Chapter
Production and Cost CHAPTER OUTLINE I. Explain how economists measure a firm’s cost of production and profit. A. The Firm’s Goal B. Accounting Cost and Profit C. Opportunity Cost 1. Explicit Costs and Implicit Costs D. Economic Profit 2. Explain the relationship between a firm’s output and labor employed in the short run. A. The Short Run: Fixed Plant B. The Long Run: Variable Plant C. Total Product D. Marginal Product 1. Increasing Marginal Returns 2. Decreasing Marginal Returns E. Average Product 3. Explain the relationship between a firm’s output and costs in the short run. A. Total Cost B. Marginal Cost C. Average Cost D. Why the Average Total Cost Curve is U-Shaped E. Cost Curves and Product Curves F. Shifts in the Cost Curves 1. Technology 2. Prices of Factors of Production 4. Derive and explain a firm’s long-run average cost curve. A. Plant Size and Cost 1. Economies of Scale 2. Diseconomies of Scale 3. Constant Returns to Scale B. The Long-Run Average Cost Curve 1. Economies and Diseconomies of Scale
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CHAPTER ROADMAP
What’s New in this Edition? Chapter 12 is slightly rewritten to improve clarity.
Where We Are In this chapter, we define economic costs and profits. We ex‐ amine the relationship between inputs, costs, and produc‐ tion. This chapter lays the groundwork for the profit‐ maximizing decisions that are made by firms, which we study in the next several chapters.
Where We’ve Been We defined what economics means in terms of scarcity, op‐ portunity cost, choice, and efficient use of resources. We’ve explored the interactions of supply and demand that bring about the efficient use of resources by equating marginal benefit to marginal cost. We’ve discussed the rationale be‐ hind the downward‐sloping demand curve using marginal utility analysis.
Where We’re Going After this chapter, we look at the demand and marginal revenue curves for firms in different industry structures. By combining the cost, demand, and revenue curves, we will see the profit‐maximizing operating decisions made by these firms.
IN THE CLASSROOM Class Time Needed You can complete this chapter in two to three class sessions. However, this is a very important chapter, so do not short change it. If you judge from your class’s reaction that you need more time, take it!
An estimate of the time per checkpoint is:
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12.1 Economic Cost and Profit—15 to 25 minutes
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12.2 Short‐Run Production—45 to 65 minutes
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12.3 Short‐Run Cost—45 to 65 minutes
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12.4 Long‐Run Cost—30 to 40 minutes
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CHAPTER LECTURE 12.1
Economic Cost and Profit
The Firm’s Goal •
The firm’s goal is to maximize profit.
Accounting Cost and Profit versus Opportunity Cost •
•
Accountants measure revenue and cost using accounting conventions in order to ensure that the firm pays the proper amount of tax and to give creditors information. But the costs as measured by accountants are the firm’s opportunity costs. The decisions the firm makes to maximize its profit respond to opportunity cost and eco‐ nomic profit. The opportunity cost of a firms use of resources is the highest‐valued alter‐ native forgone. Opportunity costs include both explicit costs and implicit costs. • An explicit cost is a cost paid in money. Explicit costs are opportunity costs. • An implicit cost is an opportunity cost incurred by a firm when it uses a factor of production for which it does not make a direct money payment.
Normal Profit and Economic Profit •
•
A firm’s owner supplies entrepreneurship by organizing the business and bearing the risk of running it. • Normal profit is the return to entrepreneurship. • Normal is part of a firm’s opportunity cost because it is the cost of persuading the en‐ trepreneur of not running another business. Economic profit is a firm’s total revenue minus its total opportunity cost. An economic profit is a profit over and above the normal profit.
12.2
Short-Run Production
A firm owner’s decisions can be categorized as short run decisions and long run decisions. • The short run is a time frame in which the quantities of some resources are fixed. The fixed resources include the firm’s management organization structure, level of technol‐ ogy, buildings and large equipment. These factors are called the firm’s plant. • The long run is a time frame in which the quantities of all resources can be varied. Long‐ run decisions are not easily reversed so usually a firm must live with the plant size that it has created for some time. Help the students to understand that the difference between the long run and short run is not related to calendar time. Compare the street vendor, who is a firm owner operating out of a food truck, to the giant automaker firm, General Motors. Ask them how long it would take for the food vendor to double the size of his or her plant (truck, oven, etc.) versus GM to double its plant size (factory buildings covering multiple blocks, sophisticated computerized assembly lines and ro‐ botics, etc.). They will realize that the length of time covered by the long run differs among firms.
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To increase its output in the short run, a firm must increase the quantity of labor employed. There are three relationships between the quantity of labor and the firm’s output.
Product Schedules • •
•
• •
• •
The total product is the total quantity of a good produced in a given period. The marginal product (MP) of labor is the Total Marginal increase in total product that results from a Labor product product one‐unit increase in the quantity of labor 0 0 employed with all other inputs remaining 10 the same. 1 10 The average product of labor is equal to the 20 total product of labor divided by the quan‐ 2 30 tity of labor. 6 The table to the right has examples of these 3 36 product schedules.
