1 Work-Life Incentive Schemes Models in this area look at the whole working career of an individual and try to make pay over the career keep the individual productive.

2 Remember workers have an incentive to shirk when the gain from doing so is greater than the cost. If G = gain from shirking, θ = probability of losing job if caught shirking w = wage in current job w* = wage in next best job N = number of years the worker might expect to continue working for the firm, Then shirk if G > θ(w – w*)N. The term to the right of the inequality represents the cost of shirking. Here I will focus on the term (w – w*) and making this as large as possible because then the individual probably would not want to shirk.

3 Years on Job – Job Tenure $ In this section we are going to use a graph like this one. A common name for a graph like this is an “earnings profile.” Here the profile would show the earnings each year at the number of years on the job. Statistical studies usually show data that is increasing as you move from left to right.

4 Years on Job – Job Tenure $ Recall from our analysis of labor demand that workers get paid a wage = VMP in a competitive labor market. The curve shown suggests that although there is increasing value to the firm from workers having more experience, the value has diminishing returns (and even declines). VMP

5 Years on Job – Job Tenure $ Here I have added a line w* and this line indicates the workers opportunity cost of remaining with the firm. When the worker is younger the w* line represents wages outside the firm and when the worker is older the line represents utility from leisure, nonlabor income and saving, pensions and social security. VMP w* T2 T1

6 Now, if the wage the worker gets, w, is equal to the VMP, then VMP>w* over much of the worker tenure. The difference is greatest at T1 and the difference shrinks after that and even becomes negative after T2. Since part of the cost of shirking is w – w*, we see after time T1 the cost of shirking is falling and thus it is more likely the worker will shirk.

7 Years on Job – Job Tenure $ The wage line w may be a way for the firm to keep the worker at a high productivity level. VMP w* T2 T1 T0 w

8 Digress Say you have $2 at time zero. If you can earn 10%, then by the end of the year you have $2.20. If you take out $1 and spend then you can earn 10% on the remaining You would then have 1.32 at the end. So, You can have 2 now, or 1 at the end of 1 year and 1.32 at the end of the 2 nd year. Or, you could take 0.50 at the end of 1 year and then have 1.87 at the end of the second year. There other possibilities, but I want to make a point about these to. Both case flows have a present value of 2. The first cash flow takes 1 and 1.32 and the second flow is 0.50 and So, the first one compared to the second one has more in the first period and less in the second period.

9 In the graph two slides back the cash flow w and VMP have the same present value. The VMP flow is greater than the w flow early on (until T0), but then the w flow is greater. Both flows have the same present value. The wage profile w is described as a work-life incentive scheme because it is designed to keep w - w* large over the whole work life of an individual and thus makes the cost of shirking high. Thus it is unlikely the individual will shirk. Issues 1) Workers might worry that after the firm pays the lower wage up to time T0 the firm will cut them loose and the firm would pocket the benefit. So, the firm has to make a credible commitment to workers – they could do this by protecting more senior workers, mainly promoting from within and the like.

10 2) Workers do not have an incentive to retire early - Digress – handy rule of 70 – an approximation rule. If you take 70 and divide by the interest rate, expressed as a decimal times 100 – like 3 %, you have the years it takes something to double. Example 10% interest Cash value1 – 2 – 4 – 8 – 16 – 32 – 64 Tenure With this example we see $1 grows to 64 in 42 years. Dollar amounts in the distant future have very little present value. When workers start out they are given a credible commitment to path w. But when the worker gets beyond T2 their VMP is lower than w*. Normally the worker would retire but the cash is too good under w. The firm may need to build in a compulsory retirement age because huge pay at the end hurts the firm.

11 3) The probation period Now since the flow w has the same present value as VMP it has a higher present value than w*. Some workers may only have the ability or desire to earn w* but they may apply for these jobs with a work-life pay scheme because they would make more money. Digress – if the interest rate is zero then one dollar can be taken as 10 cents a year for 10 years. The other way to look at this is that 10 cents a year for 10 years has a present value of 1 = 0.10 (10). Example: say workers expect to work 30 years. Say that all workers can get a job that pays $30,000 a year. With a zero discount rate the present value is $900,000. Say under a work-life scheme the firm has a 1 year probationary wage and then pays $35,000 a year for the remaining 29 years.

12 The present value for this job is Pv = probationary wage + p(35000 times 29) + (1-p)(30000 times 29), where p is the probability of making it through the probationary period. Say a low ability or desire worker has a 10% chance of making it through the probationary period. Then Pv = probationary wage = probationary wage A probationary wage of 15,500 means a low productivity worker would see either job as the same. Thus is the firm makes the probationary wage less than this the low productivity worker will not find this job as attractive as other jobs. The firm would then save on recruiting and screening costs. Workers would self-select into jobs.