Answers to the Problems and Applications
1.
Which of the following news items involves a short-run decision and which
involves a long-run decision? Explain
January, 31, 2008: Starbucks will open 75 more stores abroad than originally
predicted, for a total of 975.
This decision is a long-run decision. It increases the quantity of all of
Starbucks’ factors of production, labor and the size of Starbucks’ plant.
February, 25, 2008: For three hours on Tuesday, Starbucks will shut down every
single one of its 7,100 stores so that baristas can receive a refresher course.
This decision is a short-run decision. It involves increasing the quality of
Starbucks’ labor and so only one factor of production—labor—changes and all
the other factors remain fixed.
June, 2, 2008: Starbucks replaces baristas with vending machines.
This decision is a short-run decision. It involves changing two of Starbucks’
factors of production, labor and one type of capital. But other factors of
production, such as Starbucks’ land and other capital inputs such as the store
itself, remain fixed.
July, 18, 2008: Starbucks is closing 616 stores by the end of March.
This decision is a long-run decision. It decreases the quantity of all of
Starbucks’ factors of production, labor and
the size of Starbucks’ plant.
Labor
Output
(workers
(surfboards
2.
The table sets out Sue’s Surfboards’ total
per week)
per week)
product schedule.
1
30
a. Draw the total product curve.
2
70
To draw the total product curve measure
3
120
labor on the x-axis and output on the y4
160
axis. The total product curve is upward
5
190
sloping and is illustrated in Figure 11.1.
6
210
b. Calculate the average product of labor and
7
220
draw the average product curve.
The average product of labor is equal to total product divided by the quantity of
labor employed. For example, when 3 workers are employed, they produce 120
surfboards a week, so average product is
40 surfboards per worker. As Figure
11.2 (on the next page) shows, the
average product curve is upward sloping
when up to 3 workers are hired and then
is downward sloping when more than 4
workers are hired.
c. Calculate the marginal product of labor
and draw the marginal product curve.
The marginal product of labor is equal
to the increase in total product that
results from a one-unit increase in the
quantity of labor employed. For
example, when 3 workers are employed,
total product is 120 surfboards a week.
When a fourth worker is employed, total
product increases to 160 surfboards a
week. The marginal product of
increasing the number of workers from 3
to 4 is 40 surfboards. We plot the
marginal product at the halfway point,
so at a quantity of 3.5 workers, the
marginal product is 40 surfboards per
worker per week. As Figure 11.2 (on the
next page) shows, the marginal product
curve is upward sloping when up to 2.5
workers a week are employed and it is
downward sloping when more than 2.5
workers a week are employed.
d. Over what output range does the firm
enjoy the benefits of increased specialization and division of labor?
The firm enjoys the benefits of increased specialization and division of labor
over the range of output for which the marginal cost decreases. This range of
output is the same range over which the marginal product of labor rises. For
Sue’s Surfboards, the benefits of increased specialization and division of labor
occur until 2.5 workers are employed.
e. Over what output range does the firm experience diminishing marginal product of
labor?
The marginal product of labor decreases after 2.5 workers are employed.
f. Over what output range does this firm experience an increasing average product
of labor but a diminishing marginal product of labor?
The marginal product of labor decreases and the average product of labor
increases between 2.5 and 3.5 workers.
g. Explain how it is possible for a firm to experience simultaneously an increasing
average product but a diminishing marginal product.
As long as the marginal product of labor exceeds the average product of labor,
the average product of labor rises. For a range of output the marginal product of
labor, while decreasing, remains greater
than the average product of labor, so the
average product of labor rises. Each
additional worker, while producing less
than the previous worker hired is still
producing more than the average
worker.
3.
Sue’s Surfboards, in problem 2, hires
workers at $500 a week and its total fixed
cost is $1,000 a week.
a. Calculate total cost, total variable cost, and
total fixed cost of each output in the table. Plot these points and sketch the shortrun total cost curves passing through them.
Total cost is the sum of the costs of all the factors of production that Sue’s
Surfboards uses. Total variable cost is the total cost of the variable factors. Total
fixed cost is the total cost of the fixed factors. For example, the total variable
cost of producing 120 surfboards a week is the total cost of the workers
employed, which is 3 workers at $500 a week, which equals $1,500. Total fixed
cost is $1,000, so the total cost of producing 120 surfboards a week is $2,500.
Figure 11.3 shows these total cost curves.
b. Calculate average total cost, average fixed cost, average variable cost, and
marginal cost of each output in the table. Plot these points and sketch the shortrun average and marginal cost curves passing through them.
