Fixed and Variable Costs
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Learning Objectives
By the end of this chapter, you will be able to:
• Explain the difference between accounting profit and economic profit.
• Calculate the various short-run cost measures and illustrate their relationships graphically.
• List the reasons for economies and diseconomies of scale.
• Determine the profit-maximizing level of production.
Costs and Profits
8
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Introduction CHAPTER 8
Introduction
Consider this. . . At the end of the Carter administration and the beginning of the Reagan administration, experiments with deregulation were becoming common-place. For example, the Airline Deregulation Act of 1978 removed government con- trol over fares, routes, and market entry (of new airlines) from commercial aviation. The goal was to allow market forces to encourage entry into air transportation by new carriers, entry into new markets by current carriers, and generally reduce the rigid practices previ- ously enacted by the Civil Aeronautics Board. The first observable result of this deregula- tion was the advent of competition in the industry. Price competition was observed for the first time. Other effects of competition were greater route frequency, better on-time performance, more baggage efficiency, and expanded frequent flyer programs.
Although the average fare per passenger mile did fall from 33.3 cents in 1974 to 13 cents in 2010 (in real terms), deregulation also brought about a wave of bankruptcy filings, union disputes, and a sky-high number of passenger complaints (Breyer, 2011; Burtless & Have- man, 1987). After the deregulation, most airlines simply went out of business; a few were taken over by the major airlines.
By 2011, the number of domestic airlines was down to just seven primary carriers. Dur- ing that same year, United Airlines merged with Continental Airlines to surpass Delta Airlines and become the world’s largest airline. Although United Airlines generated $32.5 billion in passenger revenue in 2011, its net income in that same year was just $840 million. Why is United Airlines not more profitable? American Airlines generates the third largest passenger revenue, yet it posted almost $2 billion in losses in 2011 (Boehmer, 2012, p. 16). What is so costly about operating an airline? Will American Airlines and US Airways be the next merger? What happened to all the others? The discussion of costs and profits in this chapter will shed more light on this issue.
As we explained in the preceding chapter, entrepreneurs attempt to minimize costs in order to increase profit. But we need to be careful to define costs of inputs in terms of opportunity cost. Measuring costs of inputs in this way can be a problem if you are not used to thinking in terms of opportunity cost and are more used to thinking in terms of explicit cost. Explicit costs are accounting costs or money outlays. Implicit costs are those additional costs implied by the alternatives given up. When economists talk of costs, they mean all opportunity costs—explicit and implicit.
Some examples can make this clearer. Suppose you have the option of working two hours of overtime at $12 an hour or going to a movie that costs $10. The cost of attending the movie is the $10 ticket charge plus the $24 you could have earned working overtime. Attending the movie will cost you $34. The explicit cost is $10. The implicit cost is $24. Or suppose your rich aunt in Great Britain sends you her “old” Rolls Royce that is worth $100,000. She doesn’t care what you do with it. You are excited because now you can drive a classic car at very low cost. You need only pay for gas, oil, insurance, and repairs. Right? No! You have forgotten to include a calculation of the implicit cost. If you sold the car, you could invest the $100,000. You could put the money in an investment fund that earns 5 percent per year. In other words, you are giving up $5,000 per year if you choose to drive the Rolls. The total cost is the implicit cost of that $5,000 plus the explicit costs of gas, oil, insurance, and repairs. Do you still want to drive the Rolls?
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Section 8.1 Accounting Profit and Economic Profit CHAPTER 8
Economics in Action: How to Look at Years With Economic Lenses Perhaps you have opened a restaurant and want to look at what you have made over the year, which is also known as your accounting profit. But you’re also thinking about your old job, and wondering how much you could have made if you had not changed your job. This implicit cost, added to your explicit (accounting) costs, would show you the total costs to be subtracted from your total revenues in order to find your economic profit. Find out how the two compare to each other at http://www .khanacademy.org/finance-economics/microeconomics/v/economic-profit-vs-accounting-profit.
8.1 Accounting Profit and Economic Profit
In Chapter 3, Susan’s lemonade stand was used as an example of a firm as a supplier. Now suppose we can obtain Susan’s account books in order to calculate her profits. Let’s say she had total revenue of $15,000 for the summer. Her books say that she had accounting (explicit) costs of $11,500. Her accounting profit is $3,500, determined by sub- tracting her explicit costs from her total revenue. These are the profits she reported for tax purposes. Economists think that profits figured in this way are misleading because implicit costs are ignored. If Susan’s skills and talents are worth $2,000, this is an opportu- nity cost. The total of her implicit costs plus her explicit costs is $13,500. She will be earn- ing an economic profit of $1,500. Economic profit is the difference between total revenue and the total of explicit and implicit costs of production. An entrepreneur who does not earn a profit that is at least equal to his or her opportunity cost will quit the endeavor.
Opportunity Cost and Normal Profit
The opportunity cost of capital and enterprise is referred to as normal profit. A normal profit represents the rate of return that is necessary to keep capital and enterprise in an industry. Say, for example, the normal profit is 8 percent. Then a firm earning an 8 percent rate of return is earning zero economic profit because its capital and enterprise could earn 8 percent elsewhere. The concept of normal profit is used by regulators in setting prices for public utilities such as electric and telephone companies. If an electric utility is not granted a price increase and the rate of return on its capital falls below the normal profit, capital will leave that industry to try to earn its opportunity cost elsewhere.
