Chapter 13: The Costs of Production PDF

CHAPTER The Costs of Production 13 T he economy is made up of thousands of firms that produce the goods and services you enjoy every day: General Motors pr...

CHAPTER The Costs of Production 13 T he economy is made up of thousands of firms that produce the goods and services you enjoy every day: General Motors produces automobiles, General Electric produces lightbulbs, and General Mills produces breakfast cereals. Some firms, such as these three, are large; they employ thousands of workers and have thousands of stockholders who share the firms’ profits. Other firms, such as the local barbershop or café, are small; they employ only a few workers and are owned by a single person or family. In previous chapters, we used the supply curve to summarize firms’ produc- tion decisions. According to the law of supply, firms are willing to produce Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 248 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY and sell a greater quantity of a good when the price of the good is higher. This response leads to a supply curve that slopes upward. For analyzing many ques- tions, the law of supply is all you need to know about firm behavior. In this chapter and the ones that follow, we examine firm behavior in more detail. This topic will give you a better understanding of the decisions behind the supply curve. In addition, it will introduce you to a part of economics called industrial organization—the study of how firms’ decisions about prices and quan- tities depend on the market conditions they face. The town in which you live, for instance, may have several pizzerias but only one cable television company. This raises a key question: How does the number of firms affect the prices in a market and the efficiency of the market outcome? The field of industrial organization addresses exactly this question. Before turning to these issues, we need to discuss the costs of production. All firms, from Delta Air Lines to your local deli, incur costs while making the goods and services that they sell. As we will see in the coming chapters, a firm’s costs are a key determinant of its production and pricing decisions. In this chapter, we define some of the variables that economists use to measure a firm’s costs, and we consider the relationships among these variables. A word of warning: This topic is dry and technical. To be honest, one might even call it boring. But this material provides a crucial foundation for the fascinat- ing topics that follow. 13-1 What Are Costs? We begin our discussion of costs at Caroline’s Cookie Factory. Caroline, the owner of the firm, buys flour, sugar, chocolate chips, and other cookie ingredients. She also buys the mixers and ovens and hires workers to run this equipment. She then sells the cookies to consumers. By examining some of the issues that Caroline faces in her business, we can learn some lessons about costs that apply to all firms in an economy. 13-1a Total Revenue, Total Cost, and Profit We begin with the firm’s objective. To understand the decisions a firm makes, we must understand what it is trying to do. Although it is conceivable that Caroline started her firm because of an altruistic desire to provide the world with cookies or, perhaps, out of love for the cookie business, it is more likely that she started the business to make money. Economists normally assume that the goal of a firm is to maximize profit, and they find that this assumption works well in most cases. total revenue What is a firm’s profit? The amount that the firm receives for the sale of its out- the amount a firm put (cookies) is called total revenue. The amount that the firm pays to buy inputs receives for the sale (flour, sugar, workers, ovens, and so forth) is called total cost. Caroline gets to of its output keep any revenue that is not needed to cover costs. Profit is a firm’s total revenue total cost minus its total cost: the market value Profit 5 Total revenue 2 Total cost of the inputs a firm uses in production Caroline’s objective is to make her firm’s profit as large as possible. profit To see how a firm goes about maximizing profit, we must consider fully how to total revenue minus measure its total revenue and its total cost. Total revenue is the easy part: It equals total cost the quantity of output the firm produces multiplied by the price at which it sells its Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 249 output. If Caroline produces 10,000 cookies and sells them at $2 a cookie, her total revenue is $20,000. The measurement of a firm’s total cost, however, is more subtle. 13-1b Costs as Opportunity Costs When measuring costs at Caroline’s Cookie Factory or any other firm, it is import- ant to keep in mind one of the Ten Principles of Economics from Chapter 1: The cost of something is what you give up to get it. Recall that the opportunity cost of an item refers to all the things that must be forgone to acquire that item. When econ- omists speak of a firm’s cost of production, they include all the opportunity costs of making its output of goods and services. While some of a firm’s opportunity costs of production are obvious, others are less so. When Caroline pays $1,000 for flour, that $1,000 is an opportunity cost because Caroline can no longer use that $1,000 to buy something else. Similarly, when Caroline hires workers to make the cookies, the wages she pays are part of the firm’s costs. Because these opportunity costs require the firm to pay out some money, they are called explicit costs. By contrast, some of a firm’s opportunity explicit costs costs, called implicit costs, do not require a cash outlay. Imagine that Caroline input costs that require is skilled with computers and could earn $100 per hour working as a program- an outlay of money by mer. For every hour that Caroline works at her cookie factory, she gives up $100 the firm in income, and this forgone income is also part of her costs. The total cost of implicit costs Caroline’s business is the sum of her explicit and implicit costs. input costs that do not The distinction between explicit and implicit costs highlights an important require an outlay of difference between how economists and accountants analyze a business. Econo- money by the firm mists are interested in studying how firms make production and pricing decisions. Because these decisions are based on both explicit and implicit costs, economists include both when measuring a firm’s costs. By contrast, accountants have the job of keeping track of the money that flows into and out of firms. As a result, they measure the explicit costs but usually ignore the implicit costs. The difference between the methods of economists and accountants is easy to see in the case of Caroline’s Cookie Factory. When Caroline gives up the oppor- tunity to earn money as a computer programmer, her accountant will not count this as a cost of her cookie business. Because no money flows out of the business to pay for this cost, it never shows up on the accountant’s financial statements. An economist, however, will count the forgone income as a cost because it will affect the decisions that Caroline makes in her cookie business. For example, if Caroline’s wage as a computer programmer rises from $100 to $500 per hour, she might decide that running her cookie business is too costly. She might choose to shut down the factory so she can take a job as a programmer. 