Problem Set 2

Note: For numerical computations, be sure to show your work. If you use a calculator, at least show how you set up each problem.

THE RELATIONSHIP BETWEEN TOTAL AND UNIT VALUES
1.	Consider the following short-run production function: Q = 2.4 L² - 0.4 L³ The diagram of this function is attached. Use the bottom panel of the diagram to do the following:
	a.	Sketch the marginal value and average value curves. Label them with MPL for the marginal product of labor and APL for the average product of labor APL.
	b.	Indicate the range of labor input where you observe each of the following:
		(1)	increasing marginal productivity of labor.
		(2)	diminishing marginal productivity of labor.
		(3)	diminishing marginal and average productivity of labor.
		(4)	negative marginal productivity of labor.

2.	A total cost function is given by: TC = TC(Q) where TC = total cost in thousands of dollars per year and Q = quantity produced in thousands of units per year. This function has the following properties: (1) for Q=0: TC=50, MC>0, MC is falling (2) for 0<Q<25: TC>50, MC>0, MC is falling (3) for Q=25: TC>50, MC>0, MC is constant (4) for Q>25: TC>50, MC>0, MC is rising
	a.	Sketch the firm's total cost (TC) and total fixed cost (TFC) functions. Identify the regions that are concave and convex, and any inflection points.
	b.	In a diagram directly beneath your diagram from part a, sketch the firm's margincal cost (MC) function.

THE RELATIONSHIP BETWEEN MARGINAL AND AVERAGE VALUES:
4.	Decide whether following is true or false, and briefly explain your decision: If average total cost falls as output rises, then marginal cost must also be falling.

5.	(From David Friedman) Consider the attached page showing six illustrations of pairs of curves.
	a.	Which of them are examples of possible segments of MC and ATC curves?
	b.	For the examples you cited in part a, indicate which curve (1 or 2) you would label MC and which one you would label ATC.

THE FIRM AND ITS PRODUCTION COSTS

(From Frank) The Preservation Embalming Company's cost data have been partially entered in the table below. Following the sudden and unexpected death of the company's accountant, you are called on to fill in the missing entries.

Bodies embalmed Q	Total cost TC	Total fixed cost TFC	Total variable cost TVC	Average total cost ATC	Average fixed cost AFC	Average variable cost AVC	Marginal cost MC
0	24			---	---	---	---
1							16
2			50
3	108
4							52
5						39.20
6				47

Indicate which curves would shift up as a result of an increase in each of the following (consider each event separately):

	TC	TFC	TVC	ATC	AFC	AVC	MC
a. Building lease costs (a fixed cost) rise
b. Wages (a variable cost) rise

PRICE ELASTICITY OF DEMAND

Suppose that the demand for denim jeans is given by the following equation:
Demand: Qd = 81 - 3P
where P is the price in dollars, and the Q's represent the quantities of jeans (in thousands of pairs).

Complete the following table:

P	Qd	Total expenditure	Value of price elasticity of demand
18			P range: 15-18:
15
			P-range 12-15:
12
			P-range 9-12:
9

Based on your computations, does price elasticity of demand rise, fall, or remain the same as we move down a linear demand curve?

10.

Fill in the missing entries in the following table:

Price elasticity	Change in price	Change in total revenue
0.2	down
3.5		down
1.0	up
0.9		up
	down	none
6.3	down

Choose the term, "elastic," "unit elastic," or "inelastic" to complete the following sentences:

(1)

Price and total expenditure move in the same direction if demand is _____________.

(2)

Price and total expenditure move in opposite directions if demand is _____________.

(3)

Total expenditure remains constant when price changes if demand is _____________.

PRESENT VALUE

12.

You are about to graduate and are wondering what career to pursue. You have narrowed your choices to three alternatives:
            A. Go to work as a junior-level executive and work your way up.
            B. Go to business school, get an MBA, and then work as an executive.
            C. Go to graduate school, get a Ph.D., and become a university professor.
The following are your expected benefits and costs:

Alternative	Time period:	1	2	3	4
A		30,000	34,000	38,000	42,000
B		-20,000	50,000	60,000	80,000
C		-10,000	-10,000	30,000	42,000

Set up the formula for calculating the net present value of each option, assuming a 10% interest rate for lending and borrowing. (You don't have to carry out the calculations.)

Why might someone rationally choose alternative C?

13.	This problem pertains to the supplementary item, "1.9% APR." Consider a consumer who buys the Chevy Cavalier discussed in the last paragraph of the ad. Suppose the buyer considers two options:
		(1)	Pay cash and get the cash rebate indicated in the first table of the ad, or
		(2)	Pay 10 percent down and use Chevy's two-year financing plan (For simplicity, assume that each year's twelve monthly payments are all made at year-end.)
	a.	If the buyer is earning 5 percent interest on her savings, which option should she choose?
	b.	If the buyer is earning 10 percent interest on her savings, which option should she choose?
	Support your answer in both cases.

6.	(From Moore and Whitney) Answer the three questions included with the attached selection, "1987 Tax Rate Schedules."

14.	Answer questions 1, 2 and 4 included with the supplementary reading, "State's Lottery 'Millionaires' Will Be Somewhat Less Thaan."