The Employment Relationship: Difference between revisions
From Dickinson College Wiki
Jump to navigationJump to search
| Line 18: | Line 18: | ||
# The level of monitoring (''m'') | # The level of monitoring (''m'') | ||
# A termination probability defined by ''t'' ∈ [0,1] with ''t''<sub>''e'' </sub> < 0 and ''t''<sub>''m'' </sub>>0 | # A termination probability defined by ''t'' ∈ [0,1] with ''t''<sub>''e'' </sub> < 0 and ''t''<sub>''m'' </sub>>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. | |||
Revision as of 21:42, 22 April 2009
The employment relationship can be basically modeled as followed:
A company's production function is defined by the equation:
- y=y(he)+ε
- Assumptions:
- y' > 0
- y'' < 0
- h = # of hours worked (assuming 1 hour per worker)
- e ∈ [0,1] (Simply, e is the "effort" term and is equal to the amount per hour that a worker actually works)
- ε is an error term with μ=0
- Assumptions:
- 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:
- The wage (w) to be payed to the employee
- The level of monitoring (m)
- A termination probability defined by t ∈ [0,1] with te < 0 and tm >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:
