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1 CHAPTER 5 FIRM PRODUCTION, COST, AND REVENUE CHAPTER OBJECTIVES You will find in this chapter models that will help you understand the relationship between production and costs and the relationship between sales and revenues. You should know that models of production are based on the assumption that firms seek to maximize profit. Lastly, you will be shown that profit maximization dictates that firms set production CHAPTER OUTLINE CHAPTER OBJECTIVES INTRODUCTION PRODUCTION Graphical Explanation COSTS Graphical Explanation REVENUE Graphical Explanation PROFIT AND PROFIT MAXIMIZATION Graphical Explanation CHAPTER SUMMARY such that marginal cost equals marginal revenue. INTRODUCTION The business of business is making money, and the money business makes is called Profit: The money that business makes: Revenue-Cost profit. How it makes that profit is by selling its goods for more than it costs to make them. For this chapter (and for most of this book) we will make the simplifying assumption that nothing influences business other than maximizing profit. While that is an exaggeration, it is reasonably close to the truth, and acting as if it is the truth simplifies our task considerably. While there is nothing about this chapter that is simple, you might find it comforting that it could be more complicated; then again you might not. 96

2 With the simplifying assumption of myopic profit maximization in place, we can break things down into the cost side and the revenue side. Cost is the expense that Cost: the expense that must be incurred in order to produce goods for sale Revenue : the money that comes into the firm from the sale of their goods businesses must incurr in order to produce goods for sale. Revenue is the money that comes into the firm from the sale of the goods. It is important to understand why economists focus on costs that are incurred rather than simply those costs that must be paid. Accountants focus only on expenses that Economic Cost: All costs, both those that must be paid as well as those incurred in the form of forgone opportunities, of a business Accounting Cost: Only those costs that must be explicitly paid by the owner of a business must be paid in order for a business to produce but economists also consider the opportunity cost of choices. To fully understand the concepts of economic cost and accounting cost consider an upstart business where its owner quits a $50,000 a year job and cashes in a $100,000 CD (earning 6%) to get it off the ground. An accountant would not consider the $50,000 of forgone job related income or the $6,000 per year in forgone interest as costs of the business. An economist would. For the remainder of this chapter and all of the next all, costs will refer to economic costs. With that said, since profit is the difference between revenues and costs, we will be able to use what we have developed in these areas to find how much production our profit maximizing firm will choose. We will then explore the production process and the costs that it generates, move on to discuss the revenue side, and then put the two together to show how, under different circumstances, firms 97

3 choose their production levels. To pull all that off, let s use one example that will carry us from the beginning of this explication to the end. Let s assume that the industry we are talking about is the computer memory industry, the industry that makes the chips that enable computers to use and quickly access information. Let s suppose that the production of computer memory requires three things: expensive machines, highly trained people, and very inexpensive plastic and metal from which the chips themselves are made. To make things even easier, let s assume that the plastic and metal used to make the chips are free. In order to give you two ways of looking at these ideas, we will go through each of them once using a graphical explanation and then again with a numerical example. PRODUCTION Graphical Explanation To get a handle on costs we need to know how much money it takes to produce goods. To do that we need to know what resources are necessary for their production. We Production Function: a graph which shows how many resources we need to produce various amounts of output Cost Function: a graph which shows how much various amounts of production cost can then construct an input-output relationship called a production function, and we will do this in the form of a graph. Our graph will show how many resources we need to produce various amounts of output. From that production function we can find out how much various amounts of production cost. From this resulting cost function we will be able to figure out how much each one costs on average and how much each additional one costs. Of course, this is getting the cart before the horse. Before the firm decides how many to produce, it has to decide what to produce. In our example, the memory chip firm did not decide to 98

4 make chips for the fun of it. Early computer designers decided that their computers would work better if they had a short-term place to store and quickly retrieve information. Chip-making companies came into existence to provide the computer industry with the parts to make short-term storage of data possible. For the remainder of this section and this chapter we are going to assume that the firm is up and running and is simply trying to figure out how many chips to make at any given time. To make any product you typically have fixed and variable inputs. That is you have resources that you can not change and resources Fixed Inputs: resources that you cannot change Variable Inputs resources that can be easily changed that you can. In our example the plant, and the equipment in the plant, are called fixed inputs because they are not easily changed, added to, or subtracted from. On the other hand, the person power to operate those machines is easily changed. You can hire and fire more easily and quickly than you can replace a machine. People, and other resources that can be easily changed, are called variable inputs. The first step in our process of figuring out how many memory chips to make is to map out how many resources it takes to produce various numbers of these chips. Of course, without any personnel there is no production, so point A in Figure 1 is the origin (0 units of labor, 0 units output.) That is, the production function must emanate from the origin. To get the rest of Figure 1 we need to think about how people work together. If there are only a few workers, as in point B, production is not very great because workers are not able to specialize in particular parts of the production process. They waste time moving from one part of the process to another, and they take time to build up a momentum, working at each stage of production only to find 99

