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CHAPTER Production Costs and Business Decisions The economist’s stock in trade—his tools—lies in his ability to and proclivity to think about all questions in terms of alternatives The truth judgment of the moralist, which says that something is either wholly right or wholly wrong, is foreign to him The winlist, yes-no discussion of politics is not within his purview He does not recognize the either-or, the all-or-nothing situation as his own His is not the world of the mutually exclusive Instead, his is the world of adjustment, of coordinated conflict, of mutual gain James M Buchanan C ost is pervasive in human action Managers (as well as everyone else) are constantly forced to make choices, to one thing and not another Cost or more precisely, opportunity cost is the most highly valued opportunity not chosen Although money is a frequently used measure of cost, it is not cost itself Although we may not recognize it, cost also pervades our everyday thought and conversation When we say “that course is difficult” or “the sermon seemed endless,” we are indicating the cost of activities If the preacher’s extended commentary delayed the church picnic, the sermon was costly Although complaints about excessive costs sometimes indicate an absolute limitation, more often they merely mean that the benefits of the activity are too small to justify the cost Many people who “can’t afford” a vacation actually have the money but not wish to spend it on travel, and most students who find writing research papers “impossible” are simply not willing to put forth the necessary effort This chapter explores the meaning of cost in human behavior We will begin by showing how seemingly irrational behavior can often be explained by the hidden costs of a choice We will then develop the concept of marginal cost, which together with demand and the related concept of supply defines the limits of rational behavior, from personal activities like painting and fishing to business decisions like how much to produce Inevitably, points made earlier will be reviewed and extended in this chapter There is a cost in this repetition, but there is also some benefit in a few varied reiterations We will use the cost analysis to make points that seem to defy common sense in business For example, we will show that a firm should not necessarily seek to produce at the level at which the average cost of production is minimized 2 Chapter Production Costs and Business Decisions Explicit and Implicit Costs Not all costs are obvious It is not difficult to recognize an out-of-pocket expenditure— the monthly price you pay for a product or service This is called an explicit cost Explicit cost is the money expenditure required to obtain a resource, product, or service For example, the price of your book is an explicit cost of taking a course in economics Other costs are less immediately apparent Hidden costs of the course might include the time spent going to class and studying, the risk of receiving a failing grade, and the discomfort of being confronted with material that may challenge some of your beliefs These are implicit costs; together they add up to the value of what you could have done instead Implicit cost is the forgone opportunity to or squire something else or to put one’s resources to another use Although implicit costs may not be recognized, they are often much larger than the more obvious explicit costs of an action (Then, there are some “costs” that are recognized on accounting statements that should not be considered in making business decisions These costs are called “sunk costs.” See the box on the next page.) The Cost of an Education A good illustration of the magnitude of implicit costs is the cost of an education Suppose an MBA student—Eileen Payne—takes a course and pays $2,000 for tuition and $200 for books The money cost of the course is $2,200, but that figure does not include the implicit costs to the student To take a course, Eileen must attend class for about 45 hours and may have to spend twice that much time traveling to and from class, completing class assignments, and studying for examinations The total number of hours spent on any one course, then, might be 135 (30 hours in class plus 105 hours of traveling, studying, and so forth) The student could have spent that time doing other things, including working for a money wage If Eileen’s time is valued at $25 per hour (the wage she might have received if working), the time cost of the course is $3,375 (135 hours x $6) Moreover, if she experiences some anxiety because of taking the course, that psychic or risk cost must be added to the total as well If Eileen would be willing to pay $500 to avoid the anxiety, the total implicit cost of taking the course climbs to $820 Explicit costs Tuition Books Total explicit cost $2,000 200 $2,200 Implicit costs Time Anxiety Total implicit cost $3,375 500 $3,875 Total costs of course $6,075 Chapter Production Costs and Business Decisions The opportunity cost of the student’s time represents the largest component of the total cost of the course The value of one’s time varies from person to person For students who are unable to find work, the time costs of taking a