Daniel l. Rubinfeld

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206 Part 2 Producers, Consumers, and Competitive Markets Chapter 7 The Cost of Production 207 total cost (TC or C) Total economic cost of production, consisting of fixed and variable costs. fixed cost (FC) Cost that does not vary with the level of output variable cost (VC) Cost that varies as output varies. began planning the consh'uction of a nev\' building arld needed to decide on an appropriate location. Should it be built on the current site, where it Would remain near downtown Chicago law firms Or should it be moved to Evanston, where it would become physically integrated with the rest of the university The downtown location had many prominent supporters. They argued in part that it was cost-effective to locate the new building in the city because the university already m·vned the land. A large parcel of land would haye to be purchased in Evanston if the building were to be built there. Does this argument make economic sense No. It makes the common mistake of failing to appreciate opporhmity costs. From an economic point of view, it is very expensive to locate downtown because the opportunity cost of the valuable lakeshore location is high: that property could have been sold for enough money to buy the Eyanston land with substantial hmds left over. In the end, Northwestern decided to keep the law school in Chicago. This was a costly decision. It may have been appropriate if the Chicago location was particularly valuable to the law school, but it was inappropriate if it was made on the presumption that the downtown land 'was without cost. Fixed Costs and Variable Costs Some of the firm's costs vary with output, while others remain unchanged as long as the firm is producing any output at all. This distinction will be im.portant when we examine the firm's profit-maximizing choice of output in the next chapter. We therefore divide total cost (TC, or C)-the total economic cost of production-into two components: II Fixed cost (FC): A cost that does not vary with the level of output. II Variable cost (VC): A cost that varies as output varies. Dependino- on circumstances fixed costs may include expendihlres for plant o ' - maintenance, insurance, and perhaps a minimal number of employees. This cost remains the same no matter hmv much output the firm produces. Variable cost, v\,hich includes expenditures for ,,,'ages, salaries, and raw materials, increases as output increases. . . Fixed cost does not vary with the level of output-it must be pald e\'en if there is no output. Tile ollly ~uay tizat a finn ({In elimillate its fixed costs is by goiilg out of business. . Which costs are variable and which are fixed depends on the time horizon that vve are considering. Over a very short time horizon-say, one or tW months-most costs are fixed. Over such a short period, a firm is typically obl1- o-ated to receive and pay for contracted shipments of materials and Calmot easily o· h layoff workers. On the other hand, over a long time horizon-say two or tree v~ars-many costs become variable. Over a long time horizon, if the fiml wants to reduce its-output, it can reduce its workforce, purchase less raw material, and perhaps even sell off some of its capital. When a firm plans a chano-e in its operations, it usually wants to know how that change will affect its cost~. Consider, for example, a problem Delta Air Lines faced recently. Delta 'wanted to know how its costs would change if it reduced the number of its scheduled flights by 10 percent. The answer depends on whether we are considering the short run or the long run. Over the short l'un- say six months-schedules are fixed and it is difficult to layoff or discharge workers. As a result, most of Delta's short-run costs are fixed and won't be reduced significantly with the flight reduction. In the long run-say two years or more-the situation is quite different. Delta has sufficient time to sell or lease planes that ar;e not needed ~nd to discharge unneeded wo~ke.r~. In thi.s case, most of Delta s costs are vanable and thus can be reduced slgmflcantly if a 10- percent Hight reduction is put in place. Fixed versus Sunk Costs People often confuse fixed and swlk costs. Fixed costs are costs that are paid by a firm that is in business, regardless of the level of output it produces. Such costs can include, for example, the salaries of the key executives that run the business, and expenses for their office space and support staff. Fixed costs can be avoided if the firm goes out of business-the key executives, for example, will no longer be needed. Sunk costs, on the other hand, are costs that have been incurred and camlOt be recovered. An example is the cost of a factory 'with specialized equipment that is of no use in another industry. This expenditure is mostly sunk because it cannot be recovered. (Some of the cost might be recoverable if the equipment is sold for scrap.) The cost of the factory and equipment is /lot a fixed cost, because it cannot be recovered even if the firm shuts down. Suppose, on the other hand, that the firm had agreed to make payments into a worker retirement plan as long as the firm was in operation, regardless of its output or its profitability. These payments could cease only if the firm went out of business. In this case, annual payments into the retirement program should be viewed as a fixed cost. A s you progress through this book, you will see that a firm's pricing and production decisions-and its profitability-depend strongly on the structure of its costs. It is therefore important for managers to understand the characteristics of production costs and to be able to identify which costs are fixed, which are variable, and which are smlk. TIle relative si~es of these different cost components can vary considerably across industries. Good examples include the personal computer industry (where most costs are variable), the computer software induShy (where most costs are swlk), and the pizzeria business (where most costs are fixed). Let's look at each of these in rum. Companies like Dell, Gateway, Compaq, and IBM produce millions of personal computers every year. Because the computers they produce are very similar, competition is intense, and profitability depends critically on the ability to keep costs down. Most of these costs are variable-they increase in proportion to the number of computers produced each year. Most important is the cost of components: the microprocessor that does much of the actual computation, memory chips, hard disk drives and other storage devices, video and sound c~rds, etc. Typically, the majority of these components are purchased from out Side suppliers in quantities that depend on the number of computers produced. Another important part of variable cost for these companies is labor, workers are needed to assemble the computers and then to package and ship them. There is little in the wav of swlk costs because the factories cost little relative to the value of the comp~ny's annual output. Likewise, there is little in the
