COST THEORY MBA CASE STUDY

CHAPTER 5: COST THEORY LEARNING OBJECTIVES In this chapter, students will be able to: 1. Explain the relationship between cost behavior and production theory. 2. Explain and derive the concepts of average variable cost, average total cost, and marginal cost. 3. Explain the concept of minimum efficient scale. Explain why a firm that produces at this level is not necessarily maximizing profits. 4. Compare and contrast short-run cost curves with the long-run average cost curve. 5. Explain the learning curve and how firms may incorporate it into their decisions. 6. Explain the various sources of economies of scope. 7. Compare and contrast continuous cost functions with step cost functions. Overview of Huxley Maquiladora Huxley Manufacturing Company, a large firm in the defense industry, is considering a strategic move to shift production from its California plant to Mexico. Tariff reductions made possible by the North American Free Trade Agreement (NAFTA) opened up the potential to enjoy significant cost savings by shifting production south of the Mexican border. Huxley is considering three options. The simplest option is to negotiate a subcontracting arrangement in which a Mexican firm manufactures steering column components (SCCs) according to the specifications of Huxley. The subcontracting firm would then be paid by Huxley on a per-piece arrangement. A subcontracting arrangement would allow Huxley to decrease or possibly eliminate expenditures for capital items such as facilities and equipment, but would also entail the highest cost per labor hour. A second option was the shelter operation. Under a shelter arrangement, the Mexican firm would allow Huxley to maintain control over production. In return, the Mexican firm would provide various administrative, human resource management, and import/export services. A shelter arrangement would allow Huxley to enjoy a fast startup with while affording the client firm complete control over production. The shelter operation would entail more fixed costs than the subcontracting arrangement, but would also incur lower hourly labor expenses. The final possibility was to set up a wholly-owned subsidiary. This option would require Huxley to select a plant site, staff its own employees, implement its own procedures and policies, and obtain the appropriate permits and licenses to operate. Over the long run, the wholly-owned subsidiary offered the greatest potential for cost savings. Although the wholly-owned subsidiary would exhibit the highest level of fixed costs, it also promised the lowest hourly costs of the three options. Of course, Huxley might conclude that none of the options are in the firm’s best interests over the long run. In this case, the firm would continue to produce out of its San Diego facility. 2 Cost Behavior Profit-maximizing decisions require the manager to be able to determine relevant cost. Relevant costs consist exclusively of those costs that will change if the decision is implemented. Our goal in this chapter is to derive a general theory on cost behavior that should apply to most firms. Having done so, we can closely examine how managers can determine unit costs and make effective decisions. In determining relevant costs, we must distinguish between fixed and variable costs. Fixed costs do not vary with production whereas variable costs rise as output increases. In the Huxley case, no fixed costs are associated with the subcontracting arrangement. If the firm decides to go with the shelter operation, fixed costs include construction, site leasing, startup expenditures, the plant manager’s salary, corporate taxes, and various other miscellaneous expenses. Variable costs include the hourly wage, materials, and transportation costs. The wholly-owned subsidiary includes most of the same fixed costs as the shelter operation, but adds the consulting fee and Mexican legal fees. Sometimes the distinction between fixed and variable costs can become blurred. For example, is the salary of an economics professor a fixed cost or a variable cost? Presumably, your professor will be paid the same salary regardless of how many students enroll in the course. However, your college probably has a pre-determined maximum enrollment for a specific section. If demand for a particular course exceeds the maximum capacity (a common problem in economics classes), the department may have to add one or more sections. If the instructor is already teaching a full load, the excess demand may have to be accommodated by adding another instructor to the teaching staff. When 3 enrollment surpasses the maximum for one section, total salary payments to economics professors rises. Does this imply that the professors’ salaries are fixed costs or variable costs? Production Theory and Cost Theory In the previous chapter, we discussed the economic theory of production. Comprehending production theory (the relationship between inputs and output) is a necessary prerequisite to understanding cost theory (the relationship between production and costs). As we noted in the previous chapter, costs are derived from production activities. As worker productivity increases, for example, unit costs decrease. The relationship between productivity and cost was implied in the Huxley case. Most of the employees at Huxley’s San Diego plant were women. The plant experienced high employee turnover because working with metals was a dirty job. The Huxley Maquila Project Report suggested that young Mexican women might be more productive than their American counterparts because they would be more patient. Hence, even if the going wage rate south of the border was identical to that paid in San Diego, unit costs would be lower due to the increased productivity at a Mexican facility. As you may recall from the chapter on production theory, in the early stages of production, a firm is expected to encounter increasing marginal product. As inputs are used for production, they become more specialized and the resulting efficiency gains cause production to increase more than proportionately. For example, suppose one worker was capable of producing one unit/hour. By adding a second worker, each worker could assume specialized duties. Owing to specialization, the two workers are 4 capable of producing four units of output. In other words, when the number of inputs doubled, output quadrupled. Let’s convert this information into production costs. For simplicity’s sake, we will assume that labor constitutes the only variable input. Fixed costs are $10/hour. If a worker was paid a wage of $10/hour, the total cost of producing one unit of output would be $20. If the firm hires two workers, four units could be produced at a total cost of $30. Increasing production from one unit to four did not affect the firm’s fixed costs, but it caused total variable costs to rise from $10 to $20. Take special note of the proportionate changes in production and costs. Total variable costs increased as production increased, but when output quadrupled, variable costs doubled. The increase in variable costs was proportionately less than the change in production. Table 1 shows the correlation between production theory and cost theory during these stages of production. Table 1 Labor Total Output 0 1 4 1 3 Marginal Product Total Fixed Costs $10 $10 $10 Total Variable Costs $0 $10 $20 Total Costs $10 $20 $30 0 1 2 As production increases, eventually, the firm comes upon the law of diminishing returns. Because the marginal product of each additional input diminishes, progressively 