Average product 10 15 12
The marginal product curve shows the addi‐ tional output generated by each additional unit of labor. The figure shows a typical mar‐ ginal product of labor curve (MP), with an upside‐down U shape. The shape reflects the point that marginal product has increasing marginal returns initially and decreasing marginal returns eventually. • Increasing marginal returns occurs when the marginal product of an addi‐ tional worker exceeds the marginal product of the previous worker. The marginal product curve has a positive slope. At low levels of employment, in‐ creasing marginal returns is likely be‐ cause hiring an additional worker allows large gains from specialization. Eventu‐ ally these gains become small or nonexistent and decreasing marginal returns set in. • Decreasing marginal returns occur when the marginal product of an additional worker is less than the marginal product of the previous worker. The marginal prod‐ uct curve has a negative slope. The law of decreasing returns states that as a firm uses more of a variable input, with a given quantity of fixed inputs, the marginal product of the variable input eventually diminishes. The average product curve shows the average product that is generated by labor at each level of labor. The average product of labor curve (AP) has an upside‐down U shape. As the figure shows, the marginal product curve and the average product curve are re‐ lated: when the marginal product of labor exceeds the average product of labor, the aver‐
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age product of labor increases; when the marginal product of labor is less than the average product of labor, the average product of labor decreases; and the marginal product of la‐ bor equals the average product of labor when the average product of labor is at its maximum.
12.3
Short-Run Cost
Fixed Variable Average Average Average Marginal cost cost Total cost fixed cost variable cost total cost cost Labor Output (dollars) (dollars) (dollars) (dollars) (dollars) (dollars) (dollars) 0 0 50 0 50 10.00 1 10 50 100 150 5.00 10.00 15.00 5.00 2 30 50 200 250 1.66 6.67 8.33 16.67 3 36 50 300 350 1.39 8.33 9.72 The table above continues the previous product schedule table and shows different costs.
Total Cost •
Total cost (TC) is the cost of all the factors of production a firm uses. Total fixed cost (TFC) is the cost of the firm’s fixed factors of production—the cost of land, capital, and entrepreneurship. Total variable cost (TVC) is the cost of the firm’s variable inputs—the cost of labor. Total cost is the sum of total fixed cost plus total variable cost:
TC = TFC + TVC. Marginal Cost and Average Costs •
Marginal cost (MC) is the increase in total cost that results from a one‐unit increase in output.
•
Average fixed cost (AFC) is total fixed cost per unit of output. The value of AFC falls as output increases.
•
Average variable cost (AVC) is total variable costs per unit of output. At low levels of output, AVC falls as output in‐ creases but at higher levels of output, AVC rises as output increases.
•
Average total cost (ATC) is the total cost per unit of output. ATC = AFC + AVC. At low levels of output, ATC falls as output increases but at higher levels of output, ATC rises as output increases.
•
The figure illustrates typical MC, AFC, AVC, and ATC curves. As the figure
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shows, the MC curve, the AVC curve, and the ATC curve are all U‐shaped. There are other additional important points about this figure: • The vertical distance between the AVC curve and the ATC curve is the AFC. Because the AFC decreases as output increases, these curves become closer to each other as output increases. • The MC curve intersects the AVC curve and ATC curve at their minimums.
Cost Curves and Product Curves •
The shape of the cost curves is related to the shape of the productivity curves. • The shape of the AVC curve is determined by the shape of the AP curve. Over the range of output for which the AP curve is rising, the AVC curve is falling and over the range of output for which the AP curve is falling, the AVC curve is rising. • The shape of the MC curve is determined by the shape of the MP curve. Over the range of output for which the MP curve is rising, the MC curve is falling and over the range of output for which the MP curve is falling, the MC curve is rising.
Shifts in the Cost Curves •
The cost curves shift with changes in technology or changes in resource prices. • An increase in technology that allows more output to be produced from the same re‐ sources shifts the cost curves downward. If the technology requires more capital, a fixed input, then the average total cost curve shifts upward at low levels of output and downward at higher levels of output. • A fall in the price of the fixed factor of production shifts the AFC and ATC curves downward but leaves the AVC and MC curves unchanged. A fall in the price of a variable factor of production shifts the AVC, ATC, and MC curves downward but leaves the AFC curve unchanged.
12.4
Long-Run Cost
In the long run, a firm can vary the quantity of both labor and capital, so in the long run all costs are variable costs.
Plant Size and Cost •
In the long run, when a firm changes its plant size, its average total cost might rise, fall, or not change •
•
Economies of scale occur when a firm increases its plant size and labor employed by the same percentage, its output increases by a larger percentage, so its average total cost decreases. The main source of economies of scale is greater specialization of both labor and capital. Diseconomies of scale occur when a firm increases its plant size and labor employed by the same percentage, its output increases by a smaller percentage, so its average total cost increases. Diseconomies of scale arise from the difficulty of coordinating and controlling a large business.
Chapter 12 . Production and Cost
•
303
Constant returns to scale occur when a firm increases its plant size and labor employed by the same percentage, its output increases by the percentage, so its average total cost does not change.
Long-Run Costs •
In the long run, a firm can use different plant sizes. Each plant size has a differ‐ ent short‐run ATC curve. Each short‐run ATC curve is U‐shaped and the larger the plant size, the greater is the output at which the average total cost is a minimum.
•
The figure illustrates three average total cost curves for three plant sizes. ATC1 pertains to the smallest plant size and ATC3 to the largest.