In other words, normal profit is part of the implicit cost structure of firms. Just like the “free” Rolls Royce, a firm’s capital, even if it is paid for, represents wealth that could be sold and invested elsewhere. The calculation is, in principle, exactly the same as in the Rolls Royce example.
Figure 8.1 shows the relationships of the concepts of accounting profit, economic profit, and normal profit. Total revenue is the same in both bars, but the difference between eco- nomic profit and accounting profit is the implicit costs, including normal profit.
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Section 8.1 Accounting Profit and Economic Profit CHAPTER 8
Figure 8.1: Economic profit and accounting profit
Economic profit differs from accounting profit by the amount of implicit costs.
A correct definition of costs is important because economists use costs and profits to pre- dict behavior. When economic profits are positive, economists predict that new firms will enter an industry. When economic profits are negative, firms will leave the industry. When economic profits are zero, existing firms will remain and earn normal profits, but no new ones will enter. Economic profit serves as a signal, calling forth entry into or exit out of an industry. If a firm is not earning a normal profit in its present industry, its resources will flow to an industry where a higher rate of return can be earned. If more than a normal profit is being earned in an industry, resources will be attracted to it.
The Use of Accounting Profits in Economic Analysis
Economic theory is based on the concepts of economic costs and economic profit, but these data aren’t usually available for real-world analyses. Economists are suspicious of accounting costs and accounting profits for at least two reasons. The first has to do with the way in which accounting costs are gathered. The second has to do with the discrep- ancy between accounting costs and economic costs.
Accounting Profit
Accounting Costs = Explicit Costs
Implicit Costs (Including Normal
Profit)
Economic Profit
Economic Costs = Implicit Costs + Accounting Costs
Total Revenue
Accounting Costs = Explicit Costs
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Section 8.2 Cost in the Short Run CHAPTER 8
Firms may have incentives to maximize or minimize the calculation of their accounting profits depending upon the purpose for which the information will be used. Since fed- eral income tax is paid on accounting profits, firms have incentives to make profits look as small as possible for the IRS. On the other hand, a firm seeking to raise capital would want to make the profits appear as large as possible for potential investors. There are tech- niques that can be used to manipulate accounting profits. Some flexibility in measuring profits comes from the very dif- ferent ways in which firms can account for items whose value is estimated subjectively. These techniques fall into three catego- ries: altering approved account- ing methods, manipulating managers’ estimates of costs, and changing the time periods in which costs are paid and rev- enues are received.
Even though economists argue that accounting profits do not reflect economic reality and can be manipulated, that data is all that is available for them to use in studying the economy. The use of accounting profits in economic research is subject to debate. Some argue that studies that use accounting profits are meaningless. Others hold that accounting profits are the only data that is available, and as long as economists are careful, using such data can yield meaningful results. This debate will go on as long as economists attempt to measure the performance of firms and industries.
8.2 Cost in the Short Run
The production function relates inputs to outputs. The inputs in the production func-tion have prices and represent costs to the firm. These input prices, which are deter-mined in resource markets, may or may not be affected by the actions of the firm itself. Given the prices of inputs and the production function, it is possible to develop cost schedules for the firm. Although the derivation can be done formally, we will show the relationship on a graph and then determine the costs in a simpler fashion.
Defining Costs
An example of a cost profile for a firm is given in Table 8.1. Total cost (TC) is simply the sum of all the costs of production for a given level of output. Total cost is made up of two components: total fixed costs (TFC) and total variable costs (TVC). That is, TFC 1 TVC 5 TC. Total fixed costs (TFC) are the costs of the fixed inputs; they can’t be avoided or changed in the short run. These costs will be the same regardless of how many units of
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Some economists argue that accounting profits do not reflect economic reality, but that data is all that is available for them to use in studying economics.
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Section 8.2 Cost in the Short Run CHAPTER 8
output the firm produces. Total variable costs (TVC) vary directly with output. Variable costs increase as more output is produced because more of the variable inputs have to be purchased if more output is to be produced. Total fixed costs and total variable costs are shown in the second and third columns in Table 8.1. In this cost schedule, we assume that the firm has already identified that combination of inputs that minimizes the total vari- able costs for each level of output. These figures represent the cost of the economically efficient input combinations.
