The Employment Relationship

The employment relationship can be basically modeled as followed:

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

From this we can easily rearrange terms to get this:

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