•
The long-run average cost curve, LRAC, is the curve that shows the low‐ est average total cost at which it is pos‐ sible to produce each output when the firm has sufficient time to change both its plant size and labor employed. This curve is derived from the short‐run average total cost curves. It shows the lowest average total cost to produce a given level of output. In the figure, the LRAC curve is the darkened parts of the three short‐run ATC curves.
•
The LRAC slopes downward when the firm has economies of scale, is horizontal when the firm has constant returns to scale, and slopes upward when the firm has disecono‐ mies of scale.
Point out to the students that the long‐run average cost curve yields the lowest average cost of production possible when plant size is free to change. Once a firm commits to a specific plant size, it is locked into a specific short run cost curve configuration. Any significant departure from the range of output per period that best suits that configuration means the firm will incur higher short‐run average total costs than it would have had it chosen a more appropriate plant size. If the firm’s competitors chose their plant size more wisely, the firm might have a tough time sur‐ viving! This observation explains why successful firms often spend much money on long run market analysis.
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Lecture Launchers 1. This chapter is incredibly important because it serves as the basis for the next three chapters. You know this fact, I know this fact, but your students don’t know this fact. You must tell them this fact because without it you will definitely lose some of the class. How so? They won’t realize that this chapter is critical until they are unable to grasp the next three chapters. At that point, several possibilities exist, all unpleasant: These students flunk the course, these students drop the course, or these students camp out in your office. Most likely no one would be happy with any of these outcomes, so launch your lecture by motivating your students with the important in‐ formation that Chapter 12 is truly a key to Chapters 13, 14, and 15! 2. This chapter has a plethora of definitions. Students must learn the defini‐ tions, but they are secondary to the concepts they define and the insights they bring. Focus on why productivity measures and cost measures are use‐ ful for decision making. Managers must frequently make quick decisions with little information. If managers have knowledge of a useful relationship between input measures and production cost measures they can use their understanding of this link to make inferences about how production costs might behave when the firm’s output must change to accommodate market changes. 3. This chapter is one more place where an in‐class experiment has a huge payoff and is definitely recommended. The experiment teaches students about the product curves, and a related assignment that we describe later teaches them about the short‐run cost curves. Allow 30 to 40 minutes for this production experiment. This experiment motivates the students to go beyond memorizing the cost and productivity definitions by getting them directly involved with generating their own data and productivity and cost measures. This is a fun exercise that will illustrate the concept of diminish‐ ing returns to labor, as well as how short run productivity measures and cost measures are related. Students genuinely enjoy and learn from this ex‐ ercise, even though it might seem childish. You have two inputs:
Capital: A table (of which the class must have an unobstructed view), some tear‐off scratch pads with about 500 sheets of paper, a fully loaded stapler, and a back‐up stapler (also fully loaded). Labor: Provided by your students. The capital and labor are used to produce “widgets.” A widget is a piece of paper, torn from a pad, folded twice very carefully so that the corners of the paper align, and stapled. The first fold bisects the paper along its long side and the second fold is at right angles to the first. Once folded, a staple
Chapter 12 . Production and Cost
is used to hold the folds in place. A widget is fragile and breaks if it falls off the table. Start the experiment by hiring a manager from your class and appointing an auditor. Get the manager to hire a quality controller, an accountant, and some workers. Tell the manager that he or she must produce widgets as ef‐ ficiently as possible and that he or she can discuss the process with his workers and with the class. Start the experiment by defining that a day lasts for 1 minute. Get the class to keep time. On day 1, have 1 worker produce widgets. On day 2, have 2 workers, and so on. You’ll probably run for 10 to 12 days before you get to almost zero marginal product. Record the inputs and outputs in a ta‐ ble on the board. Have some fun with quality control, shirking, and cheat‐ ing. The auditor must ensure that old widgets and partly made widgets don’t get used in a subsequent day. Each day must start clean. Now comes the assignment (Stage 1): Get the students to calculate marginal product and average product from the total product numbers that you’re recorded on the board. Get them to make graphs of the total product, mar‐ ginal product, and average product curves. Get them to describe the curves and to explain their similarities with and differences to the curves for smoothies in the textbook. The first assignment covers only production. If you want, you can extend the experiment with another assignment (Stage 2): Use the data from your widget production experiment. Tell the students the cost of the capital and the wage rate of a worker. (Make up the numbers. Any will do.) Tell the students to calculate total cost, marginal cost, and average cost. Get them to make graphs of the total cost, marginal cost, and average cost curves. Get them to describe the curves and to explain their similarities with and differ‐ ences to the curves for smoothies in the textbook. This assignment and the previous one make an outstanding assignment for credit or extra credit.
4. Though perhaps this suggestion is more of a lecture closer than launcher, be sure that your students see the big picture. There are two big ideas:
First, a firm’s long‐run production costs depend on the freedom to choose all inputs. Long‐run flexibility enables firms to produce at a lower cost than is possible in the short run when some inputs are fixed. Second, in the short run, with one or more fixed inputs, production costs vary with output in a predictable way because they are directly linked to input productivity.