Table 8.1: Cost profile for a firm Output per week (Q)
Total fixed costs (TFC)
Total variable costs (TVC)
Total cost (TC)
Average fixed cost (AFC)
Average variable cost (AVC)
Average total cost (AC)
Marginal cost (MC)
0 $60 $0 $60 $_ $0 $_ $0
10 60 40 100 6 4 10 4
20 60 76 136 3 3.8 6.8 3.6
30 60 108 168 2 3.6 5.6 3.2
40 60 140 200 1.5 3.5 5 3.2
50 60 175 235 1.2 3.5 4.7 3.5
60 60 216 276 1 3.6 4.6 4.1
70 60 262 322 0.86 3.74 4.6 4.6
80 60 312 372 0.75 3.9 4.65 5.0
90 60 369 429 0.66 4.1 4.76 5.7
100 60 430 490 0.6 4.3 4.9 6.1
Consider this example using the information from the first four columns in Table 8.1: Suppose a firm hires one additional worker, and output increases from 20 to 30 units. The variable cost increases by the wage of that worker (for a given time period), which is $32, bringing the total variable cost to $108. The total fixed cost stays constant at $60, since fixed costs are not related to output. The total cost of thirty units is therefore $108 1 $60 5 $168. If the firm would like to increase its output to 40 units, the variable cost would increase another $32, bringing total variable cost to $140. The total cost of 40 units is $140 1 $60 5 $200.
Given the information in the first four columns of Table 8.1, the rest of the columns are computed as follows. Average fixed cost (AFC) is total fixed costs of production divided by the quantity of output. Average variable cost (AVC) is total variable costs divided by the number of units of output. That is,
AFC5 TFC
Q
and
AVC5 TVC
Q
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Section 8.2 Cost in the Short Run CHAPTER 8
Average total cost (AC) is equal to the total costs of producing a quantity of output divided by that level of output. That is,
AC5 TC
Q
Marginal cost (MC) is the change in total cost as a result of producing one more (or one less) unit of output. That is,
MC 5 DTC
5 DTVC
DQ DQ
Marginal costs are really marginal variable costs because there are no marginal fixed costs. When output changes, the change in fixed costs is zero.
Let’s return to the example above using the information in Table 8.1: Suppose a firm hires one additional worker and output increases from 20 to 30 units. The average variable cost (AVC) of 20 units is TVC/Q 5 $76/20 5 $3.8 per unit. The average variable cost of 30 units is $108/30 5 $3.6 per unit. Although total fixed cost stays constant at $60 across all levels of output, average fixed cost (AFC) does change, since the calculation for average fixed cost involves the quantity of output produced. For example, the average fixed cost of 20 units is $60/20 5 $3 per unit. However, the average fixed cost of 30 units is $60/30 5 $2 per unit. Average fixed cost decreases as output increases because the total fixed cost is spread out across a greater amount of output.
As shown in the formulas, the average total cost of 20 units can be calculated two differ- ent ways. Using Table 8.1 where Q 5 20, average total cost can either be TC/Q 5 $136/20 5 $6.8 per unit, or we can also calculate ATC 5 AVC 1 AFC, where ATC 5 $3.8 1 $3 5 $6.8 per unit. For Q 5 30, ATC 5 TC/Q 5 $168/30 5 $5.6 per unit, or ATC 5 AVC 1 AFC 5 $3.6 1 $2 5 $5.6. Marginal cost (MC) is the change in total cost per unit for a given change in quantity. When Q 5 20, TC 5 $136. When Q 5 30, TC 5 $168, thus MC 5 ($168 2 $136)/10 5 $3.2.
Cost Curves
We can draw a series of cost curves from the data given in Table 8.1. The total fixed costs, total variable costs, and total cost curves are shown in Figure 8.2. The shape of the produc- tion function determines the shape of the total variable cost curve and also the shape of the total cost curve because it is the summation of the fixed cost and the variable cost curve. As the amount of the variable input increases, both output and variable costs increase. If output increases more rapidly than input cost, variable cost increases at a decreasing rate. In Figure 8.2, decreasing costs are shown as output increases from zero to Q
1 . From Q
1 to
higher levels of output, output increases less rapidly than the input cost increases. Then variable costs increase at an increasing rate.
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Section 8.2 Cost in the Short Run CHAPTER 8
Figure 8.2: Total cost curves
The shapes of the total cost (TC) curve and total variable costs (TVC) curve are a reflection of the production function. From zero output to an output level of Q
1 , total cost and variable cost increase at a
decreasing rate. Beyond output level Q 1 , costs increase at an increasing rate.
Now let’s look at average and marginal costs. Figure 8.3 shows the average fixed costs (AFC), average variable costs (AVC), average cost (AC), and marginal cost (MC) curves for a firm. The AFC curve declines continuously, getting closer and closer to the horizon- tal axis of the graph. This decline occurs because fixed costs are constant. Since average fixed costs are calculated by dividing that constant amount by an ever-increasing quantity (levels of output), the average fixed costs become smaller and smaller as output increases.
0
Cost
Output/Time PeriodQ 1
TFC
TVC
TC
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Section 8.2 Cost in the Short Run CHAPTER 8
Figure 8.3: Marginal and average cost curves
The average fixed costs (AFC) curve declines continuously. The average variable costs (AVC) and average cost (AC) curves decline, reach a minimum, and then increase, resulting in a U shape. The marginal cost (MC) curve intersects the AVC and AC curves at their minimum points.
Average variable costs first decline and then increase, as does average cost. The U-shaped AVC curve represents returns to the variable inputs that at first increase and then dimin- ish. The variable inputs are being added to a given quantity of fixed input, such as a fixed- size plant. Increasing returns occur for output levels up to Q
1 in Figure 8.3.
