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(BQ) Part 2 book Economics today has contents: Perfect competition, monopolistic competition, oligopoly and strategic behavior, regulation and antitrust policy in a globalized economy, environmental economics, comparative advantage and the open economy, exchange rates and the balance of payments,...and other contents.
22 The Firm: Cost and Output The last commercial nuclear reactor plant built in the United States was completed in 1996 Since then, most media reports have suggested that concerns about safety and waste disposal have prevented energy firms from constructing additional nuclear power plants In fact, the economics of electricity generation has probably been more important in dissuading electric companies from building more nuclear plants During the late 1990s and the 2000s, energy firms found lower-cost ways of generating additional electricity using traditional power plants Hence, they had less incentive to undertake the significant expenditures required to build nuclear plants In contrast, recent technological developments in nuclear power generation may induce energy firms to start building electricity-generating nuclear reactors once again To understand why this is so, you must first study production and cost concepts covered in this chapter LEARNING OBJECTIVES Determination After reading this chapter, you should be able to: ̈ Discuss the difference between the short run and the long run from the perspective of a firm ̈ Understand why the marginal physical product of labor eventually declines as more units of labor are employed ̈ Explain the short-run cost curves a typical firm faces ̈ Describe the long-run cost curves a typical firm faces ̈ Identify situations of economies and diseconomies of scale and define a firm’s minimum efficient scale MyEconLab helps you master each objective and study more efficiently See end of chapter for details 483 484 PART ■ MARKET STRUCTURE, RESOURCE ALLOCATION, AND REGULATION Did You Know That ? the average single-item cash register receipt has grown more than inches longer since 1990? This has happened because most retailers now print additional information on receipts, such as savings from use of reward cards, discount coupons, and information about special offers Retailers have provided receipts since the advent of cash registers in 1884 Recently, however, many companies have determined that they can save hundreds of dollars per store each year if they reduce the amount of paper devoted to receipts.Wal-Mart is testing two-sided receipts, and CVS is using loyalty cards that track customer information instead of printing the data on physical receipts Lowe’s has made its receipts wider to allow for 56 characters per line instead of 38 characters, deleted all white space at the top and bottom of receipts, and put its return policy on the back—all in an effort to use less paper and reduce costs Some retailers, such as Apple, hope to eliminate the expense of paper receipts entirely by encouraging customers to accept electronic receipts sent via e-mail What are the determinants of a company’s expenses? To understand the answer to this question, you must learn about the nature of the costs that firms incur in their productive endeavors, which in turn requires contemplating how firms employ inputs in the production of goods and services.This chapter considers each of these important topics Short Run versus Long Run In Chapter 19, we discussed short-run and long-run price elasticities of supply and demand As you will recall, for consumers, the long run means the time period during which all adjustments to a change in price can be made, and anything shorter than that is considered the short run For suppliers, the long run is the time in which all adjustments can be made, and anything shorter than that is the short run Now that we are discussing firms only, we will maintain a similar distinction between the short and the long run, but we will be more specific The Short Run Short run The time period during which at least one input, such as plant size, cannot be changed Plant size The physical size of the factories that a firm owns and operates to produce its output Plant size can be defined by square footage, maximum physical capacity, and other physical measures In the theory of the firm, the short run is defined as any time period that is so short that there is at least one input, such as current plant size, that the firm cannot alter In other words, during the short run, a firm makes with whatever big machines and factory size it already has, no matter how much more it wants to produce because of increased demand for its product We consider the plant and heavy equipment, the size or amount of which cannot be varied in the short run, as fixed resources In agriculture and in some other businesses, land may be a fixed resource There are, of course, variable resources that the firm can alter when it wants to change its rate of production These are called variable inputs or variable factors of production Typically, the variable inputs of a firm are its labor and its purchases of raw