5 that when they get good at it, it is time to move on to another stage. The addition of a few more workers, as in point C, solves that problem and production levels increase greatly. Workers divide up the Division of Labor: workers divide up the tasks in such a way that each can build up a momentum and not have to switch jobs tasks in such a way that each can build up a momentum and does not have to switch jobs. This specialization is called the division of labor and its impact is such that for a small increase in labor we can get a dramatic increase in output. At some point, though, there are enough workers to get the job done, as in point D, and more workers do not add much to production. Diminishing Returns: the notion that there exists a point where the addition of resources increases production but does so at a decreasing rate In some situations, too, jobs just can not be easily divided. Although, it is usually the case that having more workers increases output, workers find that the existing plant and equipment are too limiting for them to get the most out of the new employees. As a result output increases from point C to point D but not as fast as it had from point B to point C. This phenomenon, referred to by economists as diminishing returns, is a central assumption of this chapter as well as the next. Figure 1 illustrates this with a curve that starts from the origin, slopes up slowly (as we begin production), becomes steeper (as we get more efficient), and then flattens out (as the machines begin to work at full capacity). 100

6 Output D Production Function C A B Workers Figure 1 A Production Function On a production function we assume that at the beginning, as workers are added, production is inefficient. As more workers are added, efficiency is gained as the workers begin to specialize. At the end, workers are less efficient because additional workers are not what is needed to increase production. More capital is needed. Now, let s consider the same concept using the numbers that comprise Table 1. Continuing with the memory chips example, suppose the first column represents the groups of workers, the second column represents the total output produced, and the third column represents the extra output added with the inclusion of the group. Because memory chips cannot make themselves, zero labor corresponds to zero output. Suppose that when the first group of workers is hired they produce 100 units but when a second group is added a total of 317 units is produced. That is, the second group adds 217 units to production. Suppose the third group adds somewhat less, 183 units, so that the total becomes 500. If it takes five groups of labor to produce 700, 9 to produce 900 and 12 to produce 1000, then we have a similar story to that which was told in the graphical explanation. That is, as we added workers we got more production. The first group of workers was not very efficient because they 101

7 could not specialize, whereas the second group was efficient because they could. In each case as more groups were added their efficiency waned because they were limited by the existing plant and equipment. Labor Table 1 Production Function Total Output Extra Output of the Group We have now explained production in terms of how a varying number of workers can be combined with a fixed amount of plant and equipment to make computer memory chips. We will now work on how much it costs to hire those workers and pay for that machinery. COSTS Graphical Explanation Once we know how many workers it takes to produce our memory chips we can find Fixed Costs: costs of production that we cannot change Variable Costs: costs of production that we can change 102

8 out how much it costs to make those chips. The first thing to consider is that there are costs of production that we cannot change. In our example these fixed costs are the costs of the plant and equipment that we own. Costs that we can change, like the number of workers we hire for our plant, are called variable costs. The task now is to graph the number of memory chips we make against the costs of making those chips. Looking back at Figure 1, you can see that at point A we will not have to pay anything to our workers (because we do not have any workers to pay) but we still have to pay fixed costs. As a result, point A in Figure 1 corresponds to point A in Figure 2. We have workers at point B that we have to pay and they are not all that productive. Remember that this is not their fault. There just is not enough of them so they can specialize. Point B in Figure 2 is therefore higher than point A (because we have to pay them) but not much further to the right (because they are not making that many chips). Point C in Figure 1 indicates that the workers were quite productive; so for the same amount of an increase in our costs we see a significant increase in production. Thus, point C in Figure 2 is also higher than point B but is significantly further to the right. Point D in Figure 1 shows us where extra workers did not add much to production. Again they cost money so point D in Figure 2 is higher than point C but is not that much further to the right. Connecting these points we have a Total Cost Function. Our graph shows how the function helps us understand and make decisions about the cost of production and the amount produced. 103