13-1c The Cost of Capital as an Opportunity Cost An important implicit cost of almost every business is the opportunity cost of the financial capital that has been invested in the business. Suppose, for instance, that Caroline used $300,000 of her savings to buy the cookie factory from its previous owner. If Caroline had instead left this money in a savings account that pays an interest rate of 5 percent, she would have earned $15,000 per year. To own her cookie factory, therefore, Caroline has given up $15,000 a year in interest income. This forgone $15,000 is one of the implicit opportunity costs of Caroline’s business. As we have already noted, economists and accountants treat costs differently, and this is especially true in their treatment of the cost of capital. An economist views the $15,000 in interest income that Caroline gives up every year as an Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 250 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY implicit cost of her business. Caroline’s accountant, however, will not show this $15,000 as a cost because no money flows out of the business to pay for it. To further explore the difference between the methods of economists and accountants, let’s change the example slightly. Suppose now that Caroline did not have the entire $300,000 to buy the factory but, instead, used $100,000 of her own savings and borrowed $200,000 from a bank at an interest rate of 5 percent. Caroline’s accountant, who only measures explicit costs, will now count the $10,000 interest paid on the bank loan every year as a cost because this amount of money now flows out of the firm. By contrast, according to an economist, the opportunity cost of owning the business is still $15,000. The opportunity cost equals the interest on the bank loan (an explicit cost of $10,000) plus the forgone interest on savings (an implicit cost of $5,000). 13-1d Economic Profit versus Accounting Profit Now let’s return to the firm’s objective: profit. Because economists and accoun- tants measure costs differently, they also measure profit differently. An econo- economic profit mist measures a firm’s economic profit as the firm’s total revenue minus all the total revenue minus total opportunity costs (explicit and implicit) of producing the goods and services sold. cost, including both An accountant measures the firm’s accounting profit as the firm’s total revenue explicit and implicit costs minus only the firm’s explicit costs. Figure 1 summarizes this difference. Notice that because the accountant accounting profit ignores the implicit costs, accounting profit is usually larger than economic profit. total revenue minus total For a business to be profitable from an economist’s standpoint, total revenue must explicit cost exceed all the opportunity costs, both explicit and implicit. Economic profit is an important concept because it motivates the firms that supply goods and services. As we will see, a firm making positive economic profit will stay in business. It is covering all its opportunity costs and has some reve- nue left to reward the firm owners. When a firm is making economic losses (that is, when economic profits are negative), the business owners are failing to earn enough revenue to cover all the costs of production. Unless conditions change, FIGURE 1 How an Economist How an Accountant Views a Firm Views a Firm Economists versus Accountants Economists include all opportunity Economic costs when analyzing a firm, whereas profit accountants measure only explicit costs. Therefore, economic profit is Accounting profit smaller than accounting profit. Implicit Revenue costs Revenue Total opportunity costs Explicit Explicit costs costs Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 251 the firm owners will eventually close down the business and exit the industry. To understand business decisions, we need to keep an eye on economic profit. Farmer McDonald gives banjo lessons for $20 an hour. One day, he spends QuickQuiz 10 hours planting $100 worth of seeds on his farm. What opportunity cost has he incurred? What cost would his accountant measure? If these seeds yield $200 worth of crops, does McDonald earn an accounting profit? Does he earn an economic profit? 13-2 Production and Costs Firms incur costs when they buy inputs to produce the goods and services that they plan to sell. In this section, we examine the link between a firm’s production process and its total cost. Once again, we consider Caroline’s Cookie Factory. In the analysis that follows, we make an important simplifying assumption: We assume that the size of Caroline’s factory is fixed and that Caroline can vary the quantity of cookies produced only by changing the number of workers she employs. This assumption is realistic in the short run but not in the long run. That is, Caroline cannot build a larger factory overnight, but she could do so over the next year or two. This analysis, therefore, describes the production decisions that Caroline faces in the short run. We examine the relationship between costs and time horizon more fully later in the chapter. 13-2a The Production Function Table 1 shows how the quantity of cookies produced per hour at Caroline’s factory depends on the number of workers. As you can see in columns (1) and (2), if there are no workers in the factory, Caroline produces no cookies. TABLE 1 (1) (2) (3) (4) (5) (6) A Production Function Output (quantity and Total Cost: Caroline’s of cookies Marginal Total Cost of Inputs Cookie Factory Number produced per Product of Cost of Cost of (cost of factory + of Workers hour) Labor Factory Workers cost of workers) 0 0 $30 $0 $30 50 1 50 30 10 40 40 2 90 30 20 50 30 3 120 30 30 60 20 4 140 30 40 70 10 5 150 30 50 80 5 6 155 30 60 90 Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 252 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY When there is 1 worker, she produces 50 cookies. When there are 2 workers, she produces 90 cookies and so on. Panel (a) of Figure 2 presents a graph of these two columns of numbers. The number of workers is on the horizontal axis, and the number of cookies produced is on the vertical axis. This relation- ship between the quantity of inputs (workers) and quantity of output (cookies) production function is called the production function. the relationship between One of the Ten Principles of Economics introduced in Chapter 1 is that ratio- the quantity of inputs nal people think at the margin. As we will see in future chapters, this