materials In the short run, in response to changes in demand, the firm can, by definition, change only the amounts of its variable inputs The Long Run Long run The time period during which all factors of production can be varied The long run can now be considered the period of time in which all inputs can be varied Specifically, in the long run, the firm can alter its plant size How long is the long run? That depends on each individual industry For Wendy’s or McDonald’s, the long run may be four or five months, because that is the time it takes to add new franchises For a steel company, the long run may be several years, because that’s how long it takes to plan and build a new plant An electric utility might need more than a decade to build a new plant Short run and long run in our discussion are terms that apply to planning decisions made by managers Managers routinely take account of both the short-run and the long-run consequences of their behavior While always making decisions about what to today, tomorrow, and next week—the short run as it were—they keep an eye on the long-run net benefits of all short-run actions As an individual, you have long-run plans, such as going to graduate school or having a successful career, and you make a series of short-run decisions with these long-run plans in mind CHAPTER 22 ■ The Firm: Cost and Output Determination 485 The Relationship Between Output and Inputs A firm takes numerous inputs, combines them using a technological production process, and ends up with an output There are, of course, a great many factors of production, or inputs Keeping the quantity of land fixed, we classify production inputs into two broad categories—capital and labor The relationship between output and these two inputs is as follows: Output per time period = some function of capital and labor inputs We have used the word production but have not defined it Production is any process by which resources are transformed into goods or services Production includes not only making things but also transporting them, retailing, repackaging them, and so on Notice that the production relationship tells nothing about the worth or value of the inputs or the output Production Any activity that results in the conversion of resources into products that can be used in consumption The Production Function: A Numerical Example The relationship between maximum physical output and the quantity of capital and labor used in the production process is sometimes called the production function The production function is a technological relationship between inputs and output PROPERTIES OF THE PRODUCTION FUNCTION The production function specifies the maximum possible output that can be produced with a given amount of inputs It also specifies the minimum amount of inputs necessary to produce a given level of output Firms that are inefficient or wasteful in their use of capital and labor will obtain less output than the production function will show No firm can obtain more output than the production function allows, however The production function also depends on the technology available to the firm It follows that an improvement in technology that allows the firm to produce more output with the same amount of inputs (or the same output with fewer inputs) results in a new production function How are new techniques for utilizing various types of computer software allowing companies to produce more output using the same inputs? EXAMPLE Production function The relationship between inputs and maximum physical output A production function is a technological, not an economic, relationship Virtualization Expands Feasible Production at Many Firms Database management programs, spreadsheets, and media players are examples of application software that firms commonly employ as part of the process of producing goods and services Traditionally, firms have installed such software applications on the hard drives of their computers Today, however, many firms are using a procedure called application virtualization to effectively “fool” the operating system of a computer into running application software even though the software is installed on a different computer Hence, application virtualization frees up disc space on the “fooled” computers that the company can devote to other computing tasks In addition, through application virtualization, an operating system can often be used to run previously incompatible software applications side-by-side on the same computer This allows firms to deploy the same computers and software application programs to complete more production tasks within the same period of time Thus, application virtualization enables firms to produce a larger flow of goods and services per unit of time FOR CRITICAL ANALYSIS Why you suppose that business managers regard the process of developing the best production procedures as a fundamental requirement for operating at an (efficient) point on a firm’s production function? Panel (a) of Figure 22-1 on the next page shows a production function relating maximum output in column to the quantity of labor in column Zero workers per week produce