5 more inputs are needed to produce the same quantity of output. Put differently, increases in production are proportionately smaller than increases in inputs. We can understand the impact of diminishing returns on production costs by reversing the previous scenario. After encountering increasing marginal product with the first two workers, assume that the law of diminishing returns sets in with the third worker. One worker is capable of producing one unit of output and two workers are capable of producing four units. The marginal product of the second worker, therefore, is three units. The third worker, however, only contributes two additional units of output and the fourth worker adds only one more unit. Although fixed costs never change as we increase production, total variable costs continually rise. The total variable cost associated with producing four units is $20. It rises to $30 at six units of output and increases to $40 for seven units of output. Note that when output increases by 75% (from four units to seven units), total variable costs increase by 100% ($20 to $40). In short, when facing diminishing returns, increases in total variable costs are proportionately greater than increases in output. Table 2 shows the relationship between production and costs during once diminishing returns set in. 6 Table 2 Labor Total Output 0 1 4 1 3 Marginal Product Total Fixed Cost $10 $10 $10 Total Variable Cost $0 $10 $20 Total Cost $10 $20 $30 0 1 2 3 4 6 7 2 1 $10 $10 $30 $40 $40 $50 Figures 1 and 2 reveal graphical representations of total fixed and total variable costs. The total fixed cost curve is horizontal, indicating the fixed cost expenditure does not change as output increases. Total variable costs, on the other hand, increase as production increases. The rate of increase is not linear, however. At low levels of production, the firm encounters rising marginal product. Consequently, total variable costs rise at a slower rate than production. Once the firm comes upon diminishing returns, total variable costs increase at a faster rate than output. [Figure 1 here] [Figure 2 here] When we combine total fixed and variable costs, we get total cost. Figure 3 illustrates the total cost curve. As the figure illustrates, total cost follows the same basic pattern as total variable costs. As inputs are initially added, total cost rises as a relatively slow rate. Once diminishing returns in production sets in, total costs begin to accelerate. [Figure 3 here] 7 IMPORTANT IMPLICATIONS FOR THE MANAGER: Unit costs are not likely to be constant. As inputs are initially added to production, unit costs decrease. When production experiences diminishing returns, unit costs increase. For this reason, a workplace design that delays the onset of diminishing returns will keep unit costs at a minimum. We can also utilize economic theory to predict patterns in unit costs. Table 3 illustrates average fixed cost, average variable cost, and average total cost. Note that as output increases, average fixed costs decline because the total fixed costs are spread out over more units of output. Assuming labor to be the only variable cost (as we did in Tables 1 and 2), when experiencing increasing marginal product, the average variable cost (i.e. variable cost per unit) decreases from $10 to $5. During the diminishing returns stage of production, average variable cost rises. Note, however, that whereas diminishing returns set in when output increased to six units, average variable cost did not begin to rise until the seventh unit. (We will discuss why a little later). The same can be said for average total cost (the sum of both total variable and total fixed costs divided by the number of units of output). Average total cost decreases as marginal product increases, but eventually rises at some point after the law of diminishing returns sets in. Figure 4 shows an average fixed, average variable, and average total cost curve. [Figure 4 here] 8 Table 3 Total Total Output Fixed Cost 0 1 4 6 7 $10 $10 $10 $10 $10 $10 $2.50 $1.67 $1.43 Average Fixed Cost Total Variable Cost $0 $10 $20 $30 $40 $10 $5 $5 $5.71 Average Variable Cost Total Cost Average Total Cost $10 $20 $30 $40 $50 $20 $7.50 $6.67 $7.14 Perhaps the most important cost is marginal cost. Marginal cost refers to the change in costs resulting from a given change in output. Why is marginal cost so important? Let’s take a look at Table 3. Suppose the firm has produced six units and must determine whether to produce the seventh unit. Clearly, the firm would not be willing to produce the seventh unit if it could not earn a profit. Suppose the market price of the good is $8. If the seventh unit can be sold for $8, is it worth producing? In answering this question, it’s tempting to look at the average total cost; after all, this represents what it costs, on average, to produce seven units. Because the average total cost is $7.14, the firm can apparently profit by producing the seventh unit. But is this really the case? Note that the total cost associated with six units is $40 and the total cost of producing seven units is $50. If the firm decides to produce the seventh unit, its expenses will rise by $10. Would it make sense to spend an extra $10 to produce a unit and then sell it for $8? The problem with average total cost is that it 9 represents an average; unless marginal cost is constant, average total cost does not represent the cost of production for the output under consideration. IMPORTANT IMPLICATIONS FOR THE MANAGER: Marginal cost is the most important concept in production decisions. However, most cost accounting techniques report either average variable cost or average total cost. Because fixed costs do not vary with output, marginal costs are, by definition, variable costs. Table 4 uses the variable cost information from Table 3 to derive marginal cost. Table 4 Labor Total Output Total Variable Cost $0 $10 $20 $30 $40 $10 $3.33 $5 $10 Marginal Cost 0 1 2 3 4 0 1 4 6 7 Table 4 shows that when output increased from zero units to one unit, total variable costs increased by $10 (the cost of the worker’s labor). The cost increase reflects the need to hire the first worker. Because fixed costs are incurred even if the first unit is not produced, the marginal cost of the first unit is the added cost of a worker, or 10 $10. Increasing marginal product was encountered when the second worker was hired. Here, an additional worker resulted in three additional units of output (i.e. production increased from one unit to four units). The added variable cost was $10. The cost of the additional production, therefore, was $3.33/unit ($10 divided by three additional units of output). Note that marginal cost decreased during this stage of production. Diminishing returns began when the third worker was hired. Output increased by two units (from four units to six units) whereas total variable costs increased by $10. Consequently, the marginal cost of increasing production from four units to six units is $5/unit ($10 divided by two units). When the fourth worker was hired, production increased by only one unit. Hence, the marginal cost of the seventh unit is $10. Note that once diminishing returns sets in, marginal cost increases. In sum, rising marginal product results in falling marginal costs whereas decreasing marginal product leads to rising marginal costs. Figure 5 depicts a marginal cost curve. [Figure 5 here] Earlier, we noted that average variable cost and average total cost decreased when marginal product increased. We also noted that these