Land Mines 1. If you do not create your own data using the experiment described above, be sure that when you draw the curves in this chapter you use numeric ex‐
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amples. Either make up your own numbers or use the table the text pro‐ vides, but make sure to provide your students with two things: a pre‐ printed table with the columns labeled (but not filled in) and preprinted handouts with graphs on which the axes are labeled. If you can, draw the points (not the actual curves) on the graphs that will correspond to the data in the tables. The table should provide a complete spreadsheet, with labor employ‐ ment, capital employment, output, AP, MP, TC, TFC, TVC, ATC, AFC, AVC, and MC. Work through the first part of the table (capital and labor inputs, output, fixed, variable and total costs). Label and draw these graphs. Then turn back to the table, completing the data for the average and marginal cost columns. Finally draw and explain the graphs that relate to these data. This exercise allows students to listen to the intuition and follow the exam‐ ple without being distracted trying to get the layout of the table and graphs correct. You’ll also be able to cover more material this way because you won’t be waiting for students to catch up.
2. Watch out for persistent confusion between economic profit and accounting profit. You can avoid some of this by thoroughly drilling them in opportu‐ nity cost, so that they understand that non‐money cost is still cost. 3. Students are introduced to more graphs in this chapter. When summing up the day’s lecture, the clearest way to show the differences (especially with respect to the variables on the axes) is to graph each of the curves on the board at the same time. Suggest that students practice graphing each of the curves many times noting the maximum points, minimum points, and in‐ tersections. Tell your students that it is important to draw the ATC curve and MC curve correctly, that is, so that the MC curve intersects the ATC curve when the ATC is at its minimum. 4. Distinguish between decreasing marginal product in the short run versus diseconomies of scale in the long run. Decreasing returns occur when addi‐ tional units of labor are combined with a fixed amount of capital. Dis‐ economies of scale do not occur for the same reason, because in the long run both labor and capital can change. Diseconomies of scale occur because of chaos, organizational overloads, etc. 5. The grade point average versus marginal grade example in the text is out‐ standing to use in class to describe how the marginal product and marginal cost curves relate to the average product and average cost curves. Once students can tell a story using the same intuition, they find drawing those curves much easier. While you have the curves drawn on the board or overhead, physically pull the average cost curves down (while marginal cost is below) or pull them up (when the marginal cost curve rises above). Use theatrics: raise your hands over your head and “pull down the curves.”
Chapter 12 . Production and Cost
If you have a more sports‐oriented class, you can try using a batting aver‐ age percentage and at‐bat outcome example (if you had a .300 batting aver‐ age and you struck out at your next at‐bat [the marginal factor], your bat‐ ting average is pulled down).
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ANSWERS TO CHECKPOINT EXERCISES CHECKPOINT 12.1 Economic Cost and Profit 1a. Explicit costs are the $1,500 for the lease of a Web server and $1,750 for high‐speed Internet service. The total explicit costs are $3,250. The implicit costs are the $20,000 in wages forgone, the $4,000 in rent for‐ gone, the $100 in forgone interest payments on the savings, the $55,000 in normal profit, and the $1,500 in economic depreciation for the computer. The total implicit costs are $80,600. 1b. The economic profit equals total revenue minus total opportunity costs, which is $45,000 − ($3,250 + $80,600) = −$38,850. Toni incurred an economic loss of $38,850 for the year.
CHECKPOINT 12.2 Short-Run Production 1a. The marginal product of the fourth student is the change in total product that results from hiring the fourth student. The total product with 3 stu‐ dents is 9 houses painted a week and the total product with 4 students is 12 houses painted a week. So the marginal product of the fourth student is 12 houses painted a week minus 9 houses painted a week, which equals 3 houses painted a week. 1b. The average product equals total product divided by the number of stu‐ dents. When 4 students are hired, average product is 12 houses painted a week divided by 4 students, which equals 3 houses painted a week. 1c. The marginal product decreases between 4 and 6 students. 1d. When the marginal product, though decreasing, exceeds the average prod‐ uct the average product increases as more workers are hired. Eventually as the marginal product decreases it becomes less than the average product. When the marginal product is less than the average product, the average product decreases as more workers are hired.
CHECKPOINT 12.3 Short-Run Cost 1a. Assuming a 5‐day workweek, the total cost schedules are in the table to the right.
Total Output Total (houses fixed cost variable cost Total cost (dollars (dollars (dollars painted Labor (students) per week) per week) per week) per week) 0 0 500 0 500 1 2 500 250 750 2 5 500 500 1,000 3 9 500 750 1,250 4 12 500 1,000 1,500 5 14 500 1,250 1,750 6 15 500 1,500 2,000
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b. The average cost Average Average Output Average schedules are in the (houses fixed cost variable cost total cost Labor painted (dollars per (dollars per (dollars per table to the right. house) house) house) (students) per week) 0 0 xx xx xx 1 2 250.00 125.00 375.00 2 5 100.00 100.00 200.00 3 9 55.56 83.33 138.89 4 12 41.67 83.33 125.00 5 14 35.71 89.29 125.00 6 15 33.33 100.00 133.33 c. The marginal cost schedule is in the table to the Output Marginal right. (houses cost Labor painted (dollars per d. The difference between the total cost and total house) variable cost is the same at all levels of output (students) per week) 0 0 and is equal to total fixed cost. This difference is 125.00 always equal to the total fixed cost because total 1 2 83.33 cost equals total variable cost plus total fixed 2 5 cost. 62.50 3 9 83.33 4 12 125.00 5 14 250.00 6 15
CHECKPOINT 12.4 Long-Run Cost a. If Lizzie doubles her inputs, and her output less than doubles, Lisa experi‐ ences diseconomies of scale. Average total cost rises so that her long‐run average cost curve slopes upward. b. The source of her diseconomies of scale could be management problems when she hires more students and leases more equipment. Trying to organ‐ ize more equipment and more students across different houses in different areas of the town requires more communication and coordination. If she is unable to manage the larger firm as efficiently as she was able to manage the smaller firm, her average total cost increases.
