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 traditional isocost lines, this one will be nonlinear. You may want to look at a picture. 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 to the analysis of constraints on hours per worker--
it raises the cost of production which will have a scale effect away from H/N and N.
it raises the relative price of (H/N) so there is a substitution effect toward N and away from (H/N).