Overtime Question

The isocost line for the overtime premium turns out to be a bit complicated. Here is the set up:

N = number of workers

F = fixed cost per worker

W = wage rate

(H/N) = hours per worker

OT = overtime premium

= .5W if (H/N)> 40 hours

= 0 otherwise

The firm's total cost, TC, can be written:

TC = N*F + N*(H/N)*(W+OT)

Solving for N, this can be transformed into the isocost line:

N = TC/{F + (H/N)*(W+OT)}

Unlike the isocost lines in class, this one will be nonlinear. I will discuss this in class, but you may want to look at the pictures. To download a picture of the isocost line with the parameters set to W=6, F=5, and TC=5000, you can access the EXCEL file below: OVERTIME EXCEL FILE

The analysis of the inplications of the overtime premium will be similar tro the analysis of the constraint on hours per worker it raises the relative price of (H/N) so there is a substitution effect toward N and away from (H/N).