no output Five workers per week of input produce a total output of 50 computer servers per week (Ignore for the moment the rest of that panel.) Panel (b) of Figure 22-1 displays this production function It relates to the short run, because plant size is fixed, and it applies to a single firm 486 PART ■ MARKET STRUCTURE, RESOURCE ALLOCATION, AND REGULATION FIGURE 22-1 The Production Function and Marginal Product: A Hypothetical Case Marginal product is the addition to the total product that results when one additional worker is hired (for a week in this example) Thus, in panel (a), the marginal product of adding the fourth worker is eight computer servers With four workers, 44 servers are produced, but with three workers, only 36 are produced The difference is In panel (b), we plot the numbers from columns and of panel (a) In panel (c), we plot the numbers from columns and of panel (a) When we go from to 1, marginal product is 10 When we go from one worker to two workers, marginal product increases to 16 After two workers, marginal product declines, but it is still positive Total product (output) reaches its peak at about seven workers, so after seven workers, marginal product is negative When we move from seven to eight workers, marginal product becomes Ϫ1 computer server per week Panel (b) (1) (2) Input of Labor (number of workerweeks) Total Product (output in computer servers per week) — (3) Average Physical Product (total product ÷ number of workerweeks) [servers per week] (4) Marginal Physical Product (output in servers per week) Total Output (computer servers per week) Panel (a) — 10 10.00 26 13.00 36 12.00 44 11.00 50 10.00 54 9.00 40 20 10 60 Labor Input (worker-weeks) 10 11 16 Panel (c) 56 8.00 55 6.88 53 5.89 –1 –2 Marginal Physical Product (computer servers per week) 10 20 15 10 –3 10 50 5.00 11 46 4.18 –4 Labor Input (worker-weeks) 10 11 TOTAL PHYSICAL PRODUCT Panel (b) shows a total physical product curve, or the maximum feasible output when we add successive equal-sized units of labor while holding all other inputs constant The graph of the production function in panel (b) is not a straight line It peaks at about seven workers per week and then starts to go down Average physical product Total product divided by the variable input Marginal physical product The physical output that is due to the addition of one more unit of a variable factor of production The change in total product occurring when a variable input is increased and all other inputs are held constant It is also called marginal product Average and Marginal Physical Product To understand the shape of the total physical product curve, let’s examine columns and of panel (a) of Figure 22-1 above—that is, average and marginal physical products Average physical product is the total product divided by the number of worker-weeks You can see in column of panel (a) of Figure 22-1 that the average physical product of labor first rises and then steadily falls after two workers are hired Marginal means “additional,” so the marginal physical product of labor is the change in total product that occurs when a worker is added to a production process for a given interval (The term physical here emphasizes the fact that we are measuring in terms of CHAPTER 22 ■ The Firm: Cost and Output Determination 487 material quantities of goods or tangible amounts of services, not in dollar terms.) The marginal physical product of labor therefore refers to the change in output caused by a one-unit change in the labor input as shown in column of panel (a) of Figure 22-1 on the facing page (Marginal physical product is also referred to as marginal product.) Diminishing Marginal Product Note that in Figure 22-1, when three workers instead of two are employed each week, marginal product declines The concept of diminishing marginal product applies to many situations If you put a seat belt across your lap, a certain amount of safety is obtained If you add another seat belt over your shoulder, some additional safety is obtained, but less than when the first belt was secured When you add a third seat belt over the other shoulder, the amount of additional safety obtained is even smaller Measuring Diminishing Marginal Product How we measure diminishing marginal product? First, we limit the analysis to only one variable factor of production (or input)—let’s say the factor is labor Every other factor of production, such as machines, must be held constant Only in this way can we calculate the marginal product from adding more workers and know when we reach the point of diminishing marginal product SPECIALIZATION AND MARGINAL PRODUCT The marginal productivity of labor may increase rapidly at the very beginning A firm starts with no workers, only machines The firm then hires one worker, who finds it difficult to get the work started But when the firm hires more workers, each is able to specialize in performing different tasks, and the marginal product of those additional workers may actually be greater than the marginal product of the previous few workers DIMINISHING MARGINAL PRODUCT Beyond some point, diminishing marginal product must