costs continued to decrease even after the law of diminishing returns set in, but eventually began to increase. Why didn’t the increase in average costs coincide with diminishing returns? This is due to the relationship between average and marginal costs. You may recall that the relationship between marginal and average was discussed in the production theory chapter. Marginal cost refers only to the cost of additional output whereas average costs spread the costs over all units produced. Recall the analogy with grade-pointaverages discussed in the production chapter. If your marginal (semester) GPA exceeds 11 the average (cumulative) GPA, your average (cumulative) GPA will rise. If your marginal (semester) GPA is below your average (cumulative) GPA, your average (cumulative) GPA will fall. The same is true for costs. If the next unit you produce costs less to produce than the average unit cost so far (i.e. MC < ATC), the average cost will fall. If the next unit is more expensive to produce than the average unit so far (MC > ATC), then producing the next unit will cause the average cost to rise. This explains why average variable cost and average total cost continue to decrease even after the law of diminishing returns sets in and marginal cost begins to rise. Even though marginal cost is rising, if it’s still below average variable or average total cost, the average will continue to fall. Only after marginal cost exceeds average costs will the average begin to rise. Figure 6 illustrates the relationship between marginal and average costs. [Figure 6 here] Now that we know how marginal and average costs relate to each other, let’s go back to the notion that average total cost is U-shaped. As production increases, the average cost declines but eventually increases. The output at which average total cost is lowest is called minimum efficient scale. Logically, one would expect that firms will maximize profits when they produce this quantity of output. Interestingly, however, most of the time, producing at minimum efficient scale is not consistent with profit maximization. The rationale is surprisingly intuitive. Table 3 showed that average costs were lowest when the firm produced six units of output. But what if the firm could sell seven units at $15 each? Table 3 shows the marginal cost of the seventh unit to be $10. 12 If the firm only produced six units, its profits would be $50. By producing seven units, its profits rise to $65. Now, at the risk of getting a little ahead of ourselves, let’s throw a cog into the analysis. Suppose the firm could sell six units at a price of $20 each, but would have to reduce the price to $15 to sell all seven units, as might be necessitated by the law of demand. In this case, the profit from producing six units would be $80 whereas the profit from producing seven units is $65. The lesson to be learned here (and one that will be dealt with in much detail in a future chapter) is that profit maximization is determined not by focusing on costs, but by analyzing both costs and revenues. Is minimum efficient scale useful to the business manager? One lesson that we will emphasize repeatedly is that profits invite company. If your firm is making money head-over-heels, enjoy it while you can because competitors will enter the market to get a piece of the bonanza. As competitors flood the market, prices will fall. Your ability to match the declining market prices will depend on your position on the average cost curve. The average cost associated with minimum efficient scale represents the lowest price you can charge and still remain in business. In highly competitive markets, prices will eventually move to a level quite close to minimum efficient scale. If the average cost encountered at minimum efficient scale is not competitive with market entrants, your days are numbered. 13 IMPORTANT IMPLICATIONS FOR THE MANAGER: Minimum efficient scale is the output level for which production costs are lowest. In the short run, production at minimum efficient scale is not consistent with profit maximization, which involves a comparison of both revenues and costs. However, because minimum efficient scale indicates the lowest feasible unit cost, it communicates the lowest price the firm can charge and remain in business. Consider the case of Bowmar Instruments, the manufacturer of the worldrenowned Bowmar Brain. Bowmar what, you ask? That’s the point. In 1971, Bowmar Instruments revealed the Bowmar Brain---the first handheld calculator for the masses. Its initial model, the 901B could add, subtract, multiply, and even divide! And all for a mere $250! (Don’t laugh. These were considered to be sexy little instruments when they first hit the market---a significant improvement over a slide rule or an abacus). Everyone wanted a calculator and by 1975, hundreds of firms attracted by the huge profits in the handheld calculator industry were competing with Bowmar. Prices dropped rapidly and Bowmar, whose unit costs could not keep pace with its competitors, declared bankruptcy in 1976. Long Run Average Cost Economists define the short run and long run in fairly flexible terms. Whereas accountants or marketing personnel may define the short run as one year or less, or perhaps six months or less, the economic definition of the short run is determined by the specific circumstances confronting the firm. Given a firm’s capacity to produce at a fixed point in time, it can adjust its production within its capacity constraint. But suppose 14 the firm senses a need to increase capacity. This is not a decision the firm can put into operation overnight. Until it can increase capacity, it must work within its current constraints. This is what economists mean by the short run. It is that period of time in which the firm faces at least one fixed cost. Perhaps the firm is locked into a lease. If it breaks the lease, it must pay some sort of penalty. Once the lease expires, on the other hand, the firm can relocate its operations without paying a penalty. Perhaps the firm is locked into an unfavorable collective bargaining agreement. In time, the firm may wish to re-negotiate some of its terms, but in the meantime, it must live within the terms of the agreement. Note that under the economic definition, the short run may be a period of days, weeks, or even years. The long run, conversely, is that span of time beyond which the firm can make any necessary changes in its production capacity. It is that span of time through which the firm undergoes its long-range planning. It may permanently discontinue production at certain locations or altogether. It can expand capacity to any number of plants at any number of locations. To understand the relationship between short- and long-run decision-making, let’s go back to the short run analysis. In the short run, the firm is basically stuck; that is to say, it must work within its current production constraints. If it has a single manufacturing plant with a capacity of 1,000 units/day, it must decide the quantity of output that will maximize its profits. Suppose demand increases. The firm’s current capacity may be insufficient to handle the burgeoning demand. Perhaps the firm needs to increase its capacity, either by altering the size of the plant or building a new one. Of 15 course, the objective of the firm is not to meet demand, but to maximize its profits. Increasing capacity may or may not serve the best interests of the firm. To date, all of the firm’s decisions fell within its production constraints. The marginal and average cost curves as