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ANSWERS TO CHAPTER CHECKPOINT EXERCISES 1a. Joe’s explicit costs are $2,000 rent he pays the airport and $200 in interest he pays on his credit card. So Joe’s total explicit costs are $2,200. 1b. Joe’s implicit costs are $10,000 of normal profit for running a shoeshine stand and $500 depreciation for his capital equipment, the chair, polishes, and brushes. So Joe’s total implicit costs are $10,500. 1c. Joe’s economic profit equals his total revenue minus his total opportunity costs. Joe’s total revenue is $15,000. His total opportunity costs are the sum of his explicit costs, $2,200, and his implicit costs, $10,500. Joe’s total oppor‐ tunity costs are $12,700 so his economic profit is $15,000 minus $12,700, which is $2,300. 2a. Sonya’s explicit costs are $10,000 for cards, $5,000 for rent, and $1,000 for utilities. So Sonya’s explicit costs are $16,000. 2b. Sonya’s implicit costs are $25,000 in forgone income as a real estate agent, $14,000 normal profit, $60 in forgone interest, and $400 in economic depre‐ ciation on the cash register, for a total of $39,460. 2c. Sonya’s economic profit equals her total revenue, $58,000, minus her total opportunity costs or $55,640, which is the sum of her explicit and implicit costs. Sonya’s economic profit is Total Average Marginal $58,000 − $55,640, which equals Labor product product product $2,360. 0 0 xx 20 3a. The marginal product and average 1 20 20.0 product schedules are in the table to 24 the right. 2 44 22.0 16 3 60 20.0 12 4 72 18.0 8 5 80 16.0 4 6 84 14.0 2 7 86 12.3 3b. Marginal returns increase for the first 2 workers. 3c. Marginal returns decrease after the second worker is hired.
Chapter 12 . Production and Cost
4a. The table to the right has Yolanda’s total product, marginal product, and average product schedules. 4b. Marginal returns increase for the 2nd and 3rd workers. 4c. After the third worker is hired, marginal returns decrease.
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Labor 0
Total product 0
Average product xx
1
1,000
1,000
2
2,000
1,000
3
4,000
1,333
4
5,000
1,250
Marginal product 1,000 1,000 2,000 1,000
5a. The variable costs are the Total Total Total Total costs of labor; the fixed costs product fixed cost variable cost cost are the costs of the shaping Labor (body boards) (dollars) (dollars) (dollars) 0 0 60 0 60 board equipment. Assuming 1 20 60 200 260 a 5‐day work week, the total 2 44 60 400 460 cost schedules per day are in 3 60 60 600 660 the table to right. 4 72 60 800 860 5 80 60 1,000 1,060 6 84 60 1,200 1,260 7 86 60 1,4000 1,460 5b. Total cost minus total variable cost always equals $60. The difference be‐ tween total cost and total variable cost equals total fixed cost, which does not change with the Average Total Average level of output. variable cost product fixed cost 5c. The average cost (dollars) Labor (body boards) (dollars) schedules are in the 0 0 xx xx table to the right. 1 20 3.00 10.00 2 44 1.36 9.09 3 60 1.00 10.00 4 72 .83 11.11 5 80 .75 12.50 6 84 .71 14.29 7 86 .70 16.28
Average total cost (dollars) xx 13.00 10.45 11.00 11.94 13.25 15.00 16.98
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Total Marginal 5d. The marginal cost schedule is in the table to the right. Labor product cost 5e. Len’s average total cost is at a minimum between 44 0 0 and 60 body boards a day. 10.00 5f. Len’s average variable cost is at a minimum between 1 20 8.33 44 and 60 body boards a day. 2 44 5g. Though the range of output over which the minimum 12.50 average total cost and average variable cost occur is 3 60 16.67 the same, we know that the average variable cost 4 72 equals its minimum at a lower level of output than 25.00 the average total cost. The average total cost equals 5 80 50.00 the average variable cost plus the average fixed cost. 6 84 The average fixed cost constantly falls as output 100.00 increases. So as output increases after the average 7 86 variable cost reaches a minimum and starts to rise, the average total cost continues to fall for a while because the average fixed cost falls and this fall dominates the rise in the average variable cost. Eventually the rise in the average variable cost is greater than the fall in the average fixed cost and at that level of output, the average total cost begins to rise as output increases. 6a. The variable costs are the Total Total Total costs of labor; the fixed costs Labor Output fixed cost variable cost cost are the costs of the 0 0 1,000 0 1,000 1 1,000 1,000 500 1,500 equipment. The total cost 2 2,000 1,000 1,000 2,000 schedules are in the table to 3 4,000 1,000 1,500 2,500 right. 4 5,000 1,000 2,000 3,000 6b. Total cost minus total variable cost always equals $1,000. The difference between total cost and total variable cost equals total fixed cost, which does not change with the level of output. 6c. The average cost Average Average Average schedules are in the table Labor Output fixed cost variable cost total cost to the right. 0 0 xx xx xx 1 1,000 1.00 .50 1.50 2 2,000 .50 .50 1.00 3 4,000 .25 .38 .63 4 5,000 .20 .40 .60