set in—not because new workers are less qualified but because each worker has, on average, fewer machines with which to work (remember, all other inputs are fixed) In fact, eventually the firm’s plant will become so crowded that workers will start to get in each other’s way At that point, marginal physical product becomes negative, and total production declines Using these ideas, we can define the law of diminishing marginal product: As successive equal increases in a variable factor of production are added to fixed factors of production, there will be a point beyond which the extra, or marginal, product that can be attributed to each additional unit of the variable factor of production will decline Note that the law of diminishing marginal product is a statement about the physical relationships between inputs and outputs that we have observed in many firms If the law of diminishing marginal product were not a fairly accurate statement about the world, what would stop firms from hiring additional workers forever? An Example of the Law of Diminishing Marginal Product Production of computer servers provides an example of the law of diminishing marginal product With a fixed amount of factory space, assembly equipment, and quality-control diagnostic software, the addition of more workers eventually yields successively smaller increases in output After a while, when all the assembly equipment and quality-control diagnostic software are being used, additional workers will have to start assembling and troubleshooting quality problems manually They obviously won’t be as productive as the first workers, who had access to other productive inputs The marginal physical product of an additional worker, given a specified amount of capital, must eventually be less than that for the previous workers Law of diminishing marginal product The observation that after some point, successive equal-sized increases in a variable factor of production, such as labor, added to fixed factors of production will result in smaller increases in output 488 PART ■ MARKET STRUCTURE, RESOURCE ALLOCATION, AND REGULATION GRAPHING THE MARGINAL PRODUCT OF LABOR A hypothetical set of numbers illustrating the law of diminishing marginal product is presented in panel (a) of Figure 22-1 on page 486 The numbers are presented graphically in panel (c) Marginal productivity (returns from adding more workers during a week) first increases, then decreases, and finally becomes negative When one worker is hired, total output goes from to 10 Thus, marginal physical product is 10 computer servers per week When two workers instead of one are hired, total product goes from 10 to 26 servers per week Marginal physical product therefore increases to 16 servers per week When three workers rather than two are hired, total product again increases, from 26 to 36 servers per week This represents a marginal physical product of only 10 servers per week Therefore, the point of diminishing marginal product occurs after two workers are hired THE POINT OF SATURATION Notice that after seven workers per week, marginal physical product becomes negative That means that eight workers instead of seven would reduce total product Sometimes this is called the point of saturation, indicating that given the amount of fixed inputs, there is no further positive use for more of the variable input We have entered the region of negative marginal product QUICK QUIZ See page 506 for the answers Review concepts from this section in MyEconLab The technological relationship between output and inputs is called the function It relates per time period to several inputs, such as capital and labor After some rate of output, the firm generally experiences diminishing marginal The law of diminishing marginal product states that if all factors of production are held constant except one, equal increments in that one variable factor will eventually yield increments in Short-Run Costs to the Firm Total costs The sum of total fixed costs and total variable costs You will see that costs are the extension of the production ideas just presented Let’s consider the costs the firm faces in the short run To make this example simple, assume that there are only two factors of production, capital and labor Our definition of the short run will be the time during which capital is fixed but labor is variable In the short run, a firm incurs certain types of costs We label all costs incurred total costs Then we break total costs down into total fixed costs and total variable costs, which we will explain shortly Therefore, Total costs (TC) = total fixed costs (TFC) + total variable costs (TVC) Remember that these total costs include both explicit and implicit costs, including the normal rate of return on investment After we have looked at the elements of total costs, we will find out how to compute average and marginal costs Total Fixed Costs Let’s look at an ongoing business such as Hewlett-Packard (HP) The decision makers in that corporate giant can look around and see big machines, thousands of parts, huge buildings, and a multitude of other components of plant and equipment that have