illustrated in Figure 6 show the costs associated with various units of production. If the firm decides to increase its capacity, the range of production will increase and its cost structure will change. Table 5 shows the cost structures for a small- and medium-sized plant. Table 5 Small Plant Q 0 1 4 6 7 TFC AFC TVC AVC TC ATC $10 $0 $10 $10 $10 $10 $10.00 $20 $20 $10 $2.50 $20 $5.00 $30 $7.50 $10 $1.67 $30 $5.00 $40 $6.67 $10 $1.43 $40 $5.71 $50 $7.14 Medium Plant Q 0 4 7 11 13 14 TFC AFC TVC AVC $20 $0 $20 $5.00 $15 $3.75 $20 $2.86 $25 $3.57 $20 $1.82 $35 $3.18 $20 $1.54 $45 $3.46 $20 $1.43 $55 $3.93 TC $20 $35.00 $45.00 $55.00 $65.00 $75.00 ATC $8.75 $6.43 $5.00 $5.00 $5.36 Note that if the firm wishes to produce four units of output, it is better off with the smaller plant because its average total cost ($7.50/unit) is less than what would be encountered using a larger plant ($8.75/unit). However, whereas average total cost is 16 $7.14 at seven units with the small plant, the average cost at seven units is $6.43 and still falling. Only at 14 units does the average total cost begin to rise again. This is illustrated in Figure 7. Note that at lower levels of production, the average cost from the small plant is lower than those at the medium plant. However, as production increases, the average cost of the medium plant is lower. In this case, increasing production capacity only makes sense if the firm intends to produce beyond the lowest point in the average cost curve for the small plant. [Figure 7 here] Because the medium plant yields the potential for a lower average cost than the small plant, perhaps the firm should consider an even larger plant. Table 6 compares the cost structures between the medium and large plant. At 11 units, the medium plant has a lower average cost ($5) than the large plant ($6.82). At some point, the average costs for the large plant are lower than those from the medium plant. For example, we see average total cost is $5.36 and rising when 14 units are produced at the medium plant. For the large plant, average total cost is $5.27 at 18 units and still falling. This is graphically illustrated in Figure 8. [Figure 8] So how many plants should the firm operate? Recall that these all represent short run cost curves. In the long run, the firm can operate as many or as few as it would like. 17 Table 6 Medium Plant Q 0 4 7 11 13 14 TFC AFC TVC AVC TC ATC $20 $0 $20 $20 $15 $5.00 $3.75 $35.00 $8.75 $20 $25 $2.86 $3.57 $45.00 $6.43 $20 $35 $1.82 $3.18 $55.00 $5.00 $20 $45 $1.54 $3.46 $65.00 $5.00 $20 $1.43 $55 $3.93 $75.00 $5.36 Large Plant Q 0 6 11 15 18 20 21 TFC $35 $35 $35 $35 $35 $35 $35 $6 $3 $2 $2 $2 $2 $30 $40 $50 $60 $70 $80 $5.00 $3.64 $3.33 $3.33 $3.50 $3.81 $65 $75 $85 $95 $105 $115 $10.83 $6.82 $5.67 $5.27 $5.25 $5.48 AFC TVC AVC TC ATC Figure 9 shows the big picture. If we draw a curve tangent to the three short-run cost curves we can see that over the long run, unit costs are lowest, on average, by operating a medium-sized plant. There is no advantage in increasing capacity to the large plant because average costs do not decline below the lowest point in the medium-sized plant’s average cost curve. The curve that is tangent to the three short run cost curves is called the long run average cost curve, often referred to as the planning curve. Cost theory suggests that as the firm increases the scale of its operations, its long run average costs will decline. This situation is referred to as economies of scale. Eventually, diseconomies of scale sets in and long run average costs increase. [Figure 9 here] 18 To illustrate why economists theorize a U-shaped planning curve, envision a firm that sells its good nationwide. Given the costs associated with transporting output from its East Coast plant to its West Coast market, the firm may learn that its unit costs will be lower if it builds a second plant on the West Coast. Unit costs may fall by even more if it opens up another plant in the Midwest and perhaps by even more if it opens a plant in the southern United States. It would be foolhardy to assume that building plants progressively closer to the firm’s consumer markets always lowers unit costs. If that were the case, the firm would build a plant next to each and every customer. Sooner or later, unit costs will rise as a result of progressively increasing capacity. In other words, economies of scale has its limits; eventually, diseconomies of scale sets in. Economies of scale can also reflect increased opportunities for labor specialization or highly specialized equipment. Occasionally, firms operating on a larger scale can obtain quantity discounts in materials and supplies. Sometimes they can take out loans at lower interest rates. More productive inputs, cheaper inputs, a lower cost of capital; all of these can lead to lower average costs. Diseconomies of scale often result from the relative difficulties inherent in coordinating the activities of a large-scale operation. Decisions sometimes require several levels of approval. Red-tape interferes with efficient decision-making and may grow more than proportionately with increases in the scale of production. This contributes to significant increases in overhead, which leads to rising average costs. Not all long run average cost curves are U-shaped. Many industries exhibit an Lshaped planning curve. This suggests rather rapid decreases in average costs as the production scale increases that diminish and flatten out as production continues to 19 increase. This does not necessarily imply that diseconomies of scale do not exist, but that the scale of the operation has yet to encounter such diseconomies. In making its decisions, Huxley needs to consider the long run costs if it expects the move to be permanent. Most of the fixed expenses associated with the shelter and wholly-owned subsidiaries are one-time start-up expenditures. It makes little sense for Huxley to consider a long-term commitment to its Mexican operations if it cannot recover these expenses in the future. Whereas the subcontracting arrangement entails no fixed costs, the variable cost per direct labor hour is the highest. Assuming the fixed costs associated with the other two options can be covered, it makes little sense for Huxley to consider an option with significantly higher variable costs. By combining the fixed costs associated with each option, we can establish the cost equations shown in Table 7. Because the case does not provide data on production, we must base our equation on direct labor hours (H) under the assumption that output is positively correlated with direct labor hours. Table 7 Option Subsidiary (Low estimate): One-Time Cost $498,250 Operating Cost Equation TC = $231,550 + $1.8H TC = $276,300 + $2.2H TC = $231,550 + $3.5H TC = $276,300 + $3.5H TC = $5H Subsidiary (High estimate): $807,500 Shelter (Low estimate): Shelter (High estimate): Subcontracting: $473,250 $779,500 20 Because the wholly-owned subsidiary trades off higher fixed costs in exchange for lower variable costs, we can determine the breakeven level of direct labor hours between the two options by setting the operating cost equations equal to each other and solving for H, or: $276,300 + $2.2H = $5H, or: H = 98,679 This indicates that the subsidiary will prove to be cheaper than subcontracting if the annual number of direct labor hours exceeds 98,679. Assuming employees work 42-hour weeks and are paid 52 weeks/year (including holidays), 98,679 direct labor hours equates to roughly 45 employees. Because the San Diego plant currently