The Employment Relationship

A company's production function is defined by the equation:

y=y(he)+ε

• Assumptions:
  1. y' > 0
  2. y'' < 0
  3. h = # of hours worked (assuming 1 hour per worker)
  4. e ∈ [0,1] (Simply, e is the "effort" term and is equal to the amount per hour that a worker actually works)
  5. ε is an error term with μ=0

• Note that e, the effort exerted by the worker, is a function of the wage (w), the level of monitoring (m), and an exogenously determined
  "next best alternative" we'll call z. Thus, e(w,m;z).

The Game:

The Employer Starts:

• The employer seeks to maximize profit knowing that for a given wage rate (w), the employee will exert effort e.
• At the beginning of the game the employer selects:

1. The wage (w) to be payed to the employee
2. The level of monitoring (m)
3. A termination probability defined by t ∈ [0,1] with t_e < 0 and t_m >0
   • The termination probability is simply the probability that, at the end of a given period, the worker will be fired for inadequate work. This probability is thus obviously a function of both the worker's effort and the employer's level of monitoring.

The Worker Responds:

• The worker seeks to maximize his utility given the wage rate.

1. The worker's per period utility is a function of both wage and effort.
   • u=u(w,e) with u_w ≥ 0 and u_e ≤ 0
   1. • u_e ≤ 0 does not imply that the worker prefers to not work at all. Rather, it simply implies that the derivative of utility with respect to effort is not positive because this would mean that the employee would always choose to work more in order to maximize his utility.

• The worker decides upon an e in order to maximize the present value of his utility package (v) over a rate of time (i):

1. • v=(u(w,e)+(1+t(e))v+t(e)z)/(1+i)

Note that if the employee is fired the game ends and the employee receives z

From this we can easily rearrange terms to get this:

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