already been bought and are in place HP has to take into account expenses to replace some worn-out equipment, no matter how many digital devices it produces The opportunity costs of any fixed resources that HP owns will all be identical, regardless of the rate of output In the short run, these costs are the same for HP no matter how many digital devices it produces CHAPTER 22 ■ The Firm: Cost and Output Determination We also have to point out that the opportunity cost (or normal rate of return) of capital must be included along with other costs Remember that we are dealing in the short run, during which capital is fixed This leads us to a very straightforward definition of fixed costs: All costs that not vary—that is, all costs that not depend on the rate of production—are called fixed costs Let’s now take as an example the fixed costs incurred by a producer of titanium batteries used with digital cameras, computer accessories, and other devices This firm’s total fixed costs will usually include the cost of the rent for its plant and equipment and the insurance it has to pay We see in panel (a) of Figure 22-2 on the next page that total fixed costs per hour are $10 In panel (b), these total fixed costs are represented by the horizontal line at $10 per hour They are invariant to changes in the daily output of titanium batteries—no matter how many are produced, fixed costs will remain at $10 per hour 489 Fixed costs Costs that not vary with output Fixed costs typically include such expenses as rent on a building These costs are fixed for a certain period of time (in the long run, though, they are variable) Total Variable Costs Total variable costs are costs whose magnitude varies with the rate of production Wages are an obvious variable cost The more the firm produces, the more labor it has to hire Therefore, the more wages it has to pay Parts are another variable cost To manufacture titanium batteries, for example, titanium must be bought The more batteries that are made, the more titanium that must be bought A portion of the rate of depreciation (wear and tear) on machines that are used in the assembly process can also be considered a variable cost if depreciation depends partly on how long and how intensively the machines are used Total variable costs are given in column in panel (a) of Figure 22-2 These are translated into the total variable cost curve in panel (b) Notice that the total variable cost curve lies below the total cost curve by the vertical distance of $10 This vertical distance of course, represents, total fixed costs Why Not Variable costs Costs that vary with the rate of production They include wages paid to workers and purchases of materials force firms to reduce their fixed and, hence, total costs by cutting their energy use? The level of energy that firms use in their operations usually cannot be adjusted in the short run, so firms’ energy expenses are fixed costs.Thus, if firms were to find ways to operate using less energy, their fixed costs would fall Nevertheless, requiring companies to cut back on their use of short-run energy would not necessarily reduce their total costs.The reason is that current levels of energy use already reflect firms’ efforts to balance inputs in a way that minimizes total costs If firms were forced to cut back on energy utilization, then overall cost minimization could require them to increase their use of labor or other variable inputs to maintain their output rates, which would cause their variable costs to increase.Therefore, it is possible that requiring firms to reduce energy expenses could, on net, raise their total costs Short-Run Average Cost Curves In panel (b) of Figure 22-2 on the next page, we see total costs, total variable costs, and total fixed costs Now we want to look at average cost With the average cost concept, we are measuring cost per unit of output It is a matter of simple arithmetic to figure the averages of these three cost concepts We can define them as follows: Average total costs (ATC) = Average variable costs (AVC) = Average fixed costs (AFC) = total costs (TC) output (Q) total variable costs (TVC) output (Q) total fixed costs (TFC) output (Q) You Are There To contemplate why higher variable costs depressed profits of firms that specialize in repossessing vehicles, even though the demand for their services increased during the recent economic downturn, read During Hard Times for Borrowers, a Repo Man Also Has It Tough, on page 501 490 PART ■ MARKET STRUCTURE, RESOURCE ALLOCATION, AND REGULATION FIGURE 22-2 Cost of Production: An Example In panel (a), the derivations of columns through are given in parentheses in each column heading For example, in column 6, average variable costs are derived by dividing column 3, total variable costs, by column 1, total output per hour Note that marginal cost (MC) in panel (c) intersects average variable costs (AVC) at the latter’s minimum point Also, MC intersects average total costs (ATC) at that latter’s minimum point It is a little more difficult to see that MC equals AVC and ATC at their respective minimum points in panel (a) because we are using discrete