30
AFC
(dollars
per
surfboard)
33.33
AVC
(dollars
per
surfboard)
16.67
ATC
(dollars
per
surfboard)
50.00
70
14.29
14.29
28.58
120
8.33
12.50
20.83
160
6.25
12.50
18.75
190
5.26
13.16
18.42
210
4.76
14.29
19.05
Output
(surfboards)
MC
(dollars
per
surfboard)
12.50
10.00
12.50
16.67
25.00
50.00
220
4.55
15.91
Average fixed cost is total fixed cost per
unit of output. Average variable cost is
total variable cost per unit of output.
Average total cost is the total cost per
unit of output. For example, take the case
in which the firm makes 160 surfboards a
week. Total fixed cost is $1,000, so
average fixed cost is $6.25 per surfboard;
total variable cost is $2,000, so average
variable cost is $12.50 per surfboard;
and, total cost is $3,000, so average total
cost is $18.75 per surfboard. Marginal
cost is the increase in total cost divided
by the increase in output. For example,
when output increases from 120 to 160
surfboards a week, total cost increases
20.46
from $2,500 to $3,000, an increase of $500. This $500 increase in total cost
means that the increase in output of 40 surfboards increases total cost by $500.
Marginal cost is equal to $500 divided by 40 surfboards, which is $12.50 a
surfboard. The table shows these data schedules and the curves are plotted in
Figure 11.4.
c.
Illustrate the connection between Sue’s AP, MP, AVC, and MC curves in
graphs like those in Fig. 11.6.
AP
MP
AVC
MC
Labor
Output
(surfboards (surfboards (dollars
(dollars
(workers) (surfboards)
per
per
per
per
worker)
worker)
surfboard) surfboard)
1
30
30.0
16.67
40.0
12.50
2
70
35.0
14.29
50.0
10.00
3
120
40.0
12.50
40.0
12.50
4
160
40.0
12.50
30.0
16.67
5
190
38.0
13.16
20.0
25.00
6
210
35.0
14.29
10.0
50.00
7
220
31.4
15.91
4.
The table sets out the AP and MP data used to
draw the curves. Figure 11.5 shows the curves
and the relationships. When the AP curve rises
the AVC curve falls and vice versa. When the
MP curve rises the MC curve falls and vice
versa.
Sue’s Surfboards, in problems 2 and 3, rents the
factory building and the rent is increased by $200 a
week. If other things remain the same, how do
Sue’s Surfboards’ short-run average cost curves
and marginal cost curve change.
The rent is a fixed cost, so total fixed cost
increases. The increase in total fixed cost
increases total cost but does not change total
variable cost. Average fixed cost is total fixed
cost per unit of output. The average fixed cost
curve shifts upward. Average total cost is total
cost per unit of output. The average total cost
curve shifts upward. The marginal cost curve
and average variable cost curve do not change.
Workers at Sue’s Surfboards, in problems 2 and 3, negotiate a wage increase of
$100 a week for each worker. If other things remain the same, explain how Sue’s
Surfboards’ short-run average cost curve and marginal cost curve change.
The increase in the wage rate is a variable cost, so total variable cost increases.
The increase in total variable cost increases total cost but total fixed cost does
not change. Average variable cost is total variable cost per unit of output. The
average variable cost curve shifts upward. Average total cost is total cost per
unit of output. The average total cost curve shifts upward. The marginal cost
curve shifts upward. The average fixed cost curve does not change.
6.
Sue’s Surfboards, in problem 2, buys a second plant and the output produced by
each worker increases by 50 percent. The total fixed cost of operating each plant is
$1,000 a week. Each worker is paid $500 a week.
a. Calculate the average total cost of producing 180 and 240 surfboards a week
when Sue’s Surfboards operates two plants. Graph these points and sketch the
ATC curve.
To calculate the average total cost when
two plants are operated, recall that total
cost is the cost of all the factors of
production. For example, when 4
workers are employed they now produce
240 surfboards a week. With 4 workers,
the total variable cost is $2,000 a week
and the total fixed cost is (coincidentally
also) $2,000 a week. Hence the total
cost is $4,000 a week. The average total
cost of producing 240 surfboards is
$16.67 a surfboard. Similarly the
average total cost of producing 180
surfboards is $19.44. To graph the ATC
curve the average total costs at all the
quantities are required. Figure 11.6
shows the average total cost curve, ATC2
when Sue’s operates two plants. (It also shows Sue’s average total cost curve,
ATC1, when Sue operates one plant.)
b. To produce 180 surfboards a week, is it efficient to operate one or two plants?