employs 57 workers, it would appear that the wholly-owned subsidiary is the most cost-efficient solution over the long run. Moreover, each direct labor hour exceeding 98,679 can be applied toward the one-time expenditures of $807,500. If 57 employees work 42-hour weeks, the onetime expenditures will be paid off in less than three years. Huxley must also weigh the costs and benefits of the border site with the interior location. At the present time, Huxley notes the higher employee turnover at border towns due to strains on the local infrastructure. Although these would not be present at the interior site, transportation costs would be substantially higher. In evaluating the longterm prospects at each location, the firm needs to realize that the influx of maquiladoras is likely to bid wages at the border site upward. Over the long run, wage differentials may cancel out the transportation savings at the border site. Thus, the relative savings at the border site are likely to become smaller over time. 21 IMPORTANT IMPLICATIONS FOR THE MANAGER: Although the firm’s productive capacity is limited in the short run, it can alter its production capacity to any level over the long haul. To identify the “ideal” production capacity, the firm needs to determine the unit costs associated with expansion. Increasing the firm’s productive capacity is worthwhile if allows the firm to meet demand at a lower unit cost. Global Considerations The marketplace has become increasingly globalized. A firm headquartered in the United States may have a manufacturing plant in Mexico that produces goods sold to Europe. In short, it’s no longer necessary to locate one’s manufacturing plant near the consumer. From this perspective, the long-run average cost curve may encompass the entire globe. Should the firm move its manufacturing facilities to the country with the lowest wage rates? Critics of globalization frequently argue that jobs are exported to low-wage countries, forcing domestic workers to accept Third-World-like wages to avoid losing their jobs. This perspective is rather simplistic, to say the least. Consider your own circumstances. Why did you decide to go to college or pursue an MBA? In all likelihood, you were lured by the promise of higher pay upon graduation. Why do persons with college degrees have higher salaries? 22 To understand the correlation between education and compensation, consider the case of a professional athlete such as Alex Rodriguez. As a star thirdbaseman, A-Rod pulls in over $20 million/year. How does he keep his job---after all, there must be millions of people who would be willing to play baseball for a fraction of his salary. Doesn’t he fear that franchise owners will substitute cheaper labor? The answer, of course, lies in Rodriguez’s unique skills. As a star player, A-Rod helps his team win more games, which attracts more fans, which, in turn, generates more revenue. If baseball teams believe his presence in the lineup will cause franchise revenues to rise by more than $20 million/year, it’s only to be expected that a bidding war will cause his salary to rise to reflect his value to his franchise. The same is true for your degree. Presumably, the long hours you’ve toiled on your classes have given you skills that make you valuable to employers. Who would want to hire an accountant who doesn’t know anything about accounting? The bidding war for your services may not yield the same rewards as A-Rod’s, but you stand to earn more than you would without the additional training and skills. What does this have to do with globalization? Just as the salary differentials of MBAs versus non-MBAs reflects differences in skills and abilities, so do wage differentials between countries. Workers in developed countries tend to earn more because they tend to be more skilled and hence, more productive. Many workers in lesser developed countries do not have the same set of skills. Because they are unskilled, they are less valuable to employers, and consequently, earn lower wages. Lower wages may also reflect less desirable characteristics within the country. Perhaps the country is plagued by inadequate transportation or infrastructure. Maybe the country has a long 23 history of political instability. Any of these factors may contribute to low labor demand and low wages. From the multinational firm’s perspective, the critical element is not the hourly labor cost, but unit costs. Cheap labor that is significantly less productive than more expensive labor may imply higher unit costs. Moreover, labor is just one component of unit cost; countries with low labor costs may have high capital costs. Again, in considering the location of one’s manufacturing facilities, the key factor is unit cost. IMPORTANT IMPLICATIONS FOR THE MANAGER: Multinational firms should not necessarily locate their manufacturing facilities where wages are the lowest. Low wages frequently signal an abundance of unskilled workers, poor infrastructure, and/or political instability. Hence, plant locations must be based on unit costs rather than hourly costs. Applying this concept to the Huxley case, it appears that the lower wages in Mexico will not be offset by lower worker productivity. In fact, the report suggested that Mexican women may actually be more productive than their American counterparts at the San Diego facility. Huxley does, however, have to consider the impact of higher transportation costs. Steering column components produced in Mexico must be shipped back to the United States. If the decreased labor costs are more than offset by increased transportation costs, a move to Mexico would not be advisable. The data provided in the case does not appear to support this contention, however. 24 Learning Curves A number of years ago, an MBA from a regional university opened a Thai restaurant in my town---the first (and to date, only) Thai restaurant in town. Thrilled over the possibilities of indulging in pad Thai, we showed up with our appetites in full gear on opening night. What a disaster! It took over three hours to get served despite the fact that they had relatively few customers to contend with. Each meal appeared one-at-a-time, such that by the time my daughter’s meal was served, I’d already finished mine. One wonders how many repeat customers were driven away by the dreadful experience (not to mention bad word-of-mouth---the restaurant did eventually close its doors), but we returned a few weeks later, willing to give it another chance. This time, the service was relatively prompt. After the meal, we asked the MBA owner what had changed since the opening night nightmare. He confessed that the cooking crew was entirely disorganized---no one knew where each ingredient was. Since that time, they’d invented a way to organize everything such that preparing the meal was a snap. The Thai restaurant employees were experiencing the pains of a learning curve. I’d had my share of new jobs and I always felt like a fool until I learned the system. And the company paid for my inefficiency. In time, the firm finds less costly ways of doing thing, causing average costs to decline over time and/or with increases in production. We’ve talked about various sources of economies of scale, and learning efficiencies function in much the same way. A learning curve implies the percentage decrease in average costs that one expects to occur as production increases. If one is on an 80% learning curve, this suggests that 25 the cost of producing the 200th unit will be 80% of the cost of producing the 100th unit, and that the