5 :; 208 Part 2 Producers, Consumers, and Competitive Markets 7 The Cost of Production 209 way of fixed costs-perhaps the salaries of the top executives, some security gu~rds, and electricity. Thus, when Dell and Gateway think about ways of reducina cost the" focus laraely on oaettino a better prices for components Or b I) 0 J reducing labor requirements-both of which are ways of reducing yariable cost. What about the software programs that run on these personal com,puters Microsoft produces the Windmvs operating system as well as a \'ariety of applications such as Word, Excel, and PowerPoint. But many other finns_ some large and some small-also produce software programs that run on personal computers. The costs of production for such fin~s are quite different from those facina hardware manufacturers. In sottware production o most costs are sUllk, Typically, a software firm will spend a large amount of money to develop a new application program. These expenditures cannot be recovered. Once the program is completed, the company can try to recoup its investment (and make a profit as well) by selling as many copies of the program as possible. The variable cost of producing copies of the program is very smallit is largely the cost of copying the program to Hoppy disks or CDs and then packaging and shipping the product. Like'wise, the fixed cost of production is smalL Because most costs are sunk, entering the software business can involve considerable risk. Until the development money has been spent and the product has been released for sale, an entrepreneur is unlikely to know how many copies can be sold and whether or not he ,'1'ill be able to make money. Finally, let's turn to your neighborhood pizzeria. For the pizzeria, the largest component of cost is fixed, Sunk costs are fairly low because pizza ovens, chairs, tables, and dishes can be resold if the pizzeria goes out ot business. Variable costs are also fairly low-mainly the ingredients for pizza (Hour, tomato sauce, cheese, and pepperoni for a typical large pizza might cost $1) and perhaps wages for a couple of 'workers to help produce, sen'e, and deliver the pizzas. Most of the cost is fixed-the opportunity cost of the owner's time (he might typically work a 60- or 70-hour week), rent, and utilities. Because of these high fixed costs, most pizzerias (which might charge $10 for a pizza costing about $3 in variable cost to produce) don't make very 7m2 Cost' We begin our detailed analysis of cost with the short-run case. The distinction betvveen fixed and variable costs is important here. To decide how much to produce, managers must know how variable cost increases with the level of output. It will also be helpful to consider some other measures of cost. We will use a specific example that typifies the cost situation of many firms. After we explain eac~ of the cost concepts, we will show how they relate to the analysis in Chapter 6 at the firm's production process, The data in Table 7.1 describe a firm with a fixed cost of $50. Variable cost increases 'with output, as does total cost, which is the sum of the fixed cost in colunTIl 1 and the variable cost in colunu1 2. From the figures given in columns 1 and 2, a number of additional cost variables can be defined. (UNITS PER YEAR) o 2 3 4 5 6 7 8 9 10 11 FIXED COST (DOLLARS PER YEAR) (FC) (1) 50 50 50 50 50 50 50 50 50 50 50 50 VARIABLE COST (DOl.LARS PER YEAR) (VC) (2) 0 50 78 98 112 130 150 175 204 242 300 385 AVERAGE TOTAL MARGINAL FIXED COST COST COST (DOLLARS (DOLLARS (DOLLARS PER YEAR) PER UNIT) PER UNIT) (TC) (MC) (AFC) (3) (4) (5) 50 100 50 50 128 28 25 148 20 16} 162 14 12.5 180 18 10 200 20 8.3 225 25 7J 254 29 6.3 292 38 5.6 350 58 5 435 85 4.5 Marginal cost-sometimes called illcn:lIlclltol cost-is the increase in cost that results from producing one extra unit of output. Because fixed cost does not change as the firm's le\'e! of output changes, rnarginal cost is equal to the increase in yariable cost or the increase in total cost that results from an extra unit of output. We can therefore write marginal cost as MC = ~VC/~Q = STC/~Q Marginal cost te21s us how much it will cost to expand the firm's output by one Ul11t. In Table 1.1, marginal cost is calculated from either the \'ariable cost ~column 2)r the total cost (column 3). For example, the rnarginal cost of increasmg output trom 2 to 3 units is 520 because the \'ariable cost of the firm increases from S78 to 598. (The total cost of production also increases bv 520, from 5128 to 51-18. Total cost differs from \'ariable cost onlv bv the fixed co~t, which bv definition does not change as output changes.) , - - . Average total cost, used interchangeably with WIth llI'cmgc ccollolllic cost, is the firm's total cost di\'ided bv its le\'e! of output, TCIQ. Thus the a\'erage total cost of producina at a rate o{ fi\'e units is 536-:-that is, 5180/5. Basicall;;, ayerage total cost tells u~ the per-unit cost of produCtlOl1. ATC has two components. Average fixed cost is the fixed cost (column 1 of Table 7.1) di\'il~ed by the le\'ei of output, FCIQ.. For example, the a\'e1' age fixed cost ot producing -1 units of output is 512.50 (550/-1). Because fixed cost is constant, a\'erage fixed cost declines as the rate of output increases. AVERAGE AVERAGE VARIABLE TOTAL COST COST (DOLLARS (DOLLARS PER UNIT) PERUNJT) (AVC) (ATC) (6) (7) 50 100 39 64 32.7 49.3 28 40.5 26 36 25 33.3 25 32.1 25.5 31.8 26.9 32.4 30 35 35 39.5 marginal cost (MC) Increase in cost resulting from the production of one extra unit of output average total cost (ATC) Firm's total cost di\'ided b\' its le\'el of output. - average fixed cost (AFC) Fixed cost di\'ided by the le\'el of output
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Daniel l. Rubinfeld

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