The long-run average cost curve is made up of the lowest parts of the firm's
short-run average total cost curves when the firm operates one plant and two
plants. The long-run average cost curve is illustrated in Figure 11.6 as the
darker part of the two ATC curves. At lower levels of output the LRAC curve is
derived from operating one plant while at higher levels it is derived from
operating two plants. The LRAC curve shows that to produce 180 surfboards it
is efficient to operate 1 plant.
c. To produce 160 surfboards a week, is it efficient for Sue’s to operate one or two
plants?
The LRAC curve shows that to produce 160 surfboards it is efficient to operate 1
plant.
5.
7.
Airlines Seek Out New Ways to Save on Fuel as Costs Soar
The financial pain of higher fuel prices is particularly acute for airlines because it is
their single biggest expense. … [Airlines] pump about 7,000 gallons into a Boeing
737 and as much as 60,000 gallons into the bigger 747 jet. … Each generation of
aircraft is more efficient. At Northwest, the Airbus A330 long-range jets use 38
percent less fuel than the DC-10s they replaced, while the Airbus A319 mediumrange planes are 27 percent more efficient than DC-9s. …
The New York Times, June 11, 2008
a. Is the price of fuel a fixed cost or a variable cost for an airline?
The price of fuel is a variable cost for an airline.
b. Explain how an increase in the price of fuel changes an airline’s total costs,
average costs, and marginal cost.
An increase in the price of fuel raises an airline’s total cost, its average total
cost, its average variable cost, and its marginal cost. It does not change the
airline’s average fixed cost or total fixed cost.
c. Draw a graph to show the effects of an increase in the price of fuel on an airline’s
TFC, TVC, AFC, AVC, and MC curves.
Figure 11.7 shows an airline’s TFC and TVC curves; Figure 11.8 shows an
airline’s AFC, AVC, and MC curves. The increase in the price of fuel has no
effect on the airlines fixed cost, so the TFC and AFC curves do not change. The
increase in the price of fuel raises the firm’s variable costs and its total costs. As
a result the firm’s TVC, AVC and MC curves shift upward as illustrated in the
figures from the curves labeled “0”to the curves labeled “1”.
d. Explain how a technological advance that makes an airplane’s engines more fuel
efficient changes an airline’s total product, marginal product, and average
product.
This situation is an example of technological change that is embodied in capital.
This change will allow the airline to produce more output—passenger miles—
using fewer resources. Hence the airline’s total product, marginal product, and
average product all increase.
e. Draw a graph to illustrate the effects of more fuel efficient aircraft on an airline’s
TP, MP, and AP curves.
Figure 11.9 shows the airline’s TP curves. The new engines shift the TP curve
upward from TP0 to TP1. Figure 11.10 shows the airline’s MP and AP curves.
These curves also shift upward as a result of the new fuel efficient engines.
f. Explain how a technological advance that makes an airplane’s engines more fuel
efficient changes an airline’s average variable cost, marginal cost and average
total cost.
The airline’s average variable cost and marginal cost both decrease. The new
engines that use the new technology are
presumably more expensive than the
older, less fuel efficient engines. The
engines are a fixed cost. So at lower
levels of output the new average total
cost is higher than the old average total
cost while at larger levels of output the
new average total cost is lower than the
old average total cost.
g. Draw a graph to illustrate how a
technological advance that makes an
airplane engine more fuel efficient changes an airline’s AVC, MC, and ATC
curves.
Figure 11.11 illustrates these changes. The airline’s AVC and MC curves shift
downward as indicated by the shift from the grey curves labeled “0” to the black
curves labeled “1”. At lower levels of output the ATC curve shifts upward and
at larger levels of output the ATC curve shifts downward.
8.
The table shows
Labor
Output
the production function
(workers
(rides
per day)
of Jackie’s Canoe
per day)
Plant 1
Plant 2
Plant 3
Plant 4
Rides. Jackie’s pays
10
20
40
55
65
$100 a day for each
20
40
60
75
85
canoe it rents and $50 a
30
65
75
90
100
day for each canoe
40
75
85
100
110
operator it hires.
Canoes
10
20
30
40
a. Graph the ATC
curve for Plant 1 and Plant 2.
To find the average total cost for each
plant, at the different levels of output add
the cost of the workers, $50 per worker,
and the fixed cost, the cost of the canoes,
$100 per canoe. So for plant 1, the total
cost for 20 rides is $1,500; for 40 rides is
$2,000; and, for 65 rides is $2,500. The
average total cost is calculated by
dividing the total cost by the quantity of
rides. These average total costs are
plotted in Figure 11.12. (The average
total cost curve for one plant, ATC1, is
the same as the thicker curve through the
first 4 points.)
b. On your graph in a, plot the ATC curve for
Plant 3 and Plant 4.