9 Total Cost Total Cost Function D C B A Output Figure 2 Total Cost Function The shape of the production function show that at first costs rise quickly and output rises slowly. As production gets more efficient costs climb slowly but output rises quickly. When there is not enough capital for new workers, their contribution is less and again costs rise quickly. So far we have focused on finding the Total Cost of producing various amounts of output. When we get Total Revenue, we will be able to find the profit. Before we go there, though, we are going to need four other cost functions: marginal cost, the average variable cost, the average fixed cost, and the average total cost. In higher level economics courses, students are required to derive these other cost functions from the Total Cost function. When you derive one function from another you graphically manipulate the parent function (in this case Total Cost) to draw its descendants (in this case marginal cost, average variable cost, and average total cost). Derivations are not included here, but we can offer a brief explanation. 104

10 The graph that we need is depicted in Figure 3. On it we have the four curves mentioned: Marginal Cost (MC), Average Total Cost (ATC), Average Variable Cost (AVC), and Average Fixed Cost (AFC). Marginal Cost is the increase in cost associated with a one unit increase in production. Marginal Cost: the addition to cost associated with one additional unit of output Average Total Cost: Total Cost/Output, the cost per unit of production Average Variable Cost: Total Variable Cost/Output, the average variable cost per unit of production Average Fixed Cost: Total Fixed Cost/Output, the average fixed cost per unit of production It is depicted by the slope of the total cost curve from Figure 2. Because total cost always rises, marginal cost is always positive. Because at low levels of output Total Cost rises quickly, Marginal Cost is high at low levels of output but because Total Cost rises much more slowly at moderate levels of output, Marginal Cost is much lower there. Lastly, because a rapid rise in Total Cost resumes at high levels of output, Marginal Cost is high in this range. Thus Marginal Cost is the check-shaped curve on Figure 3. Average Total Cost is the per unit cost of production. Because this includes fixed cost, which can be very high, average total cost will be high at low levels of production. It will shrink as production gets more efficient and the fixed costs become spread over greater levels of output. As production rises to higher levels where marginal costs are increasing these two effects will begin to counteract each other and the drop in average total costs will slow. Eventually the increases in marginal cost will overwhelm the effect of spreading fixed costs over higher levels of output and average total cost will rise again. This means that in Figure 3 Average Total Cost is u-shaped and that Marginal Cost cuts 105

11 through the minimum of the Average Total Cost curve. The Average Variable Cost is illustrated with a curve that is also u-shaped. Showing per-unit variable costs, its shape is dictated by the same changes in efficiency that gave us the Marginal Cost curve. Because it is an average, however, the movements are dampened; the highs are not as high and the lows are not as low. As with Average Total Cost, the values of Marginal Costs are shown to cut through the minimum of Average Variable Cost at the minimum value of the Average Variable Cost. Average Fixed Cost falls continuously because the fixed costs of production are being spread over greater and greater levels of production. In addition, graphically, Average Fixed Cost is the vertical distance between Average Total Cost and Average Variable Cost. P MC ATC AVC AFC Figure 3 Marginal Cost, Average Total Cost and Average Variable Cost Average total cost and average variable cost are both u-shaped with the gap between the two starting wide but shrinking as production increases. Marginal cost goes through the minimum of the average variable cost and the average total cost. Q These cost curves will serve as the basis for much of what follows in this chapter, the next one, and our subsequent study of issues. 106

12 Again we are dealing with concepts that may be easier to comprehend when there are numbers put to it. Following the numerical example used in Table 1, consider Table 2. The first column represents output. The second, Total Variable Cost, is based on the $25 per unit of labor from Table 1 that is required to produce that output. The third, Total Fixed Cost, is the cost of plant and equipment and is unchanging. The fourth, Total Cost, is the sum of Total Variable Cost and Total Fixed Cost. The fifth, Marginal Cost, is the increase in Total Cost from each level of production. The sixth, Average Total Cost, is the per unit cost, the seventh, Average Variable Cost, is per unit variable cost, and the eighth, Average Fixed Cost, is per unit fixed cost. Output Total VariableC ost Total Fixed Cost Table 2 Cost Functions Total Cost Marginal Cost* Average Total Cost Average Variable Cost Average Fixed Cost * change in Total Cost / 100 If you plot out the last four columns against output you will see that the curve for Marginal Cost 107

