PROBLEMS
1. Pohl Manufacturing Company finds that as it increases the number of workers it hires,
the number of hockey pucks produced daily changes as follows:
Workers Hockey Pucks
1 10
2 30
3 60
4 100
5 135
6 165
7 190
8 210
9 225
10 235
11 240
12 240
13 235
a) The price of hockey pucks can be $2, $3, or $4 each. For each number of workers,
calculate the marginal physical product, the average physical product, and the three
marginal revenue products corresponding to the three hockey puck prices.
b) On graph paper, plot the MPP and the APP.
c) On the graph, show the phases of increasing returns to labor, diminishing returns, and
negative returns.
d) Assume the price of hockey pucks is $2. If the wage rate of labor is $40 a day, how
many workers will Pohl hire? Note that there are two employment levels at which the
wage equals the MRP; why did you pick one of them?
e) When the wage rises to $60, what will the new employment level be?
f) How does employment change when the price of hockey pucks rises to $3 and then
$4, if the wage rate stays at $60?
g) (harder) Looking at your graph in part b), explain why, over part of the range of the
graph, marginal product can be falling at the same time as average product is rising.
Solution:
a)
Worker
s
Hocke
y
Pucks
MP
P APP
MR
P
MR
P
MR
P
($2) ($3) ($4)
1 10 10 10 $20 $30 $40
2 30 20 15 40 60 80
b)
c) In Figure 7.1, phases of increasing returns to labor, diminishing returns and negative
returns are shown as Phase I, Phase II, and Phase III, respectively.
d) Pohl will hire eight units of labor because at this level marginal revenue product of
2. The price of farm machines is $40,000 and the marginal physical product of those
machines is 2,000 bushels of wheat per year. The annual wage rate of farm labor is
$30,000 and the marginal physical product of labor is 1,500 bushels. What factor
proportions minimize the farmers’ cost? Suppose that the price of machines falls to
$30,000. How should the factor proportions change if the farmers still want to minimize
costs?
Suppose that new technical training programs double the marginal product of labor. How
should the factor proportions change?
Solution: Factor proportions at which MRP per dollar for the two inputs becomes equal
minimizes the farmer’s cost. When the price of the machine becomes relatively cheap, the
3. Is the number of firms in an industry likely to be large or small if:
Average cost curves are increasing at most levels of output.
There are increasing economies of scale at most levels of output.
Solution: Number of firms will be likely to be more in an industry with increasing
average cost. Under such scenario, firms cannot take advantage of large-scale production
4. Atherly Appliance Company is making plans to build a new factory to produce toasters. It
currently foresees a market of about 15,000 toasters per month, but it has hopes that with
aggressive advertising it can expand sales in the future. It has its choice of two different
technologies for this factory. Technology A is similar to the methods it is already using in
other factories; it is based heavily on manual control of the machines. Technology B is
much more extensively computerized. Either technology is expected to have a useful life
of about 15 years. Taking account of both the fixed costs and the variable costs inherent
in each technology, Atherly estimates that the average total monthly costs would probably
vary as follows:
Average Total Monthly Cost
Toasters per month Technology A Technology B
5,000 $50 $70
10,000 40 55
15,000 30 40
20,000 40 34
25,000 50 28
30,000 60 35
a) On graph paper, draw the two average cost curves.
b) Which technology is most appropriate in terms of today’s market for Atherly toasters?
c) What problem could Atherly find itself in if it chooses this technology?
d) Which choice would you recommend, and why?
Solution:
a)
5. Gopher Furnace Company has $10,000 fixed costs each week. Its total variable costs
change as the number of furnaces produced each week changes, as follows:
Furnaces Total Variable Costs
1 $600
2 1,800
3 3,600
4 6,000
5 9,000
6 12,600
7 16,800
8 21,600
9 27,000
10 33,000
a) For each level of output, calculate total cost, marginal cost, average fixed cost,
average variable cost, and average total cost.
b) On graph paper, plot the marginal cost, average fixed cost, average variable cost, and
average total cost.
c) Explain why average total cost has a U shape, when neither of its components,
average fixed cost nor average variable cost, does.
Solution:
a)
b)
c) The AC curve for a typical firm is U-shaped. We can attribute its downward-sloping
segment to increasing marginal physical products and to the fact that the firm spreads
6. Bellas Refrigeration finds that, as it increases its inputs proportionately, its total costs for
producing freezers vary as follows:
Refrigerators
(in thousands)
Total Cost
(in millions of dollars)
10 8
20 14
30 18
40 20
50 25
60 30
70 42
80 56
90 72
100 90
Over what levels of output are Bellas Refrigeration’s returns to scale increasing,
decreasing, and constant?
Solution: The firm experiences increasing returns to scale when the output level is
DISCUSSION QUESTIONS
1. Why is it wise for a firm to use inputs beyond the point of diminishing returns?
Suggested Answer: Students should discuss the law of variable proportion and the result
of using inputs beyond the point of diminishing returns. Although diminishing marginal
returns suggests that marginal costs will be increasing, the possibility of marginal revenue
greater than marginal cost is also worth discussing.
2. Discuss the likely shape of the average cost curve for firms in each of the following
industries. Are minimum average costs apt to occur at an output that is large relative to
the total output in the market, or small? What sort of economies of scale are firms in
these industries liable to face?
a) Farming
b) Telephone service
c) Steel
d) Neighborhood grocery
e) Toll bridge
Suggested Answer: The relationship between large size and low costs does not always fit
every industry. Automobile production and telecommunications are two common
3. Why may historical data not provide a good guide to analytical cost curves?
Suggested Answer: A graph of historical data on prices and quantities at different points
in time is normally not the cost curve that the decision maker needs. Historical costs
4. “It is all very well to talk about firms changing their proportions of capital, labor, and
materials when the prices of those things change, in order to minimize costs, but that is
not how things work in the real world. If firms are going to be competitive, they have to
buy the latest technology, and the technology is not flexible. Each machine requires a
certain number of operators, and a certain amount of materials. Those inputs cannot be
changed; factor proportions are fixed, no matter how their prices may change.” Discuss.
Suggested Answer: Students can discuss different technologies used for producing goods
and services. Some technologies use more labor and some use more capital. The producer
5. In the past half century, the U.S. labor force has more than doubled. We have learned in
this chapter that as labor increases, its marginal product tends to fall, and furthermore that
the price paid to a factor of production tends to be proportional to its marginal product.
One would think that the average wages of labor would have fallen. But in fact, real
wages almost tripled over this period. Why?
Suggested Answer: Students should discuss the impact of technology, education,
on-the-job training, experience, etc. on the productivity of labor. It is true that marginal