course may be quite small That is why many young people go to college Their time cost is generally lower than that of experienced workers who must give up the opportunity to earn a good wage in order to attend classes full time PERSPECTIVE: Why “Sunk Costs” Don’t Matter A sunk cost is a past cost Economists define past costs as historical costs that cannot be altered by current decisions Such costs are beyond the realm of choice Will a rational, profit-maximizing business firm base its current decisions on its historical costs? An example can help to answer this question Suppose an oil exploration firm purchases the mineral rights to a particular piece of property for $1 million After several month of drilling, the firm concludes that the land contains no oil (or other valuable mineral resources) Will the firm reason that, having spent $1 million for the mineral rights, it should continue to look for oil on the land? If the chances of finding oil are nonexistent, the rational firm will cease drilling on the land and try somewhere else The $1 million is a sunk cost that will not influence the decision to continue or cease exploration Indeed, the firm may begin drilling on land for which it paid far less for mineral rights, if management believes that the chances of finding oil are higher there than on the $1 million property The underlying reason that sunk costs not matter to current production decisions is that in the economist’s use of the term, sunk costs are not really costs The opportunity cost of an activity is the value of the best alternative not chosen In the case of an historical cost, however, there are no longer any alternatives Although the oil exploration firm at one time could have chosen an alternative way to spend the $1 million, once the choice was made the alternative ceased to be available Nor can the firm resell the mineral rights for $1 million; those rights are now worth far less because of accumulated evidence that the land contains little or no valuable minerals Sunk costs, however painful the memory of them might be, are gone and best forgotten by the firm Profits are made by looking forward, not backward The Cost of Bargains Every Wednesday, supermarkets run large newspaper ads listing their weekly specials Generally only a few items are offered at especially low prices, for store managers know that most bargain seekers can be attracted to the store with just a few carefully selected specials Once the customer has gone to the store offering a special on steak, he would have to incur a travel cost in order to buy other items in a different store Even though peanut butter may be on sale elsewhere, the sum of the sale price and the travel cost exceed the regular price in the first store Through attractive displays and packaging, customers can be persuaded to buy many other goods not on sale, particularly toiletries, which tend to bear high markups Supermarket chains not necessarily make huge profits The grocery industry is reasonably competitive, and supermarket chains as a group are not highly profitable compared to other corporations The stores manage to recoup some of the revenues lost on sale items by charging higher prices on other goods In other words, the cost of a bargain on sirloin steak may be a high price for toothpaste Chapter Production Costs and Business Decisions Some shoppers make the rounds of the grocery stores when sales are announced For such people, time and transportation are cheap A person who values his or her time at $10 an hour is not going to spend an hour trying to save a dollar or two The cost of gas alone can make it prohibitively expensive to visit several stores Because of the costs of acquiring information, many shoppers not even bother to look for sales The expected benefits are simply not great enough to justify the information cost These shoppers enter the market “rationally ignorant.” Marginal Cost So far we have been considering cost as the determining factor in the decision to undertake a particular course of action The rational person weight the cost of an action against it benefits and comes to a decision: whether to invest in an education, to shop around for a bargain, or to operate an airplane The question is, how much of a given good or service will an individual choose to produce or consume? How does cost limit a behavior once a person has decided to engage in it? The answer lies in the concept of marginal cost Rational Behavior and Marginal Cost Marginal cost is the additional cost incurred by producing one additional unit of a good, activity, or service Marginal cost is the cost incurred by reading one additional page, making one additional friend, giving one additional gift, or going one additional mile Depending on the good, activity, or service in question, marginal cost may stay the same or vary as additional units are produced For example, imagine that Jan smith wants to give Halloween candy to ten of her friends In a sense, Jan is producing gifts by procuring bags of candy If she can buy as many bags as she wants at a unit price of fifty cents, the marginal cost of each additional unit she buys is the same, fifty cents The marginal cost is constant over the range of production Marginal cost can vary