one-unit changes You can see, though, that the marginal cost of going from units per hour to units per hour is $2 and increases to $3 when we move to units per hour Somewhere in between it equals AVC of $2.60, which is in fact the minimum average variable cost The same analysis holds for ATC, which hits its respective minimum at units per day at $4.28 per unit MC goes from $4 to $5 and just equals ATC somewhere in between Panel (a) (1) (2) (3) (4) (5) (6) (7) (8) (9) Total Output (Q/hour) Total Fixed Costs (TFC) Total Variable Costs (TVC) Total Costs (TC) (4) = (2) + (3) Average Fixed Costs (AFC) (5) = (2) –: (1) Average Variable Costs (AVC) (6) = (3) –: (1) Average Total Costs (ATC) (7) = (4) –: (1) Total Costs (TC) (4) Marginal Cost (MC) Change in (8) (9) = Change in (1) $10 $ $10 — — — $10 10 15 $10.00 $5.00 $15.00 15 10 18 5.00 4.00 9.00 18 10 10 20 3.33 3.33 6.67 20 10 11 21 2.50 2.75 5.25 21 10 13 23 2.00 2.60 4.60 23 10 16 26 1.67 2.67 4.33 26 10 20 30 1.43 2.86 4.28 30 10 25 35 1.25 3.12 4.38 35 10 31 41 1.11 3.44 4.56 41 10 10 38 48 1.00 3.80 4.80 48 11 10 46 56 91 4.18 5.09 56 $5 2 Panel (b) Panel (c) Total Costs (dollars per hour) Total costs 50 40 30 Total variable costs 20 10 Total fixed costs 10 11 Output (titanium batteries per hour) Costs (dollars per titanium battery) 16 60 14 12 10 MC ATC AVC AFC 10 11 Output (titanium batteries per hour) CHAPTER 22 ■ The Firm: Cost and Output Determination 491 The arithmetic is done in columns 5, 6, and in panel (a) of Figure 22-2 on the facing page The numerical results are translated into a graphical format in panel (c) Because total costs (TC) equal variable costs (TVC) plus fixed costs (TFC), the difference between average total costs (ATC) and average variable costs (AVC) will always be identical to average fixed costs (AFC) That means that average total costs and average variable costs move together as output expands Now let’s see what we can observe about the three average cost curves in Figure 22-2 AVERAGE FIXED COSTS (AFC) Average fixed costs continue to fall throughout the output range In fact, if we were to continue panel (c) of Figure 22-2 farther to the right, we would find that average fixed costs would get closer and closer to the horizontal axis That is because total fixed costs remain constant As we divide this fixed number by a larger and larger number of units of output, the resulting AFC becomes smaller and smaller In business, this is called “spreading the overhead.” AVERAGE VARIABLE COSTS (AVC) We assume a particular form of the curve for average variable costs The form that it takes is U-shaped: First it falls; then it starts to rise (It is possible for the AVC curve to take other shapes in the long run.) AVERAGE TOTAL COSTS (ATC) This curve has a shape similar to that of the AVC curve Nevertheless, it falls even more dramatically in the beginning and rises more slowly after it has reached a minimum point It falls and then rises because average total costs are the vertical summation of the AFC curve and the AVC curve Thus, when AFC and AVC are both falling, ATC must fall too At some point, however, AVC starts to increase while AFC continues to fall Once the increase in the AVC curve outweighs the decrease in the AFC curve, the ATC curve will start to increase and will develop a U shape, just like the AVC curve How has the U.S military reduced the average total costs of developing and producing electronic weapons systems? POLICY EXAMPLE Average fixed costs Total fixed costs divided by the number of units produced Average variable costs Total variable costs divided by the number of units produced Average total costs Total costs divided by the number of units produced; sometimes called average per-unit total costs Pulling New Weapons off the Computer Games Shelf In recent years, the U.S military has procured thousands of everyday electronic products, including Sony PlayStation and Microsoft Xbox consoles, Panasonic Toughbook computers, and Apple iPods, iPhones, and iPads The U.S military uses these everyday electronic gadgets to assist in developing new weapons In the past, the creation of new weapons technologies required new types of computer hardware specifically geared to military purposes In recent years, however, computing technologies have advanced so rapidly that “new” military computer hardware has been outdated by the time it has been developed Weapons developers have found that by employing components from electronic gadgets produced by firms such as Sony, Microsoft, and Apple, they can incorporate the most up-to-date computing technologies The developers have also found that the costs incurred in developing weapons are reduced if they use the latest equipment produced by commercial firms The costs incurred in producing each additional unit of military hardware, such as robotic reconnaissance vehicles, are also lower when readily available products are utilized as components Thus, employing electronic products available to anyone—friend and foe alike—has reduced average total costs incurred in designing and producing new military hardware FOR CRITICAL ANALYSIS Has the U.S military’s