idea is used to make a good and the key to understanding the decisions a firm makes about how many workers the quantity of output of to hire and how much output to produce. To take a step toward understanding that good these decisions, column (3) in the table gives the marginal product of a worker. marginal product The marginal product of any input in the production process is the increase in the increase in output the quantity of output obtained from one additional unit of that input. When the that arises from an number of workers goes from 1 to 2, cookie production increases from 50 to 90, so additional unit of input the marginal product of the second worker is 40 cookies. And when the number of FIGURE 2 The production function in panel (a) shows the relationship between the number of workers hired and the quantity of output produced. Here the number of workers hired (on the horizon- Caroline’s Production tal axis) is from column (1) in Table 1, and the quantity of output produced (on the vertical Function and Total-Cost axis) is from column (2). The production function gets flatter as the number of workers Curve increases, reflecting diminishing marginal product. The total-cost curve in panel (b) shows the relationship between the quantity of output produced and total cost of production. Here the quantity of output produced (on the horizontal axis) is from column (2) in Table 1, and the total cost (on the vertical axis) is from column (6). The total-cost curve gets steeper as the quantity of output increases because of diminishing marginal product. (a) Production function (b) Total-cost curve Quantity Total of Output Cost (cookies $90 per hour) 160 Production 80 Total-cost function curve 140 70 120 60 100 50 80 40 60 30 40 20 20 10 0 1 2 3 4 5 6 Number of 0 20 40 60 80 100 120 140 160 Quantity Workers Hired of Output (cookies per hour) Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 253 workers goes from 2 to 3, cookie production increases from 90 to 120, so the mar- ginal product of the third worker is 30 cookies. In the table, the marginal product is shown halfway between two rows because it represents the change in output as the number of workers increases from one level to another. Notice that as the number of workers increases, the marginal product declines. The second worker has a marginal product of 40 cookies, the third worker has a marginal product of 30 cookies, and the fourth worker has a marginal prod- uct of 20 cookies. This property is called diminishing marginal product. At first, diminishing marginal when only a few workers are hired, they have easy access to Caroline’s kitchen product equipment. As the number of workers increases, additional workers have to the property whereby share equipment and work in more crowded conditions. Eventually, the kitchen the marginal product becomes so overcrowded that workers often get in each other’s way. Hence, as of an input declines as more workers are hired, each additional worker contributes fewer additional the quantity of the input cookies to total production. increases Diminishing marginal product is also apparent in Figure 2. The produc- tion function’s slope (“rise over run”) tells us the change in Caroline’s output of cookies (“rise”) for each additional input of labor (“run”). That is, the slope of the production function measures the marginal product. As the number of workers increases, the marginal product declines, and the production function becomes flatter. 13-2b From the Production Function to the Total-Cost Curve Columns (4), (5), and (6) in Table 1 show Caroline’s cost of producing cookies. In this example, the cost of Caroline’s factory is $30 per hour, and the cost of a worker is $10 per hour. If she hires 1 worker, her total cost is $40 per hour. If she hires 2 workers, her total cost is $50 per hour, and so on. With this information, the table now shows how the number of workers Caroline hires is related to the quantity of cookies she produces and to her total cost of production. Our goal in the next several chapters is to study firms’ production and pricing decisions. For this purpose, the most important relationship in Table 1 is between quantity produced [in column (2)] and total cost [in column (6)]. Panel (b) of Figure 2 graphs these two columns of data with quantity produced on the horizontal axis and total cost on the vertical axis. This graph is called the total-cost curve. Now compare the total-cost curve in panel (b) with the production function in panel (a). These two curves are opposite sides of the same coin. The total-cost curve gets steeper as the amount produced rises, whereas the production function gets flatter as production rises. These changes in slope occur for the same rea- son. High production of cookies means that Caroline’s kitchen is crowded with many workers. Because the kitchen is crowded, each additional worker adds less to production, reflecting diminishing marginal product. Therefore, the production function is relatively flat. But now turn this logic around: When the kitchen is crowded, producing an additional cookie requires a lot of additional labor and is thus very costly. Therefore, when the quantity produced is large, the total-cost curve is relatively steep. If Farmer Jones plants no seeds on her farm, she gets no harvest. If she QuickQuiz plants 1 bag of seeds, she gets 3 bushels of wheat. If she plants 2 bags, she gets 5 bushels. If she plants 3 bags, she gets 6 bushels. A bag of seeds costs $100, and seeds are her only cost. Use these data to graph the farmer’s production function and total-cost curve. Explain their shapes. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 254 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY 13-3 The Various Measures of Cost Our analysis of Caroline’s Cookie Factory demonstrated how a firm’s total cost reflects its production function. From data on a firm’s total cost, we can derive several related measures of cost, which will turn out to be useful when we ana- lyze production and pricing decisions in future chapters. To see how these related measures are derived, we consider the example in Table 2. This table presents cost data on Caroline’s neighbor—Conrad’s Coffee Shop. Column (1) in the table shows the number of cups of coffee that Conrad might produce, ranging from 0 to 10 cups per hour. Column (2) shows Conrad’s total cost of producing coffee. Figure 3 plots Conrad’s total-cost curve. The quantity of coffee [from column (1)] is on the horizontal axis, and total cost [from column (2)] is on the vertical axis. Conrad’s total-cost curve has a shape similar to Caroline’s. In particular, it becomes steeper as the quantity produced rises, which (as we have discussed) reflects diminishing marginal product. TABLE 2 (1) (2) (3) (4) (5) (6) (7) (8) The Various Measures of Output Cost: Conrad’s Coffee Shop (cups of Average Average Average coffee per Total Fixed Variable Fixed Variable Total Marginal hour) Cost Cost Cost Cost Cost Cost Cost 0 $3.00 $3.00 $0.00 — — — $0.30 1 3.30 3.00 0.30 $3.00 $0.30 $3.30 0.50 2 3.80 3.00 0.80 1.50 0.40 1.90 0.70 3 4.50 3.00 1.50 1.00 0.50 1.50 0.90 4 5.40 3.00 2.40 0.75 0.60 1.35 1.10 5 6.50 3.00 3.50 0.60 0.70 1.30 1.30 6 7.80 3.00 4.80 0.50 0.80 1.30 1.50 7 9.30 3.00 6.30 0.43 0.90 1.33 1.70 8 11.00 3.00 8.00 0.38 1.00 1.38 1.90 9 12.90 3.00 9.90 0.33 1.10 1.43 2.10 10 15.00 3.00 12.00 0.30 1.20 1.50 Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 255 Total Cost FIGURE 3 $15.00 Total-cost curve 14.00 Conrad’s Total-Cost Curve 13.00 Here the quantity of output produced (on the 12.00 horizontal axis) is from column (1) in Table 2, 11.00 and the total cost (on the vertical axis) is from column (2). As in Figure 2, the total-cost curve 10.00 gets steeper as the quantity of output increases 9.00 because of diminishing marginal product. 