At output levels above Q 1 , returns to the variable inputs decline. That is, returns are
diminishing. The AVC and AC curves are U-shaped because of decreasing costs (increas- ing average product) for small levels of output and then increasing costs (decreasing aver- age product) for higher levels of output. Average cost declines sharply at first because average fixed costs drop rapidly and then more slowly.
Note that the MC curve intersects the AC and AVC curves at their lowest points—Points A and B in Figure 8.3. These points illustrate the relationship between average and marginal values, discussed in the preceding chapter. For the AC and AVC curves to be declining, the marginal cost must be below the average cost. For the AC and AVC curves to be rising, the marginal cost must be above the average cost. Thus, marginal cost and average cost must be equal where the AC curve is at its minimum point. Think about how your grade point average goes up or down depending on your grade in an additional (marginal) course.
0
Cost
Output/Time PeriodQ 1
AC
A
B
AVC
AFC
MC
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Section 8.2 Cost in the Short Run CHAPTER 8
Also, note that when the MC curve starts to rise as output is increased, it is still below the AVC curve. Thus, average variable costs are still falling. An average value falls as long as the marginal value is below it, regardless of whether the marginal value is falling or rising.
The Relationship Between Product Curves and Cost Curves
We have said that cost curves could be derived from production functions, because both show a relationship between inputs and outputs. Figure 8.4 shows the relationship between a production function (represented by product curves) and cost curves.
Figure 8.4: Relationships between product curves and cost curves
The cost curves are closely related to the respective product curves. When the product curve is increasing, the cost curve is decreasing, and vice versa. Q
1 on the vertical axis of part (a) is the same as
Q 1 on the horizontal axis of part (b). L
1 in panel (a) represents the units of labor required to produce Q
1
units of output.
0 Labor/ Time
Period
Output/ Time
Period
(a)
Output/ Time Period
0
(b)
Cost
2Q
Q 1
L 1 L 2 Q1 Q 2
MC
AVC
TPL
APL
MPL
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Section 8.3 Cost in the Long Run CHAPTER 8
Panel (a) of Figure 8.4 shows the marginal product (MP) and average product (AP) curves discussed in the preceding chapter. In this case, the variable input is labor. Panel (b) rep- resents the cost curves that are derived from the production function that produced the product curves. The marginal cost (MC) curve is closely related to the MPL curve. At those output levels where marginal product is increasing, reflecting increasing returns, marginal cost is decreasing. When the MPL curve is at its maximum, the MC curve is at its minimum point. When marginal product is declining, reflecting diminishing returns, marginal cost is rising.
This relationship is based on simple logic. The cost curves simply measure the dollar value of inputs needed to produce a given output, and the production function measures outputs for a given amount of inputs. Given prices of resources, increasing returns have to mean decreasing marginal costs and diminishing returns have to mean increasing mar- ginal costs.
Similar relationships hold for the AP and AVC curves. When average product is increas- ing, average variable costs are decreasing, and when average product is decreasing, aver- age variable costs are increasing. The maximum and minimum points of the two curves also coincide.
8.3 Cost in the Long Run
In the long run, all productive resources are variable. Therefore, there are no fixed inputs in the long run. That means that there are also no fixed costs in the long run. All costs are variable in the long run. In fact, the long run is defined as the period long enough to vary all inputs.
Usually, the most important long-run decision is what size plant to build. Each possible size is represented by a short-run average cost (AC) curve. The long-run decision is based on the selection of the desired short-run average cost curve. That choice will be based on the output the firm expects to produce. Figure 8.5 illustrates this decision. Suppose the technological factors (given by the production function) are such that only three plant sizes are feasible. These plants are represented by curves AC
1 , AC
2 , and AC
3 in Figure 8.5.
The long-run decision of which short-run curve to operate on will depend on the planned output of the firm. If output is to be less than Q
1 , then the plant represented by AC
1 should
be built because its size will produce any output level between zero and Q 1 at a per-unit
cost that is lower than it would be for any other size. If an output level between Q 1 and Q
2
is planned, the plant represented by AC 2 should be built. If output is to be greater than Q
2
the plant represented by AC 3 should be built.
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Section 8.3 Cost in the Long Run CHAPTER 8
Figure 8.5: Alternative plant size
The determination of which size plant to build is a long-run decision of a firm. This decision is based on selection of the short-run cost curve that is optimal for the expected output level.
To expand our example, assume that more than three alternative plant sizes would be fea- sible. They would all be examined in the planning stage. The firm faces all the short-run average cost curves depicted in Figure 8.6. All these possible short-run curves are tangent to a curve that is sometimes referred to as a planning curve. A planning curve is the long- run average cost curve. It is called a planning curve because any point on the curve could be chosen in the planning stage by deciding to build a certain size of plant. Such a plan- ning curve, more commonly called the long-run average cost curve, is shown in Figure 8.6. The long-run average cost (LRAC) curve represents the lowest attainable average cost of producing any given output. It is a curve tangent to all the possible short-run average cost curves. For example, if you knew you were going to produce exactly Q
0 units of out-
put, the plant size represented by AC 4 would have the lowest average cost.