cost of producing the 300th unit will be 80% of the cost of producing the 200th unit. Identifying the learning curve is as easy as comparing average costs from one time period to another. The learning curve is simply a ratio of average costs in one time period to the average costs in the previous time period. For example, if unit costs are $40 one year and $50 in the previous year, then the firm is dealing with an 80% learning curve ($40/$50). Assuming the percentage rate of learning remains constant, unit costs next year will be $32 (.8 x $40) and $25.60 (0.80 x $32) the following year. In determining the learning curve, one should avoid comparing apples and oranges. Unit costs may change from year-to-year for reasons other than learning. Have the wage rates changed in the past year? The price paid for materials? To isolate on the learning effect, it is essential that input prices be held constant. Firms in infant industries can use learning curves to their advantage. The key is recognizing that the relatively direct costs associated with production as a function of learning. As the workers gain experience and know-how, direct costs will diminish through increased production. From this perspective, learning costs ought to be considered an investment rather than a source of inefficiency. If firms in the early stages of the product-life-cycle set prices below their average variable costs, they will encounter a negative cash flow initially, but the force-fed investment in learning should pay dividends in the future. 26 IMPORTANT IMPLICATIONS FOR THE MANAGER: An understanding of learning curves can be useful to infant firms. Current production costs may not allow the firm to charge a price above unit cost. However, although charging a price below unit cost creates a negative cash-flow in the short run, it may slide the firm down the learning curve at an accelerated rate and offer a positive return on investment. Cost of Producing Multiple Goods Although our analysis has concentrated on the production of a single product, few firms only produce one good. Sometimes when the firm produces more than one good, the cost of one good may depend on the output of the other good. When the production of two or more goods jointly is less expensive than the production of the same goods individually, we say that the firm enjoys economies of scope. Economies of scope may arise from various sources. A single production process may yield multiple products. For example, oil production gives rise to both gasoline and heating oil. Alternatively, two products may make extensive use of the same set of resources. Sometimes economies of scope arise from expertise that translates across products. Coca-Cola, for example, produces over 400 brands of soft drinks ranging from its staple product to Dr. Pepper to Canada Dry. Clearly, the knowhow associated with the production and marketing of Coca-Cola translates into other brands, leading to economies of scope. Economies of scope may also be demand-related. Although consumers most closely associate McDonald’s with hamburgers, the firm offers a wide variety of foods to complement the fast-food dining experience. 27 One advantage of economies of scope lies in its ability to allow the producer to differentiate its product to reach a different market segment. Proctor and Gamble introduced Pringles potato chips in 1968. Today, in addition to the original Pringles chips, consumers can choose between sour cream and onion, loaded baked potato, jalapeno, chili cheese, pizza, cheddar cheese, salt and vinegar, and ranch. International brands include everything from spicy Thai to ketchup-flavored. Economies of scope allows Pringles to appeal to different segments of the market without having to “re-invent the wheel” with each variation of the product. Step-Cost Functions As a social science, economics seeks to create simplified models that allow economists to predict behavior. For example, the downward-sloping demand curve is a graphical representation of the law of demand, which asserts that as prices fall, more of a good can be sold. Few individuals would contest the validity of the law of demand. Nevertheless, few would assert that any and all price changes affect the quantity demanded for a given product or service. The same applies to cost behavior. The cost curves illustrated in Figures 1-9 are merely models of cost behavior. Marginal cost, for example, may not change with each unit of output, as suggested by Figure 5. Within some relevant range of production, for example, we may experience constant marginal costs. We should not assume, however, that marginal costs are constant through any range of output. Increasing and decreasing marginal products are real phenomena and will affect marginal cost at some production levels. Rather than treat the cost curves as precise models of cost behavior that can be fit to any production facility, we need to be cognizant of the factors 28 that can alter cost behavior, as this will allow managers to anticipate changes in future unit costs. In practical situations, costs are more likely to resemble stairsteps than curves, as shown in Figure 10. For example, a given range of output may be produced at a more or less constant marginal cost. As production increases, it may become necessary for plant workers to perform overtime labor. As overtime typically pays time-and-a-half, marginal cost rises to a new level but then remain fairly constant. [Figure 10 here] IMPORTANT IMPLICATIONS FOR THE MANAGER: Managers need to recognize the marginal costs or average costs may be constant over the relevant range of production. However, in planning, they need to be aware of the patterns in costs predicted by economic theory. This is why cost theory can be so useful to the business manager. If the manager is to make a decision regarding a strategic initiative, he/she must determine the relevant cost. Cost theory illuminates the decision-making process by providing guidance on what the manager can expect. The patterns of increasing and decreasing marginal product and/or increasing and decreasing returns to scale suggest that marginal costs (and average costs) will change as production increases even if the firm encountered constant unit costs through the current range of production. 29 SUMMARY 1. A firm’s costs consist of fixed and variable costs. Fixed costs do not vary with production. Variable costs increase as production increases. 2. Total fixed costs remain constant as output increases. Total variable costs and total costs rise at varying rates. As marginal product increases, total variable costs and total costs rise at a slower rate relative to increases in output. During diminishing returns to scale, total variable cost and total cost rise at a faster rate than output. 3. Average costs convey more useful information to the decision-maker. Average fixed costs decrease as production rises because the firm’s fixed costs become spread out over more units of output. Average variable costs and average total costs decrease as marginal product increases, but eventually increase at some point after the law of diminishing returns sets in. 4. The most important cost for decision-makers is marginal cost, which refers to the cost of producing additional output. Marginal cost falls during increasing returns to scale and rises during decreasing returns to scale. 5. The output at which average total cost is minimized is called minimum efficient scale. A firm does not necessarily maximize profits by producing at this level. However, it represents the lowest price the firm can charge and remain in business. 