13 is indeed check-shaped, that the ones for Average Total Cost and Average Variable Cost are both u- shaped, and that Average Fixed Cost decreases steadily. You can also see that at 300 units of output Marginal Cost is at its minimum. Further you can see that the curve depicting Marginal Cost cuts Average Variable Cost at its minimum (at 500 units of output) and that the one for Marginal Cost cuts the one for Average Total Cost at its minimum (at 700 units of output). REVENUE Graphical Explanation The other side of any production decision is the amount of money that will come in from the sale of the goods. To get a handle on this revenue side we will need to know whether the business has competition and if so how much. For instance, if a business faces many other competitors that produce goods like the ones it produces their behavior will be different from what it would do if it had the market to itself. In some industries, like agriculture, the price that the firm receives remains unchanged regardless of how much they have to sell. In other industries, like those that supply electric power, the amount they sell affects the price. To explore this difference let s first assume our memory chip maker is one of many chip makers. Then we will see what happens when we assume that it is the only one. If our chip-making firm has many competitors, the price is set in a market that it can not control. The supply of and the demand for chips determines how much the firm can charge for its chips. To see the futility of trying to set its own price, imagine that it tried to have a price higher than the market price. If it did, computer makers could and would buy all their chips from our firm s competitors. The firm could, of course, set a price lower than the market price. If it did, it would get to sell all it produced. On 108

14 the other hand, it could do that at the market price. Because our firm wants to maximize profit and because it can always sell as much as it wants at or below the market price, it will always want to charge the market price. Figure 4 shows how the market generates the price for the firm. This price also Marginal Revenue : additional revenue the firm receives from the sale of each unit happens to be the additional revenue the firm receives from the sale of each unit. To see why this marginal revenue is the same as the price, consider a thought experiment. If the price is P* how much will revenue be if our firm sells one? Answer P*. How much will revenue be if they sell two? Answer 2P*. The increase in revenue associated with any sale is therefore P*. P S P P* P*=Marginal Revenue D Market for Memory Our Firm Figure 4 Setting the price when there are many competitors. The price is set in the market for memory so our firm has to take P* as given. P* is therefore its marginal revenue as well. If, on the other hand, we are the only ones selling computer chips, computer makers have to buy their memory chips from our firm. This situation is quite different from the case where there were 109

15 many competitors. Instead of just taking a price given to it by the market, it is setting the price. Instead of being a small insignificant part of the market, it is the market. Unfortunately, in order to sell more, the firm has no recourse other than to lower the price it charges. For instance, if it is currently selling a million chips a week and it wants to increase its sales to two million a week, it must lower the price to everyone, even those who would have bought a million at the higher price. This means that in Figure 5 the marginal revenue is not graphed with a flat line; it falls as we increase sales. P MR D Market for Memory Figure 5 Marginal Revenue when we have no competitors When the firm has no competitors it must lower the price to gain new sales. The marginal revenue line connects the vertical intercept of the demand curve with the point halfway between the origin and the demand curve s horizontal intercept. Using the same numerical example that we have been using, suppose that our firm is one of many that has no control over price. Suppose further that the price in the market for memory is $45 per unit. That means that the Total Revenue increases by $45 for each unit sold and the Marginal Revenue 110

16 is thus $45 for each unit sold. This is illustrated in Table 3 below. Table 3 Revenue When There are Many Competitors. Q Price TR MR* , , , , , , , , , , * the change in Total Revenue / 100 If there are no competitors, then the market demand for memory is simply the demand for our firm s memory. This means that our firm must lower its price to induce consumers to buy more memory. Another way of looking at precisely the same thing is to notice that a firm without competition can force the price higher by restricting its output. As before, Total Revenue is Price times Quantity, but because price does not remain the same, the Marginal Revenue falls. 111

17 * change in Total Revenue / 100 MAXIMIZING PROFIT Graphical Explanation Table 4 Revenue When There Are No Competitors Q Price TR MR* , , , , , , , , , , As mentioned above the level of output for the business that will maximize profit very much depends on whether the business is in perfect competition, i.e., one of many Perfect Competition: a situation in a market where there are many firms producing the same good Monopoly: a situation in a market where there is only one firm producing the good producing the same thing, or is a monopoly, i.e., it has no competitors. Regardless of whether it has many competitors or it has the market to itself, 112