0
Cost
Output/Time PeriodQ 1
AC 1
AC 2
Q 2
AC 3
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Section 8.3 Cost in the Long Run CHAPTER 8
Figure 8.6: Long-run average cost curve
All the possible short-run cost curves are tangent to the planning curve. This planning curve is the long- run average cost (LRAC) curve and represents the lowest attainable average cost of producing any level of output. The optimal plant size is represented by Point A, where the minimum point on a short-run average cost curve is tangent to the long-run average cost curve at its minimum point.
Only at Point A in Figure 8.6, which corresponds to an output of units, is there tangency between the minimum point on a short-run AC curve and the minimum point on the LRAC curve. This point indicates the optimal-size plant. The optimal-size plant is repre- sented by the short-run average cost curve with the lowest attainable per-unit costs.
0
Cost
Output/Time PeriodQ 0
AC 1 LRAC
A
AC 2
Q 1
AC 3 AC 4
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Section 8.3 Cost in the Long Run CHAPTER 8
Global Outlook: The Infant Industry Argument Manufacturing is quite often subject to economies of scale over a relatively large output range. As a result of these large-scale economies, policy makers have often argued that manufacturing needs to be protected from foreign competition in order to get a toehold in domestic markets and someday be able to compete with industry in developed countries. This position, called the infant industry argu- ment by economists, was strongly advocated by Alexander Hamilton (1755–1804), who served as the first Secretary of the U.S. Treasury in Washington’s cabinet. Hamilton was a promoter of economic growth and a strong federal government.
Hamilton argued that it would be very difficult for the U.S. economy to develop in a system of free trade because Great Britain had entrenched manufacturers with established trade networks. He argued that the only way U.S. firms could compete with developed foreign firms was with the “inter- ference and aid” of the federal government. These infant industries could stand on their own after a “nursing period.” An important element of this argument is that the new firm needs to grow to a size at which it enjoys economies of scale before it faces foreign competition.
Although the infant industry argument is used by many countries today, infant industry as an argu- ment for protection usually appears in other guises, such as a period of restructuring, or industrial policy. Many advocates of protection point to the success of China, which experienced rapid eco- nomic growth over two decades with very restrictive trade barriers, developed along infant industry lines. Regardless of the arguments, it’s difficult to make a convincing case for protecting an infant industry in a developed country such as the United States. Even in less developed countries, this argument is easily abused by overstating external benefits and underestimating how long it will take for the industry to become competitive. The problems with the infant industry argument should be obvious. How can policy makers recognize promising industries in advance? Are they better equipped to discover these industries than private investors? Also, unless the infant industries have a domestic market that is large enough to attain economies of scale that make them cost-competitive on world markets, the government may have to protect the industries into old age.
Economies and Diseconomies of Scale
The LRAC curve in Figure 8.6 is U-shaped. This shape means that, at first, as plant size and firm output increase, long-run average costs fall. After a certain point (Point A on Figure 8.6), however, bigness becomes costly. As the plant continues to increase in size, average cost begins to rise. Economists refer to these changes in long-run average cost due to increased plant size as economies and diseconomies of scale. Economies of scale are declines in long-run average cost that are due to increased plant size. Diseconomies of scale are increases in long-run average cost that are due to increased plant size. As scale (plant size) increases, economies (cost savings) result. After a while, further growth results in diseconomies (higher average costs).
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Section 8.3 Cost in the Long Run CHAPTER 8
Economies and diseconomies of scale are distinct from increasing and decreasing returns. Increasing and decreasing returns are the result of using a given size plant more or less intensively in the short run. Economies and diseconomies of scale result from changes in the size of a plant in the long run.
It is easy to see how economies of scale result from an increase in plant size. As a firm increases its scale of operations, it usually can employ more specialized machinery. Also, jobs can be more specialized. Equipment can be used more efficiently. By-products of the operation that might be uneconomical to recover or exploit in a small-scale plant may become economical for a large operation. A large firm is often able to obtain quantity dis- counts on intermediate products from other firms. Political influence that has economic value is also more likely to accrue to a large, rather than a small, firm. These are just a few of the reasons for the negative slope of the LRAC curve as the scale of operations increases.
Diseconomies of scale are slightly harder to grasp. However, they are familiar to anyone who has dealt with giant bureaucracies, public or private. Diseconomies result from the fact that as an organization becomes very large, communication and coordination become more difficult and time consuming, and control from the top diminishes. After a firm has taken advantage of the gains to be achieved by growing larger, it becomes more difficult for upper management to monitor production activity and easier for some workers to shirk. With further growth, the LRAC curve turns upward.
Optimal-Size Plants in the Real World
If you look at real-world industries, you see many different-sized firms operating side by side in the same industry. Steel, for example, is produced by both very large and very small firms. If there is a single, optimal size plant for each industry, why do firms of so many different sizes exist? Economists have spent much time investigating real economies of scale. Several different types of LRAC curves are represented in Figures 8.7, 8.8, and 8.9.
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Section 8.3 Cost in the Long Run CHAPTER 8
Figure 8.7: Economies of scale and a few very large plants
When economies of scale exist over large ranges of output, one large plant or a few large plants are most efficient.
