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 Inc. 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 = 20 E - E2
where E is the number of hours the Phelps jointly spend each day running Nannys Inc. The Phelps are currently in the process of trying to determine how many hours to work. The price they charge for each hour of child care (p) is $4. The going hourly wage rate (w) paid to day Mr. and Mrs. Phelps is $8 an hour ($4 each for adult). Your job, should you choose to accept it, is to help the Phelps answer the following questions. This mission is not impossible!
Create a table for the value of the following items for ascending units of E from zero to ten.
the short-run production function or total product of labor: q (E)=TPE.
the total revenue: R(q)= p∙q .
the marginal product of labor: MPE .
the value of marginal product: VMPE.
the hourly wage: w.
the total cost of production: TC( q) = w∙E.
profit: TR – TC.
Determine the profit maximizing number of hours of works for the Phelps's 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: 20 - 2E. Draw the Phelps's demand for labor. Explain how you derived their demand for labor.
Explain why the demand for labor is downward sloping is downward sloping in the short run and in the long run.
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 of $250 to retirement each month. In other words, the retirement benefits increased while real wages declined. Explain how such a change in compensation would affect the number of workers versus the hours of work each worker completes. Graph the relationship between the number of workers and the average number of hours per worker.
Suppose I-Tech pays $500,000 in short-run costs for its capital and unskilled labor. It's only short-run decision, therefore, is to determine how many high-skilled workers, E , to hire. I-Tech's production function is Q = f(E) = 100E. I-Tech also faces downward sloped demand for its output of Q = 12000 – 20p. Solve for I-Tech's short-run labor demand function.