18 we assume firms produce and sell the amount that will make them the most money possible. In economic terms this ends up meaning that every firm should produce an amount such that Marginal Revenue equals Marginal Cost (MR=MC). If you recall the Chapter 1 concept of marginal analysis, this is our first opportunity to see it at work. This is not as difficult as it seems. Remember that marginal revenue is the amount the firm brings in from selling one more, and the marginal cost is the amount of money that it costs to produce one more. To illustrate, suppose you start by selling a fixed number; say ten. If you sell an eleventh and you make money on that sale (MR>MC), you should do it again and sell at least one more. If you sell an eleventh and you lose money on that sale (MR<MC), you should reduce sales by at least one. Since Marginal Revenue is less than Marginal Cost for the eleventh chip you should not have produced it. To maximize profit you could repeat this one-by-one process until you have found the production that makes the most money. On the other hand, you now know that it is only when marginal cost equals marginal revenue that you have exhausted the profit potential on the good you are trying to sell. Of course it is possible that our entire business is a loser. In the age of word processors and cheap personal computers, the manual typewriter business would be a loser even if ours were the only firm in this industry. The exception to the rule that a firm should produce where marginal cost equals marginal revenue is that it could be best for it not to do anything; that is, sometimes the best decision is to shut down the business. This occurs when the amount that you sell a good for is not enough to cover the variable costs that went into the production of the good. The firm should shut down if the price is less than the average variable cost (P<AVC). 113

19 The Rules of Production A firm should a) produce an amount such that Marginal Revenue equals Marginal Cost (MR=MC), unless b) the price is less than the average variable cost (P<AVC). To illustrate profit maximization when there are many competitors, we need to combine the information in Tables 1 and 3; when there are no competitors we need to combine the information in Tables 3 and 4. In either case we need to pick quantity so as to maximize profit. This is done where Marginal Cost equals Marginal Revenue. Table 5 illustrates this for the case where there are many competitors, and Table 6 does it for the case where there are no competitors. In Table 5 we see that the firm that has many competitors has its profit maximized at $105 and this happens when the firm produces 8. In Table 6 we see that the firm that has no competitors has its profit maximized at $90 and this happens when it produces

20 Table 5 Profit Maximization When There Are Many Competitors Q Price TR TC MR MC Profit , , ,500 11, , ,000 12, , ,500 13, ,000 14, , ,500 16, , ,000 18, , ,500 21, , ,000 25, , ,500 31, , ,000 38, ,500 Table 6 Profit Maximization When There Are No Competitors Q Price TR TC MR MC Profit , , ,000 11, , ,000 12, ,000 13, , ,000 14, , ,000 16, , ,000 18, , ,000 21, , ,000 25, , ,000 31, , ,000 38, ,

21 CHAPTER SUMMARY This chapter has illustrated production, costs, revenues and profit maximization. For each concept and relationship we used both graphical explanations and numerical examples. We assumed that businesses choose production so as to maximize profit and that as a result they set it where Marginal Cost equals Marginal Revenue. Cost Revenue Economic Cost Accounting Cost Production Function Cost Function Fixed Inputs Variable Inputs Division of Labor KEY TERMS Diminishing Returns Variable Costs Marginal Costs Average Total Cost Average Variable Cost Marginal Revenue Perfect Competition Monopoly 116

22 Quiz Yourself A key assumption about the way firms behave is that they a) minimize costs. b) maximize market share. c) maximize profit. d) maximize revenue. When workers subdivide the tasks of a job in such a way so as to become more efficient economists refer to this as the benefits of a) the division of labor. b) the division of tasks. c) the separation of powers. d) none of these A profit maximizing firm will always produce in such a way that a) Marginal Cost equals Marginal Revenue. b) Average Total Cost is minimized. c) Total Revenue is maximized. d) Marginal Cost equals Marginal Revenue except when price is less than average variable cost. The shut down condition for a firm is to close a) if losses are made. b) if price is less than Average Total Cost. c) if price is less than marginal revenue. d) if price is less than Average Variable Cost. Marginal Revenue is a) the extra revenue associated with one additional unit of sales. b) the extra cost associated with one additional unit of output. c) the revenue associated with the first unit of sales. d) the revenue associated with the sale of the average unit. Average Total Cost is a) the addition to cost associated with one additional unit of output. b) the per unit cost of production. c) the per unit variable cost of production. d) the per unit fixed cost of production. Given the Total Cost function in the book, the Marginal Cost curve always a) is check-shaped. b) cuts through the minimum of the average variable cost curve. 117

23 c) cuts through the minimum of the average total cost curve. d) all of the above Think About This What would the Production Function look like if everyone hired added the same amount to production regardless of whether they were the first, tenth or one-hundredth person hired. What would the Total Cost Function look like? Marginal Cost? Average Total Cost? Talk About This If the division of labor makes workers more efficient who should get the benefit of that increased efficiency? The workers or the owner of the business who brings the workers together and organizes that efficiency? When might it be in the best interests of the firm to share profits with their workers? 118