A worker produces shirts. The worker prefers to work at an easy pace, producing fewer shirts per hour, if his compensation is not affected. Suppose that the worker views his "cost" per hour of producing shirts as given by the following:

C = a S ²

The interpretation is that the pain induced in producing one shirt per hour is $a, that is, the worker would not be willing to come to work and produce one shirt per hour for less than $a per hour. If the worker were required to produce two shirts per hour, this requires so much extra effort that the worker would only be willing to do this for at least $4a. For three shirts per hour he requires $9a, and so forth.

As a manager, you want to raise output of shirts and lower cost. This requires that you take into account the behaviour of the workers. Two methods are considered:

(1) Require a certain number of shirts per hour and to pay an hourly wage rate. All who do not meet the requirement are terminated.

(a) How many shirts per hour should be required and at what wage?

(b) What are profits per worker per hour?

(c) What happens if you require more shirts per hour at that wage?

(d) What happens if you lower the number of shirts required?

(e) What happens if you raise the wage per hour and the number of shirts required?

(f) What are the advantages of using the piece rate system? What are the advantages of using hourly wage rates?