Problem #1

A firm has the following short-run production function:
Q = 50L + 6L^2 - 0.5L^3
Where Q = Quantity of output per week
L = Labor (number of workers)
^ exponential power L^2 implies L square

Note: More important than the algebra is the clear explanation of the implications behind the numbers for all three problems.

1. Assume that each worker is paid $10 per hour and works a 40-hour week. How many workers should the firm hire if the price of the output is $10?
2. During economic down turn, firms reduce price in order to stay competitive. For this reason, the price of the output falls to $7.50. What do you think be the short run impact of this price reduction on the number of workers hired and why?
3. What would firms do in the long run as far as production and hiring are concerned and why if economics situation does not improve and price reduction does not help their bottom line? Consider what business usually does if economic woe persists.
4. Henry Ford, the founder of Ford Motor Company, offered in 1914 $5 workday wage, which was about twice the going wage. What is the rationale behind Ford's high-wage policy to the marginal productivity theory of employment discussed in the text book? What is the major difference in their respective goals? Be specific as to what each approach tries to achieve. Ford called "the $5-a-day wage" one of the finest cost-cutting moves.

In any hiring decision, there are typically three different problems; "adverse selection" due to "asymmetry of information" prior to hiring and of "moral hazard" after hiring in your answer. Please integrate these three terms, asymmetry of information, adverse selection, and moral hazard into your answer and explain clearly how Ford's high wage policy specifically solved these three problems associated with hiring?

Problem #2

The owner of a small car-rental service is trying to decide on the appropriate numbers of vehicles and mechanics to use in the business for the current level of operations. He recognizes that his choice represents a trade-off between the two resources. His past experience indicates that this trade-off is as follows:


Vehicles Mechanics
100 2.5 (include one part-timer)
70 5
50 10
40 15
35 25
32 35

1. Assume that annual (leasing) cost per vehicle is $6,000 and the annual salary per mechanic is $25,000. What combination of vehicles and mechanics should he employ?
2. Illustrate the problem with the use of an iso-quant/iso-cost diagram with number of vehicle leased on horizontal axis and number of mechanics hired on vertical axes. Draw two iso-cost curves: one using annual the leasing cost per vehicle ($6,000) and the annual salary per mechanics ($25,000) given in the problem. In this case leasing vehicle cost is relatively inexpensive to the annual salary per mechanics, Now, another iso-cost curve, hypothetical (no data given) this time, in which annual mechanics cost is relatively inexpensive to vehicle leasing cost. Indicate graphically the (two) optimal combinations of mechanics hired and vehicles with one iso-quant curve representing a given (target) level of vehicle leasing business with two iso-cost curves; one based on given values of the annual cost of hiring mechanics and leasing vehicles in the problem and another iso-cost curve, hypothetical one, in which mechanics cost is relatively inexpensive, i.e., two reverse cases of iso-cost curves, and discuss implication behind two different optimal combinations of resources. To be consistent vehicles leased on horizontal and mechanics on vertical axes.

Problem #3

An American company that sells consumer electronics products has manufacturing facilities in Mexico, Taiwan, and Canada. The average hourly wage, output, and annual overhead cost for each site are as follows:

Mexico Taiwan Canada

Hourly wage rate $1.50 $3.00 $6.00
Output per person 10 18 20
Fixed overhead cost $150,000 $90,000 $110,000

1. Given these figures, is the firm currently allocating its production resources optimally? If not, why do you think so? Consider output per person as a proxy for marginal product.
2. Suppose the firm wants to consolidate all of its manufacturing into one facility. Where should it locate? Is there any difference in treating cost information between (1) and (2)?
3. In deciding to consolidate its manufacturing into one facility, what are other factors the firm needs to consider? Please list and explain your reasons.
4. Nike outsources its manufacturing operation whereas New Balance does not.
In terms of marginal productivity (output per person) and hourly wage rate, explain why New Balance did not outsource its production whereas Nike did briefly.