The Employment Relationship

The employment relationship can be basically modeled as followed:

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 breaks down as follows:

• 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.

From this we can easily rearrange terms to get this:

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