Figure 8.7 shows economies of scale over a large range of output. This situation occurs in the auto industry, where there are a few very large firms. The optimal-size plant in Fig- ure 8.7 is that producing output level Q
1 , which conceivably might represent the normal
sales of the entire industry. In such industries, a natural monopoly can occur. A natural monopoly is a monopoly that emerges because of economies of scale. The size of the mar- ket is such that there is room for only one optimal-size firm. Many public utilities (such as gas and electric companies) need to have all the sales in a market in order to become large enough to be of optimal size.
0
Cost
Output/Time PeriodQ 1
LRAC
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Section 8.3 Cost in the Long Run CHAPTER 8
Figure 8.8: Many optimal-size plants of different sizes
A range of outputs for the optimal-size plant can exist. When this situation exists, plants of distinctly different sizes can all produce efficiently in the same industry.
In Figure 8.8, a large number of plants of different sizes can be of optimal size. Firms in a range of sizes can all produce efficiently in the same industry at the same per-unit (or average) cost. In Figure 8.8, any firm producing an output between Q
1 and Q
2 would be
efficient. If the demand for the product is large enough to support many firms in this size range, a very competitive situation exists. This situation prevails in many industries, such as textiles, publishing, and packaged food products.
0
Cost
Output/Time PeriodQ 2Q 1
LRAC
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Section 8.4 Profit Maximization CHAPTER 8
Figure 8.9: Many optimal-size plants of similar sizes
If there is a unique minimum point on the long-run average cost curve, all the plants in an industry will be similar in size.
Figure 8.9 illustrates an industry in which there are rapidly achievable economies of scale and diseconomies of scale. This kind of LRAC curve occurs when all the firms in an indus- try are of a similar size. The optimal-size plant in Figure 8.9 is the one whose short-run average cost curve hits a minimum point at Q
1 .
The benefit of economies of scale may not be passed along to consumers. Economies of scale mean that it is efficient to have production carried out by large firms. However, these large-scale firms may exert monopoly pricing power so that lower costs are not passed on to consumers in the form of lower prices. We will return to this problem in the chapter on monopoly.
8.4 Profit Maximization
The choice of plant size is one of several decisions that determine a firm’s profits. The firms examined here and in the next three chapters are all profit-maximizing firms. What does profit maximization mean in terms of production decisions? It means that, in the short run, the firm will attempt to choose the output that maximizes
0
Cost
Output/Time PeriodQ 1
LRAC
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Section 8.4 Profit Maximization CHAPTER 8
the difference between total revenue and total cost. Total revenue (TR) is the price an item sells for multiplied by the number of units sold. Marginal revenue (MR) is the change in total revenue from selling one more (or one less) unit.
Profit will be maximized at the level of output at which marginal revenue equals marginal cost, or MR 5 MC. For any output level where marginal revenue is greater than marginal cost (MR . MC), the firm adds to its total profit with each unit sold. For example, if the market-clearing price is $10 and, at output Q
1 , the marginal cost is $8, an additional unit
sold will raise total revenue by $2 more than it will increase marginal costs. At this level of output, with total revenue increasing faster than total cost, it is in the firm’s interest to produce and sell additional output. As long as MR continues to be greater than MC, total revenue will increase faster than total cost, and each additional unit sold will add to the firm’s profit. If, on the other hand, the firm were to reduce output from Q
1 by one unit,
total revenue would be reduced by $10, total cost would decrease by $8, and profit would fall by $2. Therefore, whenever MR is greater than MC, the firm should increase its output and sales to increase profits.
If marginal cost is greater than marginal revenue (MC . MR), an increase in output will cause total costs to increase faster than total revenue. If at output level Q
2 , marginal rev-
enue (the price) is $10 but marginal costs have risen to $10.50, an additional unit pro- duced would cause the firm’s total costs to rise by more than its total revenue, and profits would be reduced. In that situation, if the firm reduced output by one unit, would cause total costs to fall faster than total revenue, and profit would increase accordingly. When- ever marginal cost is greater than marginal revenue, the firm should reduce production to maximize profits.
To recap, if marginal revenue is greater than marginal cost, the firm should expand produc- tion and sales. If marginal cost is greater than marginal revenue, the firm should decrease production and sales. At the point at which marginal revenue and marginal cost are equal, it would be unprofitable to either increase or decrease production. The decision rule for profit maximization, then, is to produce that level of output at which marginal revenue equals marginal cost (MR 5 MC). This rule is just another way of saying, “Produce where total profit is at its maximum,” or, “Produce where total revenue exceeds total cost by the largest amount.” Generally, the MR 5 MC rule is the most convenient to work with.
It’s easy to see this relationship on a graph. In Figure 8.10, the price is fixed by the market; the firm is able to sell all of its output at this price. Thus, the total revenue (TR) curve in Figure 8.10(a) is a straight line from the origin. The marginal revenue (MR) curve in panel (b) is a horizontal line at the level of the price of the product. The total cost (TC) curve is consistent with the law of diminishing returns beyond output level Q
1 . (From zero output
to Q 2 the TC curve represents decreasing average costs.) The vertical distance between TR
and TC is greatest at output level Q 2 . At that point the slopes of TR and TC are equal. The
slope of TR is MR, and the slope of TC is MC. Thus, it is clear that MR 5 MC at output level Q
2 , as can be seen in panel (b). Note that if output were decreased below Q
2 , MC would
fall below MR, and TR would fall by more than TC. Thus, profit would fall. If output were increased above Q
2 , TC would increase more than TR, and MC would be above MR.