with the level of output, however, for two reasons The first has to with the opportunity cost of time Suppose Jan wants to give each friend a miniature watercolor, which she will paint herself over the course of the day To make time for painting, Jan can forgo any of the various activities that usually make up her day She may choose to give up recreational activities, housekeeping chores, or time spent on work or study If she behaves rationally, she will give up the activities she values least To the first painting, she may forgo straightening up her room—an activity that is low on most people’s lists of preferences The marginal cost of her first watercolor is therefore a messy room To paint the second watercolor, Jan will give up the more next-to-last item on her list of favorite activities As she produces more and more paintings, Jan will forgo more and more valuable alternatives In other words, the marginal cost of her paintings will rise with her output If the marginal cost of each new painting is plotted against the quantity of paintings produced, a curve like the one in Figure 9.1 will result Because the marginal Chapter Production Costs and Business Decisions cost of each additional painting is higher than the marginal cost of the last one, the curve slopes upward to the right Although the marginal cost curve is generally assumed to slope upward, as the one in Figure 9.1 does, that need not be the case If Jan placed equal value on all the forgone activities, her marginal cost would be constant and the marginal cost curve would be horizontal FIGURE 9.1 Rising Marginal Cost To produce each new watercolor, Jan must give up an opportunity more valuable than the last Thus the marginal cost of her paintings rises with each new work The Law of Diminishing Returns The second reason marginal cost may vary with output involves a technological relationship known as the law of diminishing marginal returns According to the law of diminishing marginal returns, as more and more units of one resource labor, fertilizer, or any other resource are applied to a fixed quantity of another resource -land, for instance the increase in total added output gained from each additional unit of the variable resource will eventually begin to diminish In other words, beyond some point less output is received for each added unit of a resource That is, more of the resource will be required to produce the same amount of output as before Beyond some point, the marginal cost of additional units of output rises Although the law of diminishing returns applies to any production process, its meaning is most easily grasped in the context of agricultural production Assume you are producing tomatoes You have a fixed amount of land (an acre) but can vary the quantity of labor you apply to it If you try to planting all by yourself dig the holes, pour the water, insert the plants, and core them up you will waste time changing tools If a friend helps you, you can divide the tasks and specialize Less time will be wasted in changing tools Chapter Production Costs and Business Decisions The time you would have spent changing tools can be spent planting more tomatoes, thus increasing the harvest At first, output may expand faster than the labor force That is, one laborer may be able to plant 100 tomatoes an hour; two working together may be able to plant 250 an hour Thus the marginal cost of planting the additional 150 plants is lower than the cost of the first 100 Up to a point, the more workers, the greater their efficiency, and the lower the marginal cost—all because of the economies of specialization At some point, however, the addition of still more laborers will not contribute as much to production as in the past, if only because a large number of workers on a single acre of ground will start bumping into one another Then the marginal cost of putting plants into the ground will begin to rise Diminishing returns are an inescapable fact of life If returns did not diminish at some point, output would expand indefinitely and the world’s food supply could be grown on just one acre of land (For that matter, it could be grown in a flower box.) The point at which output begins to diminish varies from one production process to the next, but eventually all marginal cost curves will slope upward to the right, as in Figure 9.1 Table 9.1 shows the marginal cost of producing tomatoes with various numbers of workers, assuming that each worker is paid $5 and that production is limited to one acre Working alone, one worker can produce a quarter of a bushel; two can produce a full bushel (columns and 2) The third column shows the amount each additional worker adds to total production, called the marginal product Marginal product is the increase in total output that results when one additional unit of a resource—for example, labor, fertilizer, and land is added to the production process, everything else held constant The first worker contributed 0.25 (one quarter) of a bushel; the second worker, an additional 0.75 of a bushel, and so on These are the marginal products of successive units of labor The important information is shown in the last two columns of the table Although two workers are needed to produce the first bushel (column 