the welfare of a worker who is employed and earns a real wage w

6. This function also take into account the taxes the worker paid as well as all possible future events • The events include the chances of the worker being separated from his job • Let s denote the separation rate • s is the fraction of workers who become randomly separated from their jobs every period • This happens due to firing and quits • Figure 15.6 shows function Ve(w)

7. Figure 15-6 The Welfare of an Employed Worker

8. Ve(w) increases with w • Ve(w) curve is concave because the worker experiences diminishing marginal utility from higher-paying jobs • Factors which will shift the Ve(w) function are; • Change in separation rate s • Changes in taxes or wage income

9. The welfare of an unemployed worker • Vu denotes the welfare of unemployed worker • Vu is determined by 1. the size of the unemployment benefits (UI) he received • For simplicity, we assume that this benefit is constant and takes b value

10. Vu is also determined by the frequency the unemployed worker receives job offers • We will denote this frequency by p • With these two factors determining Vu , we can summarized that; • Vu increases when b increases • Vu increases when p increases • Vu decreases if taxes on employment benefits increase

11. The reservation wage • A job offer will be made at a particular wage rate w • The unemployed worker will decide whether to accept or continue with the job searching • When w is low, rejecting it will open up some possibilities of receiving a higher wage offer in the future

12. There is a trade-off in decision between short run loses from unemployment and the uncertain long run benefits from a good job • There is some wage offer that will be sufficiently high that the unemployed worker will accept it • He would also accept any wage offer that was higher than this amount • This wage is called the reservation wage, w*

13. Figure 15-7 The Reservation Wage

14. The reservation wage is determined by the intersection of the Ve(w) and the Vu curve • The worker will turn down the job if Ve(w) < Vu • But will accept the job if Ve(w)  Vu • The reservation wage will change if there are shifts in either Ve(w) or Vu • Suppose that the unemployment benefit increases

15. Figure 15-8 An Increase in the Unemployment Insurance Benefit b

16. This causes an increase in Vu fromVu1 to Vu2 • The reservation wage increases from w1* to w2* • With the unemployment benefit increases worker will become more picky concerning the jobs he will take

17. Figure 15-9 An Increase in the Taxes on the Wage Income of the Employed

18. Secondly, when there is an increase in the tax on wage income, the welfare of an employed worker will shift down from Ve1(w) to Ve2(w) • Reservation wage will increase from w1* to w2*

19. The determination of the unemployment rate • There will be flows between a pool of employed workers and the pool of unemployed workers each period • Some employed workers will be separated from their jobs and become unemployed • Some unemployed workers will receive job offers that are sufficiently attractive to accept

20. The flow of workers from employment to unemployment will be s(1-U) • Now let H(w*) is the fraction of unemployed workers receiving a wage offer greater than w* • H(w) is decreasing with w • The flow of workers from unemployment to employment will be UpH(w*) (page 552)

21. In a long run equilibrium the flow of workers from employment to unemployment must equal to the flow of workers from unemployment to employment, or s(1-U) = UpH(w*) … (15.1) • This equation will determine U, given p, s and w* • The intersection of the two curves will give the long run equilibrium unemployment rate, U*

22. Figure 15-11 The Determination of the Unemployment Rate U* in the Search Model

23. This model can be used to analyze the effects of variables changes in the economic environment; • Increase in unemployment insurance benefits (b) • An increase in the job offer rate (p)

24. Figure 15-13 An Increase in the Unemployment Insurance Benefit b

25. The rise in UI benefit (b) increase the value of unemployment from Vu1 to Vu2 • Causing the reservation wage to increase • The flow of workers from unemployment to employment will decrease • Unemployment rate rises in the long run

26. Figure 15-14 An Increase in the Job Offer Rate p

27. When p increases, the welfare of the unemployed will also increase • The reservation wage increases from w1* to w2* • Two effects on UpH(w*) can be seen in panel (b) • p increased, flow from unemployment to employment increase • W* increases, this flow is decreased