Again, profit would fall. Profit is at a maximum at Q 2 .
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Section 8.4 Profit Maximization CHAPTER 8
Figure 8.10: Profit maximization
Profit is maximized where marginal cost is equal to marginal revenue. The vertical distance between total revenue (TR) and total cost (TC) is greatest in panel (a) at Q
2 , the same level of output where
marginal cost (MC) equals marginal revenue (MR) in panel (b).
The decision to produce that output where marginal revenue equals marginal cost will come up again and again, so it is important to make sure you understand it. It will always be true that maximum profit will be obtained by operating at the point where MR 5 MC, as long as the firm stays in business.
0
Cost
(a)
Output and Sales/ Time Period
TRTC
MC
MR = Price
0
Cost
(b)
Output and Sales/ Time Period
Q 1 Q 2
Q 1 Q 2
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Section 8.4 Profit Maximization CHAPTER 8
Policy Focus: State Gambling For many years the only state in the United States that legalized gambling to generate tax revenue was Nevada. However, in recent years most states have legalized or at least discussed the legalization of cer- tain forms of gambling. When the idea is to generate revenue for public projects, the most common form of sanctioned gambling is a state-run lottery. It has even been suggested that the federal government run a lottery and use the profits to retire the federal debt! State governments usually earmark the pro- ceeds from a lottery for some special purpose—most commonly, education.
In 2010, 43 states had state-run lottery operations. The lottery generated net revenue of over $53 billion for the states. This rapidly growing source of revenue takes some pressure off taxes as a source of funds for state projects. In the 1980s alone, state revenue from lotteries grew almost 1,000%. Some of this growth came from the expansion of lottery activ- ity. In 1980, only 14 states had lotteries; by 1990, the number had grown to 33, and 10 more states joined by 2010 (National Conference of State Legislatures, 2010).
Some people feel that lotteries are a very regressive form of tax because the poor spend a higher percentage of their income in buying lottery tickets. Others, who support the lottery concept, argue that a lottery ticket is a voluntary purchase. Thus, a lottery cannot be viewed as a tax because people purchase the tickets of their own free will. Some advocates point out that people are going to gamble anyway, so the state might as well get involved and make some profit to do “good things,” such as spending more on education. However, the odds in state lotteries are much poorer than in other games of chance. Although states spend roughly $3 billion in administrative costs to run the lottery, the states still keep an average of 32 percent of lottery bets (National Conference of State Legisla- tures, 2010). That percentage is much higher than the “house share” in casino gambling or off-track betting. In addition, large winnings are usually paid in installments over 10 to 26 years, and not all at once, unless winners are willing to take a “cash option” of 45 to 55 percent of the jackpot.
In many states, the newspapers on Sunday morning still carry a headline about the latest million- aire created by the lucky lottery drawing on Saturday night. The scene usually goes something like this: The newspaper reports that a local teacher, Margaret, was the winner of a $6 million jackpot. “It hasn’t hit me yet,” she says, smiling broadly under the brim of a new lottery baseball cap. “But I wouldn’t know what to do if I quit my job. I like to work.” (continued)
iStockphoto/Thinkstock
In recent years most states have legalized or discussed legalization of certain forms of gambling. But for many years the only state with legalized gambling was Nevada, which used gambling to generate tax revenue.
Check Point: Rules for Profit Maximization
• MR . MC Expand output. • MR 5 MC Profits maximized, leave output unchanged. • MR , MC Reduce output.
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Summary CHAPTER 8
Policy Focus: State Gambling (continued) Let’s consider the real value of Margaret’s winnings, pretending that she won the MEGA Millions jackpot in the California State Lottery. First, if Margaret chose the default option, she would not receive her $6 million all at once. Instead, she would receive 26 equal annual installments. If she chose the cash option, she would be paid now, but not $6 million. She would receive the cash that would have been invested by the state in order to provide 26 annual payments, which is around 50 percent of the total jackpot (California State Lottery, 2012).
Assuming that Margaret opts for the cash option of $3 million, she still has to settle up with her tax obligations. Lucky for Margaret, lottery prizes are exempt from California state and local personal income taxes! However, the Internal Revenue Service still expects the federal government to receive its share of the winnings. Based on Margaret’s resident status, the California Lottery must with- hold between 25 and 30 percent in federal income taxes. She may even have additional tax liability, depending on her financial situation.
At this point, Margaret is now down to roughly $2.25 million, or 37.5 percent of what the headlines reported. This is still a very nice prize, and most of us would be thrilled to be in her boots. But Mar- garet is only 40 years old and plans to live to the ripe old age of 80, so perhaps it is a good thing that Margaret “likes to work.”