4), because of the efficiencies of specialization, only one additional worker is needed to produce the second Beyond that point, however, returns diminish Each additional worker contributes less, so that two more workers are needed to produce the third bushel and give more to produce the fourth If the table were extended, each bushel beyond the fourth would require a progressively larger number of workers Column shows that if all workers are paid the same wage, $5, the marginal cost of a bushel of tomatoes will decline from $10 for the first bushel to $5 for the second before rising to $10 again for the third bushel That is, increasing marginal costs (or diminishing returns) emerge after the addition of the third worker If the marginal cost of each bushel (column 5) is plotted against the number of bushels harvested, a curve like the one in Figure 9.2 will result Although the curve slopes downward at first, for most purposes the relevant segment of the curve is the upward-sloping portion above point a, will be explained in detail later) Chapter Production Costs and Business Decisions TABLE 9.1 Marginal Costs of Producing Tomatoes Number of Workers Employed (1) Total Number of Bushels (2) Contribution of Each Worker to Production (Marginal Product) (3) 0.25 1.00 2.00 Number of Workers Required to Produce Each Additional Bushel (4) 0.25 0.75 (1st bushel) 1.00 (2nd bushel) Marginal Cost of Each Bushel, Figured at $5 per Worker (5) $10 $ $10 $25 Point at Which Diminishing Maginal Returns Emerge 10 2.60 3.00 3.30 3.55 3.75 3.90 4.00 0.60 0.40 (3rd bushel) 0.30 0.25 0.20 (4th bushel) 0.15 0.10 _ FIGURE 9.2 The Law of Diminishing Marginal Returns As production expands with the addition of new workers, efficiencies of specialization initially cause marginal cost to fall At some point, however—here, just beyond two bushels —marginal cost will begin to rise again At that point, marginal returns will begin to diminish and marginal costs will begin to rise _ The Cost-Benefit Tradeoff Just as a producer’s marginal cost schedule shows the increasing cost of supplying more goods, the demand curve, as explained earlier, shows the decreasing value or marginal benefit of those goods to the people consuming them Together, marginal costs and benefits determine how many units will be produced and consumed up to the intersection of the marginal cost and demand (marginal benefit) curves, the marginal benefit of each Chapter Production Costs and Business Decisions additional unit exceeds it marginal cost In other words, people can gain through production and consumption of those units The intersection of the two curves represents the limit of production, or the point at which welfare is maximized To see this point, consider the costs and benefits of an activity like fishing The Costs and Benefits of Fishing Gary Schmidt likes to fish What he does with the fish he catches is of no consequence to us; he can make them into trophies, give them away, or store them in the freezer Even if Gary places no money value on the fish, we can use dollars to illustrate the marginal costs and benefits of fishing to Gary (Money figures are not values, but a means of indicating relative value.) What is important is that Gary wants to fish How many fish will he catch? From our earlier analysis of Jan’s desire to paint (page 181), we know that the cost of catching each additional fish will be higher than the cost of the one before Gary will confront an upward-sloping marginal cost curve like the one in Figure 9.3 Gary’s demand curve for fishing will slope downward, for as the cost of catching each additional fish rises, Gary will be less and less inclined to spend more time on the activity (see Figure 9.3) _ FIGURE 9.3 Costs and Benefits of Fishing For each fish up to the fifth, Gary receives more in benefits than he pays in costs The first fish gives him $4.67 in benefits (point a) and costs him only $1 (point b) The fifth yields equal costs and benefits (point c), but the sixth costs more than it is worth Therefore Gary will catch no more than five fish From the positions of the two curves, we can see that Gary will catch up to five fish before he packs up his rod and heads for home He places a relatively high value of $4.67 on the first fish (point a in the figure) and places the relatively low marginal cost of $1 on forgone opportunities for it (point b) In other words, he gets $3.67 more value from using his time, energy, and other resources to fish than he wold receive from his nexr best alternative The marginal benefit of the second fish also exceeds its marginal cost, although by a small amount ($2.75-$4.25 $1.50) Gary continues to gain with the third and fourth fishes, but the fifth fish is a matter of indifference to him Its marginal value equals its marginal cost (point c) Although we cannot say that Gary will actually bother to catch a fifth fish, we know that five is the limit toward which he will aim Chapter Production Costs and Business Decisions He will not catch a sixth—at least during the period of time offered by the graph— because it would cost him more than he would receive in benefits The Costs and Benefits of Preventing Accidents All of us would prefer to avoid accidents In that sense we have a