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
(workers
per week) | Output
(surfboards
per week) | 1 | 30 | 2 | 70 | 3 | 120 | 4 | 160 | 5 | 190 | 6 | 210 | 7 | 220 |
2. The table sets out Sue’s Surfboards’ total product schedule.
a. Draw the total product curve.
To draw the total product curve measure labor on the x-axis and output on the y-axis. The total product curve is upward sloping and is illustrated in Figure 11.1.
b. Calculate the average product of labor and 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 short-run 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 short-run average and marginal cost curves passing through them. Output
(surfboards) | AFC
(dollars per surfboard) | AVC
(dollars per surfboard) | ATC
(dollars per surfboard) | MC
(dollars per surfboard) | 30 | 33.33 | 16.67 | 50.00 | | | | | | 12.50 | 70 | 14.29 | 14.29 | 28.58 | | | | | | 10.00 | 120 | 8.33 | 12.50 | 20.83 | | | | | | 12.50 | 160 | 6.25 | 12.50 | 18.75 | | | | | | 16.67 | 190 | 5.26 | 13.16 | 18.42 | | | | | | 25.00 | 210 | 4.76 | 14.29 | 19.05 | | | | | | 50.00 | 220 | 4.55 | 15.91 | 20.46 | |
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 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. Labor
(workers) |
Output
(surfboards) | AP
(surfboards per worker) | MP
(surfboards per worker) | AVC
(dollars per surfboard) | MC
(dollars per 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 | |
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.
4. 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.

5. 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.
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 medium-range 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 the production function of Jackie’s Canoe Rides. Jackie’s pays $100 a day for each canoe it rents and $50 a day for each canoe operator it hires. Labor
(workers
per day) | Output
(rides per day) | | Plant 1 | Plant 2 | Plant 3 | Plant 4 | 10 | 20 | 40 | 55 | 65 | 20 | 40 | 60 | 75 | 85 | 30 | 65 | 75 | 90 | 100 | 40 | 75 | 85 | 100 | 110 | 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 93-year-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 short-run 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.