Summary
Consider again. . . We may find a partial answer to the exit of over a hundred firms from the airline industry in the concept of economies and diseconomies of scale. Smaller airlines could not reach the size economies that are needed to spread some costly expenditures over large numbers of passengers. The first cost that can be spread is the cost of flight frequency. Most business passengers prefer frequent flights in order to accommodate schedule changes. If you are a business traveler, you prefer an airline that flies ten flights a day between two cities over an airline that has only two flights per day. The convenience of the more frequent flights is a cost to the airline. A second cost is the expense of maintaining sophisticated reservation systems and customer service phone lines that are well staffed. Travelers want easy access to flight information and prices and do not want to be put on hold or face other types of inconvenience when they need assis- tance. Finally, smaller airlines could not offer enough service to establish “hub and spoke” service systems. In fact, most of the small carriers that were taken over by the major air- lines were the “spoke” airlines, flying into “hubs.” When these airlines were purchased, the service that they provided was available at lower cost because the larger carrier was able to take advantage of economies of scale. As long as economies of scale are still avail- able, the airlines may continue to merge, and American Airlines could be next.
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Key Terms CHAPTER 8
Key Points
1. Economists calculate both implicit and explicit costs of production. Implicit costs are those costs implied by alternatives given up. Explicit costs are money expen- ditures, or accounting costs. When total cost (both implicit and explicit costs) is equal to total revenue, economists say there is zero economic profit. This means the firm is covering all economic costs, including a normal profit. When costs exceed revenues, firms and resources will leave an industry in order to earn the opportunity cost associated with those resources.
2. In the short run, as variable inputs are added to the fixed inputs, the firm may experience increasing returns at low levels of output. Eventually, the firm will incur diminishing returns at some higher levels of output.
3. The U shape of the long-run average cost (LRAC) curve is due to economies and diseconomies of large-scale production.
4. Profit maximization means that an entrepreneur will produce that level of output that equates marginal cost and marginal revenue. Profits are the greatest when total revenue exceeds total cost by the largest possible amount.
Key Terms
accounting profit The difference between total revenue and explicit costs.
average fixed cost (AFC) Total fixed costs of production divided by number of units of output.
average total cost (ATC) Total costs of producing a level of output divided by the number of units of output.
average variable cost (AVC) Total variable costs of production divided by the number of units of output.
diseconomies of scale Increases in long- run average cost that are due to increased plant size.
economic profit The difference between total revenue and the total of explicit and implicit costs of producing.
economies of scale Declines in long-run average cost that are due to increased plant size.
long-run average cost (LRAC) curve A curve tangent to all the possible short-run cost curves and representing the lowest attainable average cost of producing any given output.
marginal cost (MC) The change in total cost from producing one more (or one less) unit of output.
marginal revenue (MR) The change in total revenue from selling one more (or one less) unit.
natural monopoly A monopoly that emerges because economies of scale mean that there is room for only one firm in that market.
normal profit The opportunity cost of capital and enterprise, or the rate of return that is necessary for a firm to remain in a competitive industry.
optimal-size plant The plant represented by the short-run average cost curve with the lowest attainable per-unit costs.
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Critical Thinking and Discussion Questions CHAPTER 8
planning curve The long-run average cost curve used in the planning stage.
total cost (TC) The sum of all the costs of production for a given level of output.
total fixed costs (TFC) The costs of the fixed inputs of production, which can’t be avoided in the short run.
total variable costs (TVC) The total of costs that vary directly with the level of output, increasing as more output is produced.
Critical Thinking and Discussion Questions
1. Why are cost curves normally U-shaped in the long run? Are they U-shaped in the short run for the same reason?
2. How does accounting profit differ from economic profit? 3. What is normal profit? Why is it important for a firm to earn at least normal
profit in the long run? 4. What is the difference between diminishing returns and diseconomies of scale? 5. What occurs when marginal cost equals marginal revenue? Why is this
important? 6. ECON CORP produces Widgets for everyday use. The total cost schedule is
given in the table below. In the table, TFC is total fixed cost, TVC is total variable cost, AFC is average fixed cost, AVC is average variable cost, ATC is average total cost. Complete the table.
Widgets (per day)
Total cost (dollars)
TFC TVC AFC AVC ATC
0 $12
1 $20
2 $26
3 $30
4 $32
7. How can you discern from the table in Question 6 that the total fixed cost (TFC) is equal to $12?
8. Calculate the marginal cost for each Widget in Question 6. How does the mar- ginal cost compare to the average total cost for each quantity?
9. Graph the values of AFC, AVC, ATC, and MC using the completed table in Ques- tion 6.
10. Why does marginal cost intersect average variable cost and average total cost at their minimum?
11. There is a famous statement that claims, “There is no such thing as a free lunch.” Based on the concepts in this chapter, what does this mean in terms of opportu- nity cost?
12. At what size do universities start experiencing diseconomies of scale? What does the existence of many different sizes of universities indicate about the optimal size?
13. What is the length of time that distinguishes between short- and long-run costs? Can it be different for different firms? Provide an example.
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Critical Thinking and Discussion Questions CHAPTER 8
14. What is the infant industry argument? How has it been used by the United States in the past?
15. There are many issues that governments face when determining whether or not to regulate a natural monopoly. Provide an example of a natural monopoly and describe how it could be regulated.
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