Question

. A firm hires two workers to assemble bicycles. The firm values each bicycle assembled at $12. Alisha’s marginal cost of allocating effort to the production process is 2N, where N is the number of bicycles assembled per hour. Kyle’s marginal cost is 3N.

a) If the firm pays piece rates of $12 per bicycle assembled, what will be each worker’s hourly wage, and how many bikes will they each assemble in an 8-hour day?

Alisha’s wage: __________               # bikes assembled by Alisha: __________

Kyle’s wage: __________                  # bikes assembled by Kyle: __________

b) Suppose the firm instead pays a time rate of $12 per hour and fires any worker who does not assemble at least 1 bicycle per hour. How many bicycles will each worker assemble in an 8 hour day?

# bikes assembled by Alisha: _________      # bikes assembled by Kyle: _________

Answer 1

a) The firm will set the piece rate at $12/assembly because the firm values each bicycle assembled at $12. So, the MR=12. We know that the worker will aim to maximize the utility, so, we will set MR=MC. We know that Alisha's marginal cost=2N and Kyle's marginal cost is 3N. So, we can find the bikes assembled by Alisha & Kyle per hour as follows:

Bikes assembled by Alisha: 12=2N, so, N=12/2=6/hour

Bikes assembled by Alisha in an 8-hr day=6X8=48

Since, Alisha assembles 6 bicycles per hour, so, Alisha's hourly wage will be $72.

Bikes assembled by Kyle: 12=3N, so, N=12/3=4/hour

Bikes assembled by Kyle in an 8-hr day=4X8=32

Since, Kyle assembles 4 bicycles per hour, so, her hourly wage will be $48.

Therefore, hourly wages of worker's and bikes assembled by worker's in 8 hr day will be:

Alisha’s wage: $72/hr # bikes assembled by Alisha: 48

Kyle’s wage: $48/hr # bikes assembled by Kyle: 32

b) Now, when the firm pays a time rate of $12 per hour and fires any worker who does not assemble at least 1 bicycle per hour.

In this case, in order to prevent themselves from being fired, each worker will do the minimum amount of work required, so, each worker will assemble only 1 bicycle per hour, therefore, bicycles that each worker will assemble in an 8 hour day will be 1X8=8 bicycles.

# bikes assembled by Alisha: 8 # bikes assembled by Kyle: 8