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6d. The marginal cost schedule is in the table to the right. Marginal 6e. From the numbers in the average cost table, Labor Output cost Yolanda’s average total cost is at a minimum when 0 0 .50 she produces 5,000 bullfrogs a week. 1 1,000 6f. Yolanda’s average variable cost is at a minimum .50 when she produces 4,000 bullfrogs a week. 2 2,000 .25 6g. Average total cost equals average variable cost plus 3 4,000 .50 average fixed cost. Average fixed cost constantly falls 5 5,000 as output increases. So as output increases after average variable cost reaches a minimum and starts to rise, average total cost continues to fall for a while because average fixed cost falls and this fall dominates the rise in average variable cost. Eventually, the rise in average variable cost is greater than the fall in average fixed cost and at that level of output, average total cost be‐ gins to rise as output increases. 7. The completed table L TP TVC TC AFC AVC ATC MC is to the right. 0 0 0 100 xx xx xx 13.50 10.00 3.50 13.50 1 10 35 135 2.50 4.17 2.91 7.08 2 24 70 170 2.50 2.63 2.76 5.39 3 38 105 205 5.83 2.27 3.18 5.45 4 44 140 240 11.67 5 47 175 275 2.13 3.72 5.85 8. A = $1,050. Calculate A using TVC = TC − TFC. Total cost is given in the row. For total fixed cost, TFC, note that TFC = TC − TVC. Use the informa‐ tion in the top row to get TFC = $500. So A = $1,550 − $500, which equals $1,050. B = $1,200. Calculate B by adding TVC + TFC, with TFC from part (a) as $500. Then B = $700 + $500, which equals $1,200. C = $5. Calculate C by calculating TFC ÷ TP, which is $500 ÷ 100 = $5. D = $8.50. Calculate D by calculating TC ÷ TP, which is $850 ÷ 100= $8.50. E = $2.50. Calculate E as the change in TC divided by the change in TP, which is ($1,550 − $1,200) ÷ (380 − 240) = $2.50. 9.
The long‐run average cost curve, LRAC, shows the lowest average total cost of producing any level of output when the firm has had sufficient time to change both its plant size and labor employed. To construct the
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LRAC curve, calculate the ATC curve for each plant size. The ATC that is the lowest for each level of output is the LRAC for that level of output. 10.
A firm that is producing at the lowest aver‐ age cost might be able to lower its average cost further by increasing its production. Figure 12.1 shows an example. If the firm is producing at point A, the firm can increase its production by hiring more labor and in‐ creasing the size of its plant and move to point B. At point B the average cost is lower than at point A. Between point A and point B, the firm enjoys economies of scale.
11.
The sources of economies to scale are specialization of labor and capital. The sources of diseconomies of scale are difficulties of management coordination and communication. In Figure 12.2, economies of scale occur up to point A, 45,000 units of output a day, because the long‐run average cost (generally) falls as output increases. Diseconomies of scale occur at output levels greater than 45,000 units a day because the long‐run average cost (generally) rises as output increases.
12. Your students’ answers will differ, but economies of scale occur in indus‐ tries that are high tech and in agriculture. High tech industries, such as
Chapter 12 . Production and Cost
server farms, can service thousands of customers in one location. The ATM example in the book provides a good example. In agriculture, large, commercial farms can hire many workers to specialize in the many specific tasks that are required. For instance, on a dairy farm many tasks are required: breeding cows, growing feed, milking, selling, and delivering milk. A large corporate farm can hire specialists for all these tasks, versus a single farmer trying to do all of the jobs on a farm.
13. Your students’ answers will differ from these answers. Diseconomies of scale probably occur in large conglomerate companies such as General Elec‐ tric, Tyco, or TimeWarner. Managing these types of companies is very complex because the different business often can have little in common. For example, General Electric produces light bulbs, locomotives, and CNBC. Management is already struggling to run these disparate divisions, so if the company increases still more in size, it is probable that the added complex‐ ity results in average cost rising. Diseconomies of scale also occur in the electricity industry. We see electrical utilities buying electricity from other suppliers during extreme weather that occurs infrequently. If the utility had built a plant to meet demand on these very cold or very hot days, it would experience diseconomies of scale. As a result, the utility uses a smaller plant size that minimizes average total cost on normal days (the vast majority of days), but it must buy additional power during extreme weather.
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Critical Thinking 14.
The cost of the fiber‐optic system is a long‐run cost. It also is a sunk cost. It is a sunk cost because it has already been paid.
15a.