These are drawn in Figure 11.12.
c. On Jackie’s LRAC curve, what is the average cost of producing 40, 75, and 85
rides a week?
The long-run average total cost curve is illustrated in Figure 11.12 as the thicker
curve. It is comprised of the parts of the short-run average total cost curves that
are the minimum average total cost for the different levels of output. From this
curve, the average cost of producing 40 rides is $50; of producing 75 rides is
$40; and the average cost of producing 85 rides is $47.06.
d. What is Jackie’s minimum efficient scale?
Jackie’s minimum efficient scale is the smallest quantity at which the long-run
average cost is the lowest. Jackie’s minimum efficient scale is 65 canoe rides
where, with one plant, the average total cost is $38.46.
e. Explain how Jackie’s uses its LRAC cost curve to decide how many canoe to rent.
Jackie’s will use its long-run average total cost curve by building the size of the
plant that minimizes its long-run average cost at the level of output that Jackie’s
expects to produce.
f. Does Jackie’s production function feature economies of scale or diseconomies of
scale?
Jackie’s has both economies of scale for up to 65 canoe rides and then
diseconomies of scale for more than 65 canoe rides.
9.
Business Boot Camp
At a footwear company called Caboots, sales rose from $160,000 in 2000 to $2.3
million in 2006. But in 2007 sales dipped to $1.5 million. Joey and Priscilla
Sanchez, who run Caboots, blame the decline partly on a flood that damaged the
firm’s office and sapped morale.
Based on a Fortune article, CNN, April 23, 2008
If the Sanchezes are correct in their assumptions and the prices of footwear didn’t
change
a. Explain the effect of the flood on the total product curve and marginal product
curve at Caboots.
The total product curve shifted downward as a result of the flood and sapped
morale. That is, the factors of production produced less footwear in 2007 than in
2006. The downward shift in the total product curve decreased the marginal
product so the marginal product curve also shifted downward.
b. Draw a graph to show the effect of the flood on the total product curve and
marginal product curve at Caboots.
Figure 11.13 shows the downward shift in the total product curve and Figure
11.14 shows the downward shift in the marginal product curve. The flood and
lack of morale shift the TP and MP curves downward from TP1 to TP2 and from
MP1 to MP2.
10. No Need for Economies of Scale
Illinois Tool Works Inc. might not seem like an incubator for innovation. The 93year-old company manufactures a hodgepodge of mundane products, from
automotive components and industrial fasteners to zip-strip closures for plastic
bags … and dedicates production lines and resources to high-volume products. A
line will run only those three or four products. … Runs are much longer and more
efficient. By physically linking machines … they are able to eliminate work in
process and storage areas … All the material handling and indirect costs are
reduced.
Business Week, October 31, 2005
a. How would you expect “physically linking machines” to affect the firm’s shortrun product curves and short-run average cost curves?
By “physically linking machines,” for any amount of labor the firm can produce
more than before. The plant’s total product increases so the short-run total
product curve shifts upward. The marginal product and average product curves
also shift upward. As a result of the increase in the average product, the firm’s
short-run average variable cost and average total cost both decrease so that the
average variable cost curve and average total cost curve shift downward.
b.
Draw a graph to show your predicted effects of “physically linking machines” on
the firm’s short-run product curves and cost curves.
Figure 11.15 shows the effect of
physically linking machines on
Illinois Tool’s total product curve.
The total product curve shifts upward
from TP1 to TP2. Figure 11.16 shows
the effects on Illinois Tool’s marginal
product and average product curves.
These curves shift upward from AP1
to AP2 for the average product of
labor and from MP1 to MP2 for the
marginal product of labor. Figure
11.17 shows the effect of physically
linking machines on Illinois Tool’s
cost curves. The costs fall so that all
the cost curves shift downwards: The
average variable cost curve shifts
downward from AVC1 to AVC2, the average total cost curve shifts downward
from ATC1 to ATC2, and the marginal cost curve shifts downward from MC1 to
MC2.
c. Explain how concentrating “production lines and resources to high-volume
products” can influence long-run average cost as the output rate increases.
By specializing in “high-volume products” the firm will be able to enjoy
economies of scale. In other words, with this specialization, as the firm
increases its production its long-run average costs will decline.
11.
Grain Prices Go the Way of the Oil Price
Every morning millions of Americans confront the latest trend in commodities
markets at their kitchen table. … Rising prices for crops … have begun to drive up
the cost of breakfast.
The Economist, July 21, 2007
Explain how the rising price of crops affects the average total cost and marginal
cost of producing breakfast cereals.
When producing cereal, the cereal crops used are a variable factor of
production. An increase in the price of these crops boosts the firms’ average
total cost and the firms’ marginal cost of producing cereal.