6. With respect to selecting a country to locate one’s manufacturing facilities, low wage rates in a country often reflect an abundance of unskilled workers, inadequate infrastructure, and/or political instability. Hence, the firm should base its decisions on unit costs rather than hourly costs. 30 7. The long run average cost curve, or planning curve, allows the firm to determine the plant size or number of plants that will minimize its unit costs over the long run. Usually, as the scale of the firm’s operations increase, long run average costs decline, resulting in economies of scale. Eventually, however, long run average costs to rise as production increases; this is called diseconomies of scale. 8. Learning curves refer to decreases in average costs attributed to learning-on-the-job. Firms in infant industries can use learning curves to their advantage in price setting. 9. Economies of scope occur when a firm can produce two or more goods jointly at a lower cost than producing them separately. They can arise because a single production process results in more than one product, shared resources or knowhow, or demandrelated considerations. 10. Actual cost curves are likely to be stairsteps rather than continuous curves. 31 Mini-Case THE FERDINAND COMPANY Trevor Green is production supervisor for the Ferdinand Company, a small manufacturer of nitrogen fertilizer. His company is capable of producing fertilizer in lot sizes of 100 tons/day. Currently, the firm produces 300 tons of nitrogen fertilizer per day. The industry is extremely competitive and market prices usually run in the neighborhood of $325/ton. Green relies heavily on accounting data. Recent accounting information revealed the following unit cost figures. Lot Size 100 200 300 400 Unit Cost $300 $280 $310 $340 Recently, a surge in demand caused the price to top $360. At the current production level, Ferdinand’s profits rose to $15,000. Examining the accounting data, Green decided he could capitalize on the higher market price by increasing production from 300 tons/day to 400 tons/day, given that the $35 increase in the market price exceeded the $30 increase in unit cost from expanding production. 32 PROBLEMS 1. Charles was the new product manager for a line of silver flatware. He believed the firm should be more aggressive in selling its products. Cost accounting data revealed a unit cost of $50. The firm historically priced its flatware at 33% above unit cost, or $66 for a set. However, Charles advocated an aggressive strategy of setting prices at 10% above unit cost, or $55. He believed the $11 loss of contribution margin would be more than made up by an increase in sales volume. Although the aggressive pricing strategy caused sales to surge, overall profits declined. Moreover, the contribution margin fell to only $2. What was likely the cause of the problem? 2. Ashton was the production supervisor at his manufacturing facility. His employees were going to be paid a bonus at the end of the year if they could reduce unit costs by 5%. Incorporating theories of efficient production, Ashton was able to reduce unit costs by 6.5%. However, this was accomplished by increasing production by 15%. In time, this created problems for the firm. If it continued to charge its current price, it could not sell all of its production, leading to high carrying costs from the rising stock of unsold inventory. The alternative was to drop the price to eliminate the production surplus. However, the company accountants showed the firm’s profits would decrease if it pursued this strategy. What went wrong? 3. Comfort Flooring is a manufacturer of carpeting. The company currently operated five manufacturing facilities in Portland, ME, Wichita Falls, TX, Valdosta, GA, Lynchburg, VA, and Logan, UT. One of the managers, Chad Poston, advocated increasing the number of facilities to ten. In making his case, he pointed out that unit costs had declined by 12% after the Logan and Lynchburg facilities were built. He 33 predicted an additional decrease of 15% would be realized by building plants in Bismarck, ND, Buffalo, NY, and Ames, IA. What factors should the firm consider before going ahead with the expansion? 4. Samson Electronics is the latest entrant into the low-end digital camera market. Although its market share after its first year was less than 1%, the company is very optimistic about its opportunities for future growth. The current problem resides in its high unit costs. First-year production costs for its 4-megapixel camera averaged $150; well above the unit cost necessary to sell in a market in which low-end cameras tend to sell for around $150. Second-year productions costs fell to $140. Although the lower unit costs allowed the firm to meet the market pricewise, its profit contributions were not sufficient to cover fixed costs. Because its product lacked brand awareness, corporate headquarters believed further market penetration required setting a price below the competition. However, with current production costs hovering around $140, the managers wondered if it would be wise to charge a price below $140. What would you recommend? 5. U-Washum Car Wash pays $1,000/day for the lease on its facility. It employs five workers who are paid $8/hour. Water and soap expenses total $40/day. The car wash is open eight hours/day. On average, five cars per hour are washed. Determine the daily total fixed cost, total variable cost, total cost, average fixed cost, average variable cost, average total cost, and marginal cost. 34 6. Hungry Dog is a producer of dog food. Accounting produced the following average total cost data. Q 100 101 102 ATC $5 $5.05 $5.10 The firm believes it can sell the 102nd unit for $5.50. Should the 102nd unit be produced? 7. Strategic management must determine whether it should opt for a plant with a capacity of 500 units or one with a capacity of 1,000 units. Estimates of the costs associated with each plant size are shown below. Capacity = 500 units Q 0 100 200 300 400 500 TFC $200 $200 $200 $200 $200 $200 TVC $0 $100 $190 $350 $550 $800 Capacity = 1,000 units Q 0 200 400 600 800 TFC $350 $350 $350 $350 $350 TVC $0 $180 $330 $550 $810 $1,110 1,000 $350 What size plant do you recommend for the firm? 35 8. In its first year of operation, Obee Pest Company produced 1,000 units of the Skeeter Eater. Two thousand direct labor hours were used at a cost of $8/hour and direct materials expenses totaled $10,200. The following year, 2,700 direct labor hours were used to produce 2,000 units at a cost of $8.50 hour, with direct materials expenses totaling $19,200. Obee Pest believed the production process has become more efficient as a result of the production workers gaining experience. Project the firm’s unit costs if it were to produce 3,000 units. The firm believes its sales could reach 3,000 if it charges a price of $15. Would you recommend the firm charge $15? 9. Tex’s oil fields are capable of producing 500 barrels of oil per day. Oil is currently trading for $52/barrel. Tex’s company currently produces 400 barrels/day. The average total cost associated with each production level is shown in the table. Barrels 100 200 300 400 500 Average Total Cost $20 $18 $16 $24 $32 Drilling recently began after the discovery of an untapped oil field in Alaska. With the added production of oil in the market, oil prices slipped to $46/barrel. Should the new price of oil affect Tex’s production? If so, how? 36 HANDS-ON EXERCISES PRODUCTION AND TOTAL COSTS The firm encounters fixed costs of $100. Its only variable cost is the workers’ wages, or $10/hour. The below table shows the quantity of output produced each hour by each quantity of labor. L—Quantity of Labor Q—Total output per hour TFC---Total Fixed Cost TVC---Total Variable Cost TC-----Total Cost L 0 1 2 3 4 5 Q 0 2 5 9 11 12 TFC ______ ______ ______ ______ ______ ______ TVC ______ ______ ______ ______ ______ ______ TC ______ ______ ______ ______ ______ ______ b. As output rises, what happens to total fixed costs? 