The cost of the human teller is primarily the cost of labor, a variable cost, with only a slight amount of capital cost. The cost of the ATM is primarily the cost of the capital, a fixed cost, with only a small amount of labor cost. So the cost of an ATM shows substantial economies of scale whereas the cost of a human teller reaches its minimum at a lower scale of transac‐ tions and then starts to rise. As long as the bank forecasts a reasonably large number of transactions at a location, with the low cost of an ATM, it makes sense for the bank to lo‐ cate an ATM at that location. Branches of banks that are located in very small towns and that have rela‐ tively few customers will not have ATMs. For two reasons, ATMs are not as common in China as in the United States. First, the cost of capital is higher in China and the cost of labor is lower. So, ATMs do not enjoy as large a cost advantage in China as they do in the United States. Second, the demand for bank services is lower in China than in the United States. So, ATMs are less likely to achieve the large scale of transactions necessary for them to be less expensive than human tellers.
15b.
15c. 15d.
16a. 16b.
The cost of using human tellers does not change. The cost of using ATMs increases, so the average total cost curve for ATMs shifts upward. The tax increases the scale at which it is less expensive to use an ATM instead of a human teller. As a result, banks hire more human tellers and create fewer ATMs.
Chapter 12 . Production and Cost
Web Exercises 17a. The marginal cost of growing larger frogs probably increases because the price of larger frogs exceeds the price of smaller frogs. The marginal cost of growing additional numbers of similar sized frogs does not appear to in‐ crease because any number of similar sized frogs can be purchased for the same price. 17b. A firm’s cost and production curves are such that when the marginal cost is increasing, then the marginal product is decreasing. Because the marginal cost of growing larger frogs seems to be increasing, then bull frog farming displays decreasing marginal returns. 17c. For some people, the value from a larger frog is worth the additional cost over a smaller frog. Depending on what the consumer does with the bull frog, larger frogs might have significantly better survival rates (though, of course, all frogs croak in the end), might be able to jump farther, or might have noticeably more meat on their legs. 18a. The survivor technique measures economies of scale over the long run by observing the evolution of the surviving firms. If surviving firms grow over time while small firms decline, then economies of scale must be present. 18b. The survivor technique works because firms whose costs are higher than others do not survive—they go bankrupt or are purchased by survivors. 18c. These survivor technique indicates that significant economies of scale exist in the banking industry and that economies of scale are available at low as‐ set levels. Banks with assets of $300 million or more appear to have a cost advantage over smaller banks. 18d. Figure 12.3 illustrates a long‐run average cost that is consistent with what is found using the survivor technique.
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19a. The costs fall into 5 categories: 1) land preparation; 2) planting; 3) fertilization; 4) fungicide‐insecticide applications; and, 5) harvest costs. Details of what these costs include are in answer (b) below. 19b. The issue of what is a fixed cost and what is a variable cost depends on when the costs are being considered, so your students’ answers might vary. Assume we are studying a farmer who, in the spring, is determining what to grow on an acre of soil. So the farmer has already prepared the ground but has not yet purchased any seed. In this case, the land preparation cost, $72.36 an acre, is a fixed cost; the planting cost, $313.38 an acre and which includes the seed and actual planting, is a variable cost; the fertilization cost, $166 an acre, is a variable cost; the pest control cost, $744.85 per acre, is a variable cost; and, the harvesting cost, $291 an acre, is a variable cost. Any cost to rent the land is a fixed cost and was not specifically given on the web page. 19c. Your students’ answers will vary, depending on the assumptions they make. The web page mentions 5 ton, 8 ton, and 10 ton crops. The assumption I make is that if the farmer does not fertilize or spray, the harvest is 5 tons; if the farmer fertilizes 1/3 the recommended amount and does 1/3 the recommended spraying, the harvest is 8 tons; and if the farmer fertilizes the recommended amount and does all the recommended spraying, the harvest is 10 tons. With these assumptions, for 5 tons, TFC is $72, TVC is $604, TC is $676, AFC is $14, AVC is $121, and ATC is $135. For 8 tons, TFC is $72, TVC is $907, TC is $979, AFC is $9, AVC is $113, and ATC is $122. For 10 tons, TFC is $72, TVC is $1,513, TC is $1,585, AFC is $7, AVC is $151, and ATC is $158. The MC between 5 and 8 tons is $101 a ton and be‐ tween 8 and 10 tons is $303. These data are illustrated in Figure 12.4. 19d. The minimum point on the AVC curve is at about 7 tons of pumpkins and the minimum point on the ATC curve is at about 8 tons of pumpkins.