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0 1 2 3 4 5 6 7 8 9 10 Quantity of Output (cups of coffee per hour) 13-3a Fixed and Variable Costs Conrad’s total cost can be divided into two types. Some costs, called fixed costs, fixed costs do not vary with the quantity of output produced. They are incurred even if costs that do not vary the firm produces nothing at all. Conrad’s fixed costs include any rent he pays with the quantity of because this cost is the same regardless of how much coffee he produces. Sim- output produced ilarly, if Conrad needs to hire a full-time bookkeeper to pay bills, regardless of the quantity of coffee produced, the bookkeeper’s salary is a fixed cost. The third column in Table 2 shows Conrad’s fixed cost, which in this example is $3.00. Some of the firm’s costs, called variable costs, change as the firm alters the quan- variable costs tity of output produced. Conrad’s variable costs include the cost of coffee beans, costs that vary with milk, sugar, and paper cups: The more cups of coffee Conrad makes, the more of the quantity of output these items he needs to buy. Similarly, if Conrad has to hire more workers to make produced more cups of coffee, the salaries of these workers are variable costs. Column (4) in the table shows Conrad’s variable cost. The variable cost is 0 if he produces noth- ing, $0.30 if he produces 1 cup of coffee, $0.80 if he produces 2 cups, and so on. A firm’s total cost is the sum of fixed and variable costs. In Table 2, total cost in column (2) equals fixed cost in column (3) plus variable cost in column (4). 13-3b Average and Marginal Cost As the owner of his firm, Conrad has to decide how much to produce. One issue he will want to consider when making this decision is how the level of production affects his firm’s costs. Conrad might ask his production supervisor the following two questions about the cost of producing coffee: How much does it cost to make the typical cup of coffee? How much does it cost to increase production of coffee by 1 cup? Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 256 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY These two questions might seem to have the same answer, but they do not. Both answers are important for understanding how firms make production decisions. To find the cost of the typical unit produced, we divide the firm’s costs by the quantity of output it produces. For example, if the firm produces 2 cups of coffee per hour, its total cost is $3.80, and the cost of the typical cup is $3.80/2, or $1.90. average total cost Total cost divided by the quantity of output is called average total cost. Because total cost divided by the total cost is the sum of fixed and variable costs, average total cost can be expressed quantity of output as the sum of average fixed cost and average variable cost. Average fixed cost is the fixed cost divided by the quantity of output, and average variable cost is the average fixed cost variable cost divided by the quantity of output. fixed cost divided by the Average total cost tells us the cost of the typical unit, but it does not tell us how quantity of output much total cost will change as the firm alters its level of production. Column (8) in average variable cost Table 2 shows the amount that total cost rises when the firm increases production variable cost divided by by 1 unit of output. This number is called marginal cost. For example, if Conrad the quantity of output increases production from 2 to 3 cups, total cost rises from $3.80 to $4.50, so the marginal cost of the third cup of coffee is $4.50 minus $3.80, or $0.70. In the table, marginal cost the marginal cost appears halfway between any two rows because it represents the increase in total cost the change in total cost as quantity of output increases from one level to another. that arises from an extra It may be helpful to express these definitions mathematically: unit of production Average total cost 5 Total cost/Quantity ATC 5 TC/Q, and Marginal cost 5 Change in total cost/Change in quantity MC 5 ∆TC/∆Q Here ∆, the Greek letter delta, represents the change in a variable. These equa- tions show how average total cost and marginal cost are derived from total cost. Average total cost tells us the cost of a typical unit of output if total cost is divided evenly over all the units produced. Marginal cost tells us the increase in total cost that arises from producing an additional unit of output. As we will see more fully in the next chapter, business managers like Conrad need to keep in mind the concepts of average total cost and marginal cost when deciding how much of their product to supply to the market. 13-3c Cost Curves and Their Shapes Just as we found graphs of supply and demand useful when analyzing the behav- ior of markets in previous chapters, we will find graphs of average and marginal cost useful when analyzing the behavior of firms. Figure 4 graphs Conrad’s costs using the data from Table 2. The horizontal axis measures the quantity the firm produces, and the vertical axis measures marginal and average costs. The graph shows four curves: average total cost (ATC), average fixed cost (AFC), average variable cost (AVC), and marginal cost (MC). The cost curves shown here for Conrad’s Coffee Shop have some features that are common to the cost curves of many firms in the economy. Let’s exam- ine three features in particular: the shape of the marginal-cost curve, the shape of the average-total-cost curve, and the relationship between marginal cost and average total cost. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 257 Costs FIGURE 4 $3.50 Conrad’s Average-Cost and 3.25 Marginal-Cost Curves 3.00 This figure shows the average total 2.75 cost (ATC), average fixed cost (AFC), average variable cost (AVC), and 2.50 marginal cost (MC) for Conrad’s 2.25 Coffee Shop. All of these curves MC 2.00 are obtained by graphing the data in Table 2. These cost curves show 1.75 three common features: (1) Marginal 1.50 ATC cost rises with the quantity of out- 1.25 put. (2) The average-total-cost curve AVC is U-shaped. (3) The marginal-cost 1.00 curve crosses the average-total-cost 0.75 curve at the minimum of average 0.50 total cost. 0.25 AFC 0 1 2 3 4 5 6 7 8 9 10 Quantity of Output (cups of coffee per hour) Rising Marginal Cost Conrad’s marginal cost rises as the quantity of output pro- duced increases. This upward slope reflects the property of diminishing marginal product. When Conrad produces a small quantity of coffee, he has few workers, and much of his equipment is not used. Because he can easily put these idle resources to use, the marginal product of an extra worker is large, and the mar- ginal cost of an extra cup of coffee is small. By contrast, when Conrad produces a large quantity of coffee, his shop is crowded with workers, and most of his equipment is fully utilized. Conrad can produce more coffee by adding workers, but these new workers have to work in crowded conditions and may have to wait to use the equipment. Therefore, when the quantity of coffee produced is already high, the marginal product of an extra worker is low, and the marginal cost of an extra cup of coffee is large. U-Shaped Average Total Cost Conrad’s average-total-cost curve is U-shaped, as shown in Figure 4. To understand why, remember that average total cost is the sum of average fixed cost and average variable cost. Average fixed cost always declines as output rises because the fixed cost is getting spread over a larger num- ber of units. Average variable cost usually rises as output increases because of diminishing marginal product. Average total cost reflects the shapes of both average fixed cost and average variable cost. At very low levels of output, such as 1 or 2 cups per hour, average total cost is very high. Even though average variable cost is low, average fixed cost is high because the fixed cost is spread over only a few units. As output Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 258 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY increases, the fixed cost is spread over more units. Average fixed cost declines, rapidly at first and then more slowly. As a result, average total cost also declines until the firm’s output reaches 5 cups of coffee per hour, when average total cost is $1.30 per cup. When the firm produces more than 6 cups per hour, however, the increase in average variable cost becomes the dominant force, and average total cost starts rising. The tug of war between average fixed cost and average variable cost generates the U-shape in average total cost. The bottom of the U-shape occurs at the quantity that minimizes average total efficient scale cost. This quantity is sometimes called the efficient scale of the firm. For Conrad, the quantity of output the efficient scale is 5 or 6 cups of coffee per hour. If he produces more or less than that minimizes average this amount, his average total cost rises above the minimum of $1.30. At lower total cost levels of output, average total cost is higher than $1.30 because the fixed cost is spread over so few units. At higher levels of output, average total cost is higher than $1.30 because the marginal product of inputs has diminished significantly. At the efficient scale, these two forces are balanced to yield the lowest average total cost. The Relationship between Marginal Cost and Average Total Cost If you look at Figure 4 (or back at Table 2), you will see something that may be surprising at first. Whenever marginal cost is less than average total cost, average total cost is falling. Whenever marginal cost is greater than average total cost, average total cost is rising. This feature of Conrad’s cost curves is not a coincidence from the particular num- bers used in the example: It is true for all firms. To see why, consider an analogy. Average total cost is like your cumulative grade point average. Marginal cost is like the grade you get in the next course you take. If your grade in your next course is less than your grade point average, your grade point average will fall. If your grade in your next course is higher than your grade point average, your grade point average will rise. The mathematics of average and marginal costs is exactly the same as the mathematics of average and marginal grades. This relationship between average total cost and marginal cost has an import- ant corollary: The marginal-cost curve crosses the average-total-cost curve at its min- imum. Why? At low levels of output, marginal cost is below average total cost, so average total cost is falling. But after the two curves cross, marginal cost rises above average total cost. As a result, average total cost must start to rise at this level of output. Hence, this point of intersection is the minimum of average total cost. As we will see in the next chapter, minimum average total cost plays a key role in the analysis of competitive firms. 13-3d Typical Cost Curves In the examples we have studied so far, the firms have exhibited diminishing marginal product and, therefore, rising marginal cost at all levels of output. This simplifying assumption was useful because it allowed us to focus on the key features of cost curves that are useful in analyzing firm behavior. Yet actual firms are usually more complicated than this. In many firms, marginal product does not start to fall immediately after the first worker is hired. Depending on the production process, the second or third worker might have a higher marginal product than the first because a team of workers can divide tasks and work more productively than a single worker. Firms exhibiting this pattern would experience increasing marginal product for a while before diminishing marginal product set in. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 259 FIGURE 5 Costs Cost Curves for a Typical Firm $3.00 Many firms experience increasing marginal product before diminishing marginal product. As a result, they 2.50 have cost curves shaped like those MC in this figure. Notice that marginal 2.00 cost and average variable cost fall for a while before starting to rise. 1.50 ATC AVC 1.00 0.50 AFC 0 2 4 6 8 10 12 14 Quantity of Output Figure 5 shows the cost curves for such a firm, including average total cost (ATC), average fixed cost (AFC), average variable cost (AVC), and marginal cost (MC). At low levels of output, the firm experiences increasing marginal prod- uct, and the marginal-cost curve falls. Eventually, the firm starts to experience diminishing marginal product, and the marginal-cost curve starts to rise. This combination of increasing then diminishing marginal product also makes the average-variable-cost curve U-shaped. Despite these differences from our previous example, the cost curves in Figure 5 share the three properties that are most important to remember: Marginal cost eventually rises with the quantity of output. The average-total-cost curve is U-shaped. The marginal-cost curve crosses the average-total-cost curve at the minimum of average total cost. Suppose Honda’s total cost of producing 4 cars is $225,000 and its total QuickQuiz cost of producing 5 cars is $250,000. What is the average total cost of producing 5 cars? What is the marginal cost of the fifth car? Draw the marginal-cost curve and the average-total-cost curve for a typical firm, and explain why these curves cross where they do. 13-4 Costs in the Short Run and in the Long Run We noted earlier in this chapter that a firm’s costs might depend on the time horizon under consideration. Let’s examine more precisely why this might be the case. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 260 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY 13-4a The Relationship between Short-Run and Long-Run Average Total Cost For many firms, the division of total costs between fixed and variable costs depends on the time horizon. Consider, for instance, a car manufacturer such as Ford Motor Company. Over a period of only a few months, Ford cannot adjust the number or sizes of its car factories. The only way it can produce additional cars is to hire more workers at the factories it already has. The cost of these factories is, therefore, a fixed cost in the short run. By contrast, over a period of several years, Ford can expand the size of its factories, build new factories, or close old ones. Thus, the cost of its factories is a variable cost in the long run. Because many decisions are fixed in the short run but variable in the long run, a firm’s long-run cost curves differ from its short-run cost curves. Figure 6 shows an example. The figure presents three short-run average-total-cost curves—for a small, medium, and large factory. It also presents the long-run average-total-cost curve. As the firm moves along the long-run curve, it is adjusting the size of the factory to the quantity of production. This graph shows how short-run and long-run costs are related. The long-run average-total-cost curve has a much flatter U-shape than the short-run average- total-cost curve. In addition, all the short-run curves lie on or above the long-run curve. These properties arise because firms have greater flexibility in the long run. In essence, in the long run, the firm gets to choose which short-run curve it wants to use. But in the short run, it has to use whatever short-run curve it has, based on decisions it has made in the past. The figure shows an example of how a change in production alters costs over different time horizons. When Ford wants to increase production from 1,000 to 1,200 cars per day, it has no choice in the short run but to hire more workers at its existing medium-sized factory. Because of diminishing marginal product, average total cost rises from $10,000 to $12,000 per car. In the long run, however, Ford can expand both the size of the factory and its workforce, and average total cost returns to $10,000. FIGURE 6 Average Total ATC in short ATC in short ATC in short Average Total Cost in the Cost run with run with run with small factory medium factory large factory ATC in long run Short and Long Runs Because fixed costs are variable in the long run, the average-total-cost curve in the short run differs from the average-total-cost curve in the $12,000 long run. 10,000 Economies Constant of returns to scale scale Diseconomies of scale 0 1,000 1,200 Quantity of Cars per Day Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 261 How long does it take a firm to get to the long run? The answer depends on the firm. It can take a year or more for a major manufacturing firm, such as a car company, to build a larger factory. By contrast, a person running a coffee shop can buy another coffee maker within a few days. There is, therefore, no single answer to the question of how long it takes a firm to adjust its production facilities. 13-4b Economies and Diseconomies of Scale The shape of the long-run average-total-cost curve conveys important informa- tion about the production processes that a firm has available for manufacturing a economies of scale good. In particular, it tells us how costs vary with the scale—that is, the size—of a the property whereby firm’s operations. When long-run average total cost declines as output increases, long-run average total there are said to be economies of scale. When long-run average total cost rises as cost falls as the quantity output increases, there are said to be diseconomies of scale. When long-run aver- of output increases age total cost does not vary with the level of output, there are said to be constant diseconomies of scale returns to scale. As we can see in Figure 6, Ford has economies of scale at low the property whereby levels of output, constant returns to scale at intermediate levels of output, and long-run average total diseconomies of scale at high levels of output. cost rises as the quantity What might cause economies or diseconomies of scale? Economies of scale of output increases often arise because higher production levels allow specialization among workers, which permits each worker to become better at a specific task. For instance, if constant returns to scale Ford hires a large number of workers and produces a large number of cars, it can the property whereby reduce costs using modern assembly-line production. Diseconomies of scale can long-run average total arise because of coordination problems that are inherent in any large organization. cost stays the same as The more cars Ford produces, the more stretched the management team becomes, the quantity of output and the less effective the managers become at keeping costs down. changes FYI Lessons from a Pin Factory “J ack of all trades, master of none.” This well-known adage sheds light on the nature of cost curves. A person who tries to do everything usually ends up doing nothing very well. If a firm wants its workers to be workers had chosen to work separately, rather than as a team of spe- as productive as they can be, it is often best to give each worker a limited cialists, “they certainly task that she can master. But this organization of work is possible only could not each of them if a firm employs many workers and produces a large quantity of output. make twenty, perhaps not In his celebrated book An Inquiry into the Nature and Causes of the one pin a day.” In other words, Wealth of Nations, Adam Smith described a visit he made to a pin factory. because of specialization, a large pin factory could achieve higher output Smith was impressed by the specialization among the workers and the per worker and lower average cost per pin than a small pin factory. resulting economies of scale. He wrote, The specialization that Smith observed in the pin factory is preva- lent in the modern economy. If you want to build a house, for instance, One man draws out the wire, another straightens it, a third cuts it, a you could try to do all the work yourself. But most people turn to a fourth points it, a fifth grinds it at the top for receiving the head; to builder, who in turn hires carpenters, plumbers, electricians, painters, make the head requires two or three distinct operations; to put it on is and many other types of workers. These workers focus their training and a peculiar business; to whiten it is another; it is even a trade by itself experience in particular jobs, and as a result, they become better at to put them into paper. their jobs than if they were generalists. Indeed, the use of specialization Smith reported that because of this specialization, the pin factory pro- to achieve economies of scale is one reason modern societies are as duced thousands of pins per worker every day. He conjectured that if the prosperous as they are. