Mr. and Mrs. Phelps have just had a baby, and they both wish to stay home
and take care of the child. To achieve this end, they have decided to run
a day care center (Nannys Inc.) out of their home. Since the Phelps would
reside in their home even without the business, Nannys' operation costs consist
of the labor payments to the Phelps. The production function for the number
of child hours of day care (q) is given as follows: q = 20E - E2, where E
is the number hours the Phelps jointly spend a day running Nannys. The Phelps
are currently in the process of trying to determine how many hours to work.
The price of a child hour of day care (p) is $4. The going wage rate (w) paid
to joint day care workers is $8 an hour ($4 each for Mr. and Mrs. Phelps).
Your job, should you choose to accept it, is to help the Phelps answer the
following questions. This mission is not impossible!
Find the value of the following items for ascending units of E between
zero and ten. Place these results in a summary table.
the short-run production function or total product of labor (q(E)=TPE)
the total revenue (TR=p´q)
the marginal product of labor (MPE)
the value of marginal product (VMPE)
the hourly wage (w)
the total cost (TC=w´E)
profit (p=TR-TC)
Determine the profit maximizing number of hours for the Phelps in Nannys
Inc. based on a comparison of the VMPE and the wage. Explain how the VMPE
can be used to maximize profit.
Suppose it is known that the slope of the short-run production function
is given by: slope = 20 - 2E. Draw the Phelps's demand for labor. Explain
how you derived their demand for labor.
Labor Demand.
Briefly explain why the demand for labor in the short run is downward
sloping.
Briefly explain why the demand for labor in the long run is downward
sloping.
Show graphically the difference between the relationship between the short
and long run demand for labor when labor and capital are more or less substitutable:
In the early 1980s, the public employees union in Oregon agreed to a settlement
where they would forgo pay increases over several years in exchange for the
state picking up the employee contribution to retirement. In other words,
the retirement benefits increased, while their real wage declined. Assuming
that there is a fixed component to the pension plan, explain how such a change
in compensation would affect the use of workers versus hours by the state
of Oregon. Use a worker-hour graph to aid your explanation.
