1. The menu at Joe's coffee shop consists of a variety of

coffee drinks, pastries, and sandwiches. The marginal

product of an additional worker can be defined as

the number of customers that can be served by that

worker in a given time period. Joe has been employing

one worker, but is considering hiring a second and a

third. Explain why the marginal product of the second

and third workers might be higher than the first. Why

might you expect the marginal product of additional

workers to diminish eventually?

2. Suppose a chair manufacturer is producing in the short

run (with its existing plant and equipment). The manufacturer

has observed the following levels of production

corresponding to different numbers of workers:

NUMBER OF WORKERS NUMBER OF CHAIRS

1 10

2 18

3 24

4 28

5 30

6 28

7 25

a. Calculate the marginal and average product of

labor for this production function.

b. Does this production function exhibit diminishing

returns to labor? Explain.

c. Explain intuitively what might cause the marginal

product of labor to become negative.

3. Fill in the gaps in the table below.

QUANTITY OF

VARIABLE

INPUT

TOTAL

OUTPUT

MARGINAL

PRODUCT OF

VARIABLE INPUT

AVERAGE

PRODUCT OF

VARIABLE INPUT

0 0

1 225

2 300

3 300

4 1140

5 225

6 225

4. A political campaign manager must decide whether

to emphasize television advertisements or letters to

potential voters in a reelection campaign. Describe the

production function for campaign votes. How might

information about this function (such as the shape of

the isoquants) help the campaign manager to plan

strategy?

5. For each of the following examples, draw a representative

isoquant. What can you say about the marginal

rate of technical substitution in each case?

a. A firm can hire only full-time employees to produce

its output, or it can hire some combination of fulltime

and part-time employees. For each full-time

worker let go, the firm must hire an increasing

number of temporary employees to maintain the

same level of output.

b. A firm finds that it can always trade two units of

labor for one unit of capital and still keep output

constant.

c. A firm requires exactly two full-time workers to

operate each piece of machinery in the factory.

6. A firm has a production process in which the inputs

to production are perfectly substitutable in the long

run. Can you tell whether the marginal rate of technical

substitution is high or low, or is further information

necessary? Discuss.

7. The marginal product of labor in the production of

computer chips is 50 chips per hour. The marginal rate

of technical substitution of hours of labor for hours of

machine capital is 1/4. What is the marginal product

of capital?

8. Do the following functions exhibit increasing, constant,

or decreasing returns to scale? What happens to

the marginal product of each individual factor as that

factor is increased and the other factor held constant?

a. q 3L 2K

b. q (2L 2K)1/2

c. q 3LK2

d. q L1/2K1/2

e. q 4L1/2 4K

9. The production function for the personal computers of

DISK, Inc., is given by

q = 10K0.5L0.5

where q is the number of computers produced per day,

K is hours of machine time, and L is hours of labor

input. DISK's competitor, FLOPPY, Inc., is using the

production function

q = 10K0.6L0.4

a. If both companies use the same amounts of capital

and labor, which will generate more output?

b. Assume that capital is limited to 9 machine hours,

but labor is unlimited in supply. In which company

is the marginal product of labor greater? Explain.