use of widely available electronic products reduced its average fixed costs, its average variable costs, or both? Explain Marginal Cost We have stated repeatedly that the basis of decisions is always on the margin— movement in economics is always determined at the margin This dictum also holds true within the firm Firms, according to the analysis we use to predict their behavior, are very concerned with their marginal costs Because the term marginal means “additional” or “incremental” (or “decremental,” too) here, marginal costs refer to costs that result from a one-unit change in the production rate For example, if the Marginal costs The change in total costs due to a one-unit change in production rate 492 PART ■ MARKET STRUCTURE, RESOURCE ALLOCATION, AND REGULATION production of 10 titanium batteries per hour costs a firm $48 and the production of 11 of these batteries costs $56 per hour, the marginal cost of producing 11 rather than 10 batteries per hour is $8 Marginal costs can be measured by using the formula Marginal cost = change in total cost change in output We show the marginal costs of production of titanium batteries per hour in column of panel (a) in Figure 22-2 on page 490, computed according to the formula just given In our example, we have changed output by one unit every time, so the denominator in that particular formula always equals one This marginal cost schedule is shown graphically in panel (c) of Figure 22-2 Just like average variable costs and average total costs, marginal costs first fall and then rise The U shape of the marginal cost curve is a result of increasing and then diminishing marginal product At lower levels of output, the marginal cost curve declines The reasoning is that as marginal physical product increases with each addition of output, the marginal cost of this last unit of output must fall Conversely, when diminishing marginal product sets in, marginal physical product decreases (and eventually becomes negative) It follows that the marginal cost must rise when the marginal product begins its decline These relationships are clearly reflected in the geometry of panels (b) and (c) of Figure 22-2 In summary: As long as marginal physical product rises, marginal cost will fall When marginal physical product starts to fall (after reaching the point of diminishing marginal product), marginal cost will begin to rise The Relationship Between Average and Marginal Costs Let us now examine the relationship between average costs and marginal costs There is always a definite relationship between averages and marginals Consider the example of 10 football players with an average weight of 250 pounds An eleventh player is added His weight is 300 pounds That represents the marginal weight What happens now to the average weight of the team? It must increase That is, when the marginal player weighs more than the average, the average must increase Likewise, if the marginal player weighs less than 250 pounds, the average weight will decrease AVERAGE VARIABLE COSTS AND MARGINAL COSTS There is a similar relationship between average variable costs and marginal costs When marginal costs are less than average costs, the latter must fall Conversely, when marginal costs are greater than average costs, the latter must rise When you think about it, the relationship makes sense The only way average variable costs can fall is if the extra cost of the marginal unit produced is less than the average variable cost of all the preceding units For example, if the average variable cost for two units of production is $4.00 a unit, the only way for the average variable cost of three units to be less than that of two units is for the variable costs attributable to the last unit—the marginal cost—to be less than the average of the past units In this particular case, if average variable cost falls to $3.33 a unit, total variable cost for the three units would be three times $3.33, or almost exactly $10.00 Total variable cost for two units is two times $4.00 (average variable cost), or $8.00 The marginal cost is therefore $10.00 minus $8.00, or $2.00, which is less than the average variable cost of $3.33 A similar type of computation can be carried out for rising average variable costs The only way average variable costs can rise is if the average variable cost of additional units is more than that for units already produced But the incremental cost is the marginal cost In this particular case, the marginal costs have to be higher than the average variable costs ... 5.00 4.00 9.00 18 10 10 20 3.33 3.33 6.67 20 10 11 21 2. 50 2. 75 5 .25 21 10 13 23 2. 00 2. 60 4.60 23 10 16 26 1.67 2. 67 4.33 26 10 20 30 1.43 2. 86 4 .28 30 10 25 35 1 .25 3. 12 4.38 35 10 31 41 1.11... MyEconLab Study Plans 22 .2, 22 .3 • Animated Figure 22 -1 KEY FIGURE Figure 22 -2, 490 • MyEconLab Study Plans 22 .4, 22 .5 • Animated Figure 22 -2 • Video: Short-Run Costs to the Firm • Economics Video:... FIGURES Figure 22 -5, 498 Figure 22 -6, 500 • MyEconLab Study Plans 22 .7, 22 .8 • Animated Figures 22 -5, 22 -6 • Video: Reasons for Economies of Scale • Economics Video: No Smoking Employees • Economics