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ADDITIONAL EXERCISES FOR ASSIGNMENT Questions CHECKPOINT 12.1 Economic Cost and Profit 1. In 2005, Roma was a schoolteacher and earned $40,000. But she enjoys creat‐ ing cartoons, so at the beginning of 2006, Roma quit teaching and set to work as a cartoonist. She stopped renting out her basement for $5,000 a year and began to use it as her office. She used $5,000 from her savings ac‐ count to buy a new computer, and she leased a printer for $150 a year. Dur‐ ing 2006, Roma paid $1,250 for paper, utilities, and postage; the bank paid 5 percent a year on savings account balances; and Roma sold $50,000 of car‐ toons. Normal profit is $3,000 a year. At the end of 2006, Roma was offered $4,000 for her computer. For 2006, calculate Romaʹs: 1a. Explicit costs. 1b. Implicit costs. 1c. Economic profit. CHECKPOINT 12.2 Short-Run Production 2. Lisa has a lawn‐mowing business. Lisa hires Total product Labor students to mow the lawns. The table sets out (students per day) lawns cut per day) 0 0 Lisaʹs total product schedule. 1 20 2a. Calculate the marginal product of the fourth 2 44 student. 3 70 2b. Calculate the average product of four 4 94 students. 5 114 6 120 2c. Over what numbers of students does marginal product decrease? 2d. When marginal product decreases, compare average product and marginal product. 3. Create some hypothetical short‐run production data for a firm’s labor em‐ ployment and output. Calculate the firm’s average product and marginal product schedule. Carefully graph the data. What happens at the minimum of the average product curve? CHECKPOINT 12.3 Short-Run Cost 4. Lisa has a lawn‐mowing business. Lisa hires students at $40 a day to mow lawns. Lisa leases 5 lawn mowers for $200 a day. The table gives the daily output. 4a. Construct the total variable cost and total cost schedules.
Total product Labor (students per day) (lawns cut per day) 0 0 1 . 20 2 44 3 70 4 94 5 114 6 120
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4b. Construct the average fixed cost, average variable cost, and average total cost schedules. 4c. Construct the marginal cost schedule. 4d. Check that the gap between total cost and total variable cost is the same at all outputs. Explain why. 5. Create hypothetical short‐run production data for a firm’s labor employ‐ ment, amount of capital, and output. Select wages and the cost of the capi‐ tal and then calculate the total cost, marginal cost, average fixed cost, aver‐ age variable cost, and average total cost schedules and curves.
Answers CHECKPOINT 12.1 Economic Cost and Profit 1a. Explicit costs are the $150 printer lease and $1,250 for paper, utilities, and postage. So explicit costs are $1,400. 1b. Implicit costs are $40,000 in wages forgone, $5,000 in rent forgone, $3,000 in normal profit, $250 in forgone interest payments on the savings, and $1,000 in economic depreciation on the computer. So implicit costs are $49,250. 1c. Economic profit equals total revenue minus total opportunity cost, which is the sum of the explicit costs and implicit costs. So Roma’ economic profit is $50,000 − ($1,400 + $49,250), which equals −$650. Roma incurs an economic loss of $650 for the year. CHECKPOINT 12.2 Short-Run Production 2a. The total product with 3 workers is 70 lawns mowed and the total product with 4 workers is 94 lawns mowed. So, the marginal product of the fourth student is 24 lawns. 2b. The average product of four students is (94 lawns) ÷ (4 students), which is 23.5 lawns. 2c. The marginal product decreases between 4 and 6 students. 2d. When marginal product decreases, eventually it become less than average product. Before it is less than average product (that is, when marginal product, though decreasing, exceeds average product) average product in‐ creases as more workers are hired. When marginal product is less than av‐ erage product, average product decreases as more workers are hired. 3. Students will have individual answers. Make sure their average product curve is U‐shaped and that the marginal product curve intersects the aver‐ age product curve at the minimum of the average product curve. Also make sure that the axes are labeled correctly.
Chapter 12 . Production and Cost
CHECKPOINT 12.3 Short-Run Cost 4a. The total costs are in the table to the right. Labor 0 1 2 3 4 5 6
Output 0 20 44 70 94 114 120
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Total Total fixed cost variable cost 200 0 200 40 200 80 200 120 200 160 200 200 200 240
Average Average Labor Output fixed cost variable cost 4b. The average costs are 0 0 xx xx in the table to the 1 20 10.00 2.00 right. 2 44 4.55 1.82 3 70 2.86 1.71 4 94 2.13 1.70 5 114 1.75 1.75 6 120 1.67 2.00 4c. The marginal cost is in the table to the right. 4d. The gap between total cost and total variable cost is Labor Output the same at all levels of output because total cost 0 0 minus total variable cost equals total fixed cost. 1 20 Note in the answer to part (a), that the difference between total variable cost and total cost is always 2 44 $200, the amount of total fixed cost. 3 70 4
94
5
114
6
120
5. Students will have individual answers. Make sure graphs and axes are labeled correctly. By generating their own data, stu‐ dents learn the interaction of output and different costs.
Total cost 200 240 280 320 360 400 440
Average total cost xx 12.00 6.37 4.57 3.83 3.50 3.67 Marginal cost 2.00 1.67 1.54 1.67 2.00 6.67
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USING EYE ON THE U.S. ECONOMY The ATM and the Cost of Getting Cash The article provides interesting data and ATC curves for ATMs. The story and curves clearly show why large banks do a lot of their business via ATMs as a re‐ sult of a large customer base. Smaller banks, on the other hand, face a small client base and so it is not efficient (cost‐effective) for them to provide ATMs to this small number. It is cheaper for the small banks to use tellers. Ask your students if they think that smaller banks and credit unions would be less likely to charge their own customers for using other banks’ ATM ma‐ chines. You can conduct a quick poll of the class to determine if any of the stu‐ dents have actual experience with this question. The point is that by not charging its customers for using other bank’s ATMs, the smaller bank can increase its scale without having to actually change its plant size. The answer to the question de‐ pends, in part, on the charges the smaller bank has to pay to allow its customers to be part of the larger network.