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 262 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY This analysis shows why long-run average-total-cost curves are often U-shaped. At low levels of production, the firm benefits from increased size because it can take advantage of greater specialization. Coordination problems, meanwhile, are not yet acute. By contrast, at high levels of production, the benefits of specialization have already been realized, and coordination problems become more severe as the firm grows larger. Thus, long-run average total cost is falling at low levels of production because of increasing specialization and rising at high levels of production because of growing coordination problems. If Boeing produces 9 jets per month, its long-run total cost is $9.0 million QuickQuiz per month. If it produces 10 jets per month, its long-run total cost is $9.5 million per month. Does Boeing exhibit economies or diseconomies of scale? 13-5 Conclusion The purpose of this chapter has been to develop some tools to study how firms make production and pricing decisions. You should now understand what econ- omists mean by the term costs and how costs vary with the quantity of output a firm produces. To refresh your memory, Table 3 summarizes some of the defini- tions we have encountered. By themselves, a firm’s cost curves do not tell us what decisions the firm will make. But they are a key component of that decision, as we will see in the next chapter. TABLE 3 Mathematical The Many Types Term Definition Description of Cost: A Summary Explicit costs Costs that require an outlay of money by the firm Implicit costs Costs that do not require an outlay of money by the firm Fixed costs Costs that do not vary with the FC quantity of output produced Variable costs Costs that vary with the quantity VC of output produced Total cost The market value of all the inputs TC 5 FC 1 VC that a firm uses in production Average fixed cost Fixed cost divided by the quantity AFC 5 FC / Q of output Average variable cost Variable cost divided by the quantity AVC 5 VC / Q of output Average total cost Total cost divided by the quantity of ATC 5 TC / Q output Marginal cost The increase in total cost that arises MC 5 ΔTC / ΔQ from an extra unit of production Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 263 CHAPTER QuickQuiz 1. Xavier opens up a lemonade stand for two hours. 4. A firm is producing 20 units with an average total He spends $10 for ingredients and sells $60 worth cost of $25 and a marginal cost of $15. If it were to of lemonade. In the same two hours, he could have increase production to 21 units, which of the follow- mowed his neighbor’s lawn for $40. Xavier has an ing must occur? accounting profit of _____ and an economic profit of a. Marginal cost would decrease. ____. b. Marginal cost would increase. a. $50, $10 c. Average total cost would decrease. b. $90, $50 d. Average total cost would increase. c. $10, $50 5. The government imposes a $1,000 per year license d. $50, $90 fee on all pizza restaurants. As a result, which cost 2. Diminishing marginal product explains why, as a curves shift? firm’s output increases, a. average total cost and marginal cost a. the production function and total-cost curve both b. average total cost and average fixed cost get steeper. c. average variable cost and marginal cost b. the production function and total-cost curve both d. average variable cost and average fixed cost get flatter. 6. If a higher level of production allows workers to c. the production function gets steeper, while the specialize in particular tasks, a firm will likely exhibit total-cost curve gets flatter. ________ of scale and ________ average total cost. d. the production function gets flatter, while the a. economies, falling total-cost curve gets steeper. b. economies, rising 3. A firm is producing 1,000 units at a total cost c. diseconomies, falling of $5,000. If it were to increase production to d. diseconomies, rising 1,001 units, its total cost would rise to $5,008. What does this information tell you about the firm? a. Marginal cost is $5, and average variable cost is $8. b. Marginal cost is $8, and average variable cost is $5. c. Marginal cost is $5, and average total cost is $8. d. Marginal cost is $8, and average total cost is $5. SUMMARY The goal of firms is to maximize profit, which equals Variable costs are costs that change when the firm total revenue minus total cost. alters the quantity of output produced. When analyzing a firm’s behavior, it is important to From a firm’s total cost, two related measures of cost include all the opportunity costs of production. Some of are derived. Average total cost is total cost divided by the opportunity costs, such as the wages a firm pays its the quantity of output. Marginal cost is the amount by workers, are explicit. Other opportunity costs, such as the which total cost rises if output increases by 1 unit. wages the firm owner gives up by working at the firm When analyzing firm behavior, it is often useful to rather than taking another job, are implicit. Economic graph average total cost and marginal cost. For a profit takes both explicit and implicit costs into account, typical firm, marginal cost rises with the quantity whereas accounting profit considers only explicit costs. of output. Average total cost first falls as output A firm’s costs reflect its production process. A typical increases and then rises as output increases further. firm’s production function gets flatter as the quantity The marginal-cost curve always crosses the average- of an input increases, displaying the property of dimin- total-cost curve at the minimum of average total cost. ishing marginal product. As a result, a firm’s total-cost A firm’s costs often depend on the time horizon con- curve gets steeper as the quantity produced rises. sidered. In particular, many costs are fixed in the short A firm’s total costs can be divided into fixed costs and run but variable in the long run. As a result, when the variable costs. Fixed costs are costs that do not change firm changes its level of production, average total cost when the firm alters the quantity of output produced. may rise more in the short run than in the long run. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 264 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY KEY CONCEPTS total revenue, p. 248 production function, p. 252 average variable cost, p. 256 total cost, p. 248 marginal product, p. 252 marginal cost, p. 256 profit, p. 248 diminishing marginal product, p. 253 efficient scale, p. 258 explicit costs, p. 249 fixed costs, p. 255 economies of scale, p. 261 implicit costs, p. 249 variable costs, p. 255 diseconomies of scale, p. 261 economic profit, p. 250 average total cost, p. 256 constant returns to scale, p. 261 accounting profit, p. 250 average fixed cost, p. 256 QUESTIONS FOR REVIEW 1. What is the relationship between a firm’s total 5. Define total cost, average total cost, and marginal cost. revenue, profit, and total cost? How are they related? 2. Give an example of an opportunity cost that an 6. Draw the marginal-cost and average-total-cost accountant would not count as a cost. Why would the curves for a typical firm. Explain why the curves have accountant ignore this cost? the shapes that they do and why they intersect where 3. What is marginal product, and what does it mean if it they do. is diminishing? 7. How and why does a firm’s average-total-cost curve 4. Draw a production function that exhibits diminishing differ in the short run compared with the long run? marginal product of labor. Draw the associated 8. Define economies of scale and explain why they might total-cost curve. (In both cases, be sure to label the axes.) arise. Define diseconomies of scale and explain why they Explain the shapes of the two curves you have drawn. might arise. PROBLEMS AND APPLICATIONS 1. This chapter discusses many types of costs: a. Define opportunity cost. opportunity cost, total cost, fixed cost, variable cost, b. What is your aunt’s opportunity cost of running average total cost, and marginal cost. Fill in the type of the hardware store for a year? If your aunt thinks cost that best completes each sentence: she can sell $510,000 worth of merchandise in a a. What you give up in taking some action is called year, should she open the store? Explain. the ______. 3. A commercial fisherman notices the following rela- b. _____ is falling when marginal cost is below it and tionship between hours spent fishing and the quantity rising when marginal cost is above it. of fish caught: c. A cost that does not depend on the quantity produced is a(n) ______. Quantity of Fish d. In the ice-cream industry in the short run, ______ Hours (in pounds) includes the cost of cream and sugar but not the cost of the factory. 0 hours 0 lb. e. Profits equal total revenue minus ______. 1 10 f. The cost of producing an extra unit of output is 2 18 the ______. 3 24 4 28 2. Your aunt is thinking about opening a hardware store. 5 30 She estimates that it would cost $500,000 per year to rent the location and buy the stock. In addition, she a. What is the marginal product of each hour spent would have to quit her $50,000 per year job as an fishing? accountant. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 13 THE COSTS OF PRODUCTION 265 b. Use these data to graph the fisherman’s Your current level of production is 600 devices, production function. Explain its shape. all of which have been sold. Someone calls, desperate c. The fisherman has a fixed cost of $10 (his pole). to buy one of your music players. The caller offers The opportunity cost of his time is $5 per hour. you $550 for it. Should you accept the offer? Graph the fisherman’s total-cost curve. Explain Why or why not? its shape. 6. Consider the following cost information for a pizzeria: 4. Nimbus, Inc., makes brooms and then sells them door- to-door. Here is the relationship between the number Quantity Total Cost Variable Cost of workers and Nimbus’s output during a given day: 0 dozen pizzas $300 $0 Average 1 350 50 Marginal Total Total Marginal 2 390 90 Workers Output Product Cost Cost Cost 3 420 120 4 450 150 0 0 ___ ___ 5 490 190 ___ ___ 6 540 240 1 20 ___ ___ ___ ___ a. What is the pizzeria’s fixed cost? 2 50 ___ ___ b. Construct a table in which you calculate ___ ___ the marginal cost per dozen pizzas using the 3 90 ___ ___ information on total cost. Also, calculate the ___ ___ marginal cost per dozen pizzas using the infor- 4 120 ___ ___ mation on variable cost. What is the relationship ___ ___ between these sets of numbers? Explain. 5 140 ___ ___ 7. Your cousin Vinnie owns a painting company with ___ ___ fixed costs of $200 and the following schedule for 6 150 ___ ___ variable costs: ___ ___ 7 155 ___ ___ Quantity of Houses 1 2 3 4 5 6 7 a. Fill in the column of marginal products. What Painted pattern do you see? How might you explain it? per Month b. A worker costs $100 a day, and the firm has fixed costs of $200. Use this information to fill in the Variable $10 $20 $40 $80 $160 $320 $640 column for total cost. Costs c. Fill in the column for average total cost. (Recall Calculate average fixed cost, average variable cost, that ATC 5 TC/Q.) What pattern do you see? and average total cost for each quantity. What is the d. Now fill in the column for marginal cost. (Recall efficient scale of the painting company? that MC 5 ∆TC/∆Q.) What pattern do you see? 8. The city government is considering two e. Compare the column for marginal product tax proposals: with the column for marginal cost. Explain the A lump-sum tax of $300 on each producer of relationship. hamburgers. f. Compare the column for average total cost A tax of $1 per burger, paid by producers of with the column for marginal cost. Explain the hamburgers. relationship. a. Which of the following curves—average fixed 5. You are the chief financial officer for a firm that sells cost, average variable cost, average total cost, digital music players. Your firm has the following and marginal cost—would shift as a result of the average-total-cost schedule: lump-sum tax? Why? Show this in a graph. Label the graph as precisely as possible. Quantity Average Total Cost b. Which of these same four curves would shift as a result of the per-burger tax? Why? Show this 600 players $300 in a new graph. Label the graph as precisely as 601 301 possible. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 266 PART V FIRM BEHAVIOR AND THE ORGANIZATION OF INDUSTRY 9. Jane’s Juice Bar has the following cost schedules: 10. Consider the following table of long-run total costs for three different firms: Quantity Variable Cost Total Cost Quantity 1 2 3 4 5 6 7 0 vats of juice $0 $ 30 1 10 40 Firm A $60 $70 $80 $90 $100 $110 $120 2 25 55 Firm B 11 24 39 56 75 96 119 3 45 75 Firm C 21 34 49 66 85 106 129 4 70 100 5 100 130 Does each of these firms experience economies of scale 6 135 165 or diseconomies of scale? a. Calculate average variable cost, average total cost, and marginal cost for each quantity. b. Graph all three curves. What is the relationship between the marginal-cost curve and the average-total-cost curve? Between the marginal-cost curve and the average-variable- To find additional study resources, visit cengagebrain.com, cost curve? Explain. and search for “Mankiw.”