37 c. As output rises, what happens to total variable cost? Total cost? c. Recall that as inputs are initially added, the marginal product of each additional worker is rising. Identify the portion of the table that exhibits increasing marginal product. By what percentage does output increase? By what percentage does total variable cost increase? By what percentage do total costs increase? Why do you suppose this relationship exists? d. Diminishing returns implies that the marginal product of each additional worker is falling. Identify the portion of the table that exhibits diminishing returns. By what percentage does output increase? By what percentage does total variable cost increase? By what percentage do total costs increase? Why do you suppose this relationship exists? 38 PRODUCTION AND PER UNIT COSTS Total fixed costs equal $100. Variable costs consist of the workers’ wages, or $10/hour. The below table shows the quantity of output produced each hour by each quantity of labor. L—Quantity of Labor Q—Total output per hour AFC---Average Fixed Cost AVC---Average Variable Cost ATC-----Average Total Cost L 0 1 2 3 4 5 Q 0 2 5 9 11 12 AFC AVC ATC ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ a. What happens to average fixed cost as output increases? Why? 39 b. As output rises, what happens to average variable cost? Average total cost? c. If the goal of the firm were to minimize average variable cost, how many units of output would it produce? d. If the goal of the firm were to minimize average total cost, how many units of output would it produce? e. Identify the portion of the table that corresponds to rising marginal product. What is happening to average variable cost and average total cost? 40 f. Identify the portion of the table that exhibits diminishing returns. Does rising average variable cost and average total cost coincide with this point? 41 AVERAGE COSTS AND MARGINAL COST Variable costs are the workers’ wages, or $10/hour. The below table shows the quantity of output produced each hour by each quantity of labor. L—Quantity of Labor Q—Total output per hour AVC---Average Variable Cost MC----Marginal Cost L 0 1 2 3 4 5 Q 0 2 5 9 11 12 TVC AVC MC ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ a. Identify the portion of the table that corresponds with rising marginal product. What happens to marginal cost? Why does this relationship exist? 42 b. Identify the portion of the table that exhibits diminishing returns. What happens to marginal cost? Why does this relationship exist? c. What happens to average variable cost when marginal cost is less than average variable cost? What happens to average variable cost when marginal cost is less than average variable cost? Why does this relationship exist? 43 THE IMPORTANCE OF MARGINAL COST Q 0 2 5 9 11 12 AVC $5 $4 $3.33 $3.64 $4.17 a. Suppose you relied on average cost data supplied by accounting to make production decisions. You currently produce nine units and are contemplating increasing production to 11 units. The market price is $4.25. Calculate the profit contribution at 11 units. Does producing 11 units seem worthwhile? 44 b. Fill in the blanks for total variable cost and marginal cost. Q 0 2 5 9 11 12 AVC TVC MC $5 $4 $3.33 $3.64 $4.17 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ b. Determine the added revenue if you increase production from nine units to 11 units. c. Determine the additional cost of increasing production from nine units to 11 units. d. Is it worthwhile to increase production from nine units to 11 units? e. Why was average variable cost misleading? 45 LONG RUN AVERAGE COSTS The below tables show the costs associated with three different plant sizes. Small plant Q 0 10 25 40 50 56 TFC $100 $100 $100 $100 $100 $100 AFC _____ _____ _____ _____ _____ _____ TVC $0 $10 $20 $30 $45 $60 AVC TC _____ ATC _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ Medium plant Q 0 12 28 46 60 70 TFC $125 $125 $125 $125 $125 $125 AFC _____ _____ _____ _____ _____ _____ TVC $0 $11 $20 $30 $48 $56 _____ _____ _____ _____ _____ AVC TC _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ ATC 46 Large plant Q 0 14 34 52 70 80 TFC $150 $150 $150 $150 $150 $150 AFC _____ _____ _____ _____ _____ _____ TVC $0 $12 $23 $33 $48 $72 _____ _____ _____ _____ _____ AVC TC _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ ATC a. Compare the average total cost associated with the lower production levels at the small plant with those at the medium-sized plant. At these output levels, which size plant can production take place most efficiently? b. Compare the average total cost associated with the higher production levels at the small plant with those at the medium-sized plant. At these output levels, which size plant can production take place most efficiently? 47 c. Compare the average total cost associated with the lower production levels at the medium-sized plant with those at the large plant. At these output levels, which size plant can production take place most efficiently? d. Compare the average total cost associated with the higher production levels at the medium plant with those at the large plant. At these output levels, which size plant can production take place most efficiently? e. Determine the minimum average total cost associated with each plant size. Small: _________ Medium: _______ Large: _______ f. In the long run, which size of plant can minimize average total cost? 48 LEARNING CURVES a. Determine average variable costs for years 1 and 2. Year 1 2 Q 100 200 TVC $500 $800 AVC ____ _____ b. By what percentage have average variable costs decreased between years 1 and 2? c. Suppose you attribute the decrease in average variable costs to learning. Using the percentage change in average variable costs from part b, estimate the average variable costs for each of the below production levels. Q 300 400 500 600 AVC _____ _____ _____ _____ 49 d. At the production level experienced in year 2, could the firm generate a positive profit contribution if it were to charge $3? e. Suppose the firm believed that by charging $3, it could increase its sales to 600 units. Is charging a price below current average variable costs worthwhile? 50 Figure 1 Total Fixed Cost $10 Total Fixed Cost 1 4 6 7 Quantity 51 Figure 2 Total Variable Costs $40 Total Variable Costs $30 Increasing Marginal Product $20 $10 Decreasing Marginal Product 1 4 6 7 Quantity 52 Figure 3 $ Total Cost $50 $40 $30 $20 Total Variable Cost $10 0 1 4 6 7 Total Fixed Cost Quantity 53 Figure 4 $ $20 Average Total Cost Average Variable Cost $10 $7.50 $5.71 $5 $2.50 $1.67 $1.43 1 4 6 7 Average Fixed Cost Quantity 54 Figure 5 $ Decreasing Marginal Product Marginal Cost Increasing Marginal Product $10 $5 $3.33 1 4 6 7 Quantity 55 Figure 6 $ Marginal Cost Average Total Cost Average Variable Cost Quantity 56 Figure 7 $ Average Cost (Small) $8.75 Average Cost (Medium) $7.50 $7.14 $6.43 4 7 Quantity 57 Figure 8 $ Average Cost (Medium) Average Cost (Large) Quantity 58 Figure 9 $ Small Medium Large Quantity 59 Figure 10 $ Marginal Cost Quantity 60