demand for accident prevention, whose curve should slope downward like all other demand curves Preventing accidents also entails costs, however, whether in time, forgone opportunities, or money Should we attempt to prevent all accidents? Not if the cost of ensuring that you will never stumble down the stairs is $100 (again, we are using dollars to indicate relative value) If the only injury you expect to suffer were a bruised knee, would you spend $100 to prevent the accident? As with the question of how long to fish, marginal cost and benefit curves can help illustrate the point at which preventing accidents ceases to be cost effective Suppose Al Rosa’s experience indicates that he can expect to have ten accidents over the course of the year If he tries to prevent all of them, the value of preventing he last one, as indicated by the demand curve in Figure 9.4, will be only $1 (point a) The marginal cost of preventing it will be much greater: approximately $6 (point b) If Al is rational, he will not try to prevent the last accident As a matter of fact, he will try to prevent only five accidents (point c) As with the tenth accident, it will cost more than it is worth to Al to prevent the sixth through ninth accidents He would try to prevent all ten accidents only if his demand for accident prevention were so great that his demand curve intersected the marginal cost curve at point b Some accidents may be unavoidable In that case, the marginal cost curve will eventually become vertical Other accidents may be avoidable in the sense that it is physically possible to take measures to prevent them—although the rational course may be to allow them to happen _ FIGURE 9.4 Accident Prevention Given the increasing marginal cost of preventing accidents and the decreasing marginal value of preventing the accidents, c accidents will be prevented _ The Production Function in Pictures Business firms combine various factors of production in order to produce various goods and services Although there are thousands of different factors of production, or inputs, Chapter Production Costs and Business Decisions 10 for simplicity we often use a model with only two factors, labor and capital We can then study how the two inputs can be combined to produce an output The relationship between inputs and output is called the production function The general equation for the production function is: Q = f (L, K) where Q is output, L is labor, K is capital, and f is the functional relationship between inputs and output In the short run, we assume that capital cannot be varied; labor is therefore, the only variable factor To increase output, then, a firm must increase the amount of labor The relationship between the amount of the variable input (labor) and output can be illustrated with a total product curve such as that in the upper half of Figure 9.5 Suppose that the curve is that of a commercial fishing firm The firm’s capital—the boat and equipment—is fixed in the short run Only the number of workers can vary As the amount of labor increases from zero, the fish catch (output) increases Between zero and workers, output increases at an increasing rate As more workers are hired total output continues to increase, although at a decreasing rate, until 15 workers are hired Beyond that point, hiring more workers reduces output The reason the total product curve has that particular shape can be seen more clearly in the lower half of Figure 9.5, which shows the average and marginal product curves The average product of labor is total output divided by the amount of labor, or Q/L The marginal product of labor is the change in total output brought about by changing the amount of labor by one unit Because at least some workers are needed to operate the boat and the equipment, the first few workers hired greatly increase total output; marginal product is rising Between and 15 workers, the marginal product of labor falls, although the average product continues to rise (because it is less than marginal product) Total product continues to rise, but no longer at an increasing rate The law of diminishing marginal returns has taken effect At seven workers, marginal product equals average product and average product is maximized As more workers are hired average product falls Note that as long as marginal product is positive, more labor means more output and the total product curve will have a positive slope Beyond 15 workers, marginal product becomes negative and total product falls The boat may be so crowded that workers bump into each other and reduce the amount of work that each does To catch more fish once this stage has been reached, the firm must buy a larger boat Some economists divide the production function of Figure 9.5 into three stages In stage one, from zero to seven workers, total product and average product of labor both rise In stage two, between seven and 15 workers, total product rises while average product falls In stage three, beyond 15 workers, total product and average product both fall (and marginal product is negative) Chapter Production Costs and Business Decisions 11 Price and Marginal Cost: Producing to Maximize Profits “Production” is not generally an end in itself in business Most firms seek to