28. It is not clear how the unemployment rate is affected • In our figure, it is shown as decreasing

29. Figure 15-16 Taxes on Labor Income and Unemployment Benefits

30. Taxes on labor income and unemployment benefits • If taxes fall equally on labor income and unemployment benefits, there is no effect on the reservation wage, and no effect on the unemployment rate

31. The efficiency wage model • In this model workers’ wage affect their on-the-job performance • A firm may be willing to pay its workers a real wage higher than the market wage • Therefore in equilibrium there will be unemployment

32. In this model, a worker’s effort will increase with the wage he receives • Let e(w) denote the effort of each worker • w is the real wage • The effective labor input for the firm will be e(w)N, where N is the hours worked by all workers • e(w)N is also the total effort

33. Figure 15-17 Effort of the Worker as a Function of His or Her Wage

34. Two reasons can explain the positive relationship between worker effort and the real wage • They are associated with information problems in the labor market • Problems of adverse selection in the labor market • A moral hazard problem

35. Adverse selection • Occur in markets where there are different type of workers; high ability and low ability workers • Firms cannot distinguish between these workers • High ability workers will have high reservation wage, since they have better options in the labor market • When firm offers higher wage rate, the they are able to attract high ability workers, and increase the quality of its workers

36. A moral hazard problem • Arises if a firm has difficulty in monitoring the on the job effort of its workers • The firm can threaten to fire a worker if he is caught shirking • When firm pays higher wage rate than the market wage rate, the loss to a worker being fired will be high • Workers will try not to be fired • So with higher wage rate, workers will give more effort

37. Optimization by the firm: the choice of Employment and the efficiency wage • The production function for the firm is Y = zF(K,e(w)N) • K is assumed to be fixed in the short run • In this model, the firm will maximize profit when = F(K,e(w)N) – wN

38. The marginal product of labor is given by MPN =e(w)MP e(w)N • Effort of the worker at wage w, • Marginal product of effective units of labor • The firm will hire labor N until the marginal product of labor is equal to the real wage orMPN =e(w)MP e(w)N = w … (15.2) • Equation (15.2) is also the firm’s demand curve for labor

39. Figure 15-18 The Demand for Labor in the Efficiency Wage Model

40. The demand curve is downward sloping • It tells us how much labor N the firm wants to hire given any real wage w • The firm will maximize the effort received from the worker per unit of real wage paid to the worker or (e(w)/w)

41. Figure 15-19 The Ratio of Effort to the Real Wage

42. The firm will choose a wage such that a line from the origin to a point on the curve e(W) is just tangent to the curve • w* is the optimal wage for the firm to choose • w* is called the efficiency wage • If the firm sets the real wage at efficiency wage, the workers will be supplying the optimal amount of effort in the job.

43. Figure 15-20 Determination of the Efficiency Wage

44. Labor market equilibrium in the efficiency wage model • This model implied that there can be unemployment in equilibrium • In figure 15-21a, the efficiency wage w* is above the market clearing wage w** • The firm will not reduce the real wage to w** because this would decrease its profits • The quantity of unemployment is N1s – N*

45. Figure 15-21 Unemployment in the Efficiency Wage Model

46. The real wage rigidity in this model is permanent • Which is different from the rigidity in the Keynesian sticky wage model, which is temporary and will disappear in the long run • In the Keynesian model, unemployment will disappear in the long run as the nominal wage adjusted • We can also find the efficiency wage to be smaller than the market clearing real wage (figure 15.21b)

47. In this case, at the efficiency wage w*, the firm cannot hire all the workers it likes to hire • It is force to bid wages to the point where the market is clear, or to w**, where the quantity of labor the firm wants to hire is equal to the quantity that workers want to supply

48. The efficiency wage model and business cycles • If there is unemployment in the efficiency model, the quantity of employment is determined by the labor demand curve • So the output supply is vertical because it does not have any effect on employment and output • (figure 15.2)

49. Figure 15-22 The Output Supply Curve in the Efficiency Wage Model

50. Given the vertical output supply curve, changes in the demand for output will not increase the aggregate output • For example an increase in G will not change aggregate output, only increase unemployment and interest rate (figure 15.23)