make a profit How can we think about how they go about the task of trying to maximize profits? The total and marginal product curves need to be converted to cost curves Only then can we engage in familiar cost-benefit analyses Granted, many business people derive intrinsic reward from their work They may value the satisfaction of producing a product that meets a human need just as much as the profits they earn Some business people may even accept lower profits so their products can sell at lower prices and serve more people For most business people, however, the profit generated by sales is the major motivation for doing business FIGURE 9.5 Total, Average, and Marginal Product Curves The total product curve shows how output changes when the amount of the variable input, labor, changes Total product rises first at an increasing rate (0 to workers), then at a decreasing rate (5 to 15 workers), before declining (beyond 15 workers) The marginal and average product curves reflect what is happening to total product Marginal product rises when total product is rising at an increasing rate and falls when total product is rising at a decreasing rate Marginal product is positive when total product is rising and negative when total product is falling How much will a profit-maximizing firm produce? Assume its marginal cost curve is like the one in Figure 9.6(a) Assume further that the owners can sell as many units as they want at a price of P1 Because this firm is in business to make a profit, the price of its product can be thought of as the marginal benefit of each additional unit P1 is also the firm’s marginal revenue Marginal revenue is the additional revenue a firm Chapter Production Costs and Business Decisions 12 acquires by selling an additional unit of output Each time the firm sells one additional unit, its revenues rise by P1 Clearly, a profit-maximizing firm will produce and sell any unit for which the marginal revenue acquired (MR) exceeds the marginal cost (MC) (Profits are the difference between total costs and total revenues Therefore a firm’s profits rise whenever an increase in revenues exceeds the increase in its costs.) At a price of P1 , then, this firm will produce up to, and no more than, Q1 , products For every unit up to Q1 , price is greater than marginal cost FIGURE 9.6 Marginal Costs and Maximization of Profit At price P1 (part (a)), this firm’s marginal revenue, shown by the shaded area under P1, exceeds its marginal cost up to an output level of Q1 At that point total profit, shown in part (b), peaks (point a) At price P2 , marginal revenue exceeds marginal cost up to an output level of Q2 The increase in price shifts the profit curve in part b upward, from TP1 to TP2 , and profits peak at b Chapter Production Costs and Business Decisions 13 The vertical distance between P1 and the marginal cost of each unit, as shown by the marginal cost curve, is the additional profit obtained from each additional unit produced By summing the vertical distance between P1 and the marginal cost curve for all units up to Q1 , we can obtain the firm’s total profits (See the color-shaded area in Figure 9.5(a).) Total profits can also be represented as a curve, as in the line TP1 in Figure 9.5(b) Notice that the curve peaks at Q1 the point at which the firm chooses to stop producing Beyond Q1 , marginal cost is greater than marginal revenue, and total profits fall, as shown by the downward slope of the total profits curve What will the firm if the price of its product rises from P1 to P2 ? For the firm that can sell all it wants at a constant price, a rise in price means a rise in marginal revenue Once the price rises to P2 , the marginal revenue of an additional Q2 – Q1 products exceeds their marginal cost At the higher price, a larger number of units can be profitably produced and sold The firm will seek to produce up to the point at which marginal cost equals the new, higher marginal revenue, P2 , or output, Q2 , in Figure 9.5 (a) As before, profit is equal to the vertical distance between the rice line, P2 , and the marginal cost curve, or the color-shaded area plus the gray-shaded area in Figure 9.5 (a) The total profit curve shifts to the position of the line TP2 in Figure 9.5(b) From Individual Supply to Market Supply If a portion of the upward-sloping marginal cost curve is the firm’s supply curve, and if market supply is the amount all producers are willing to produce at various prices, we can obtain the market supply curve by adding together the elevation portions of the individual firms’ marginal cost curves (This procedure resembles the one followed in determining the market demand curve in an earlier chapter.) Figure 9.7 shows the supply curves SA and SB, derived from the marginal cost curves of two producers, A and B At a price of P1 , only producer B is willing to produce anything, and it is willing to offer only Q1 The total quantity supplied to the market at P1 is therefore Q1 At the higher prices of P2 , however, both producers are willing to compete Producer A offers Q1 , while producer B offers more, Q2 The total quantity supplied is therefore Q3 the sum of Q1 and Q2 The market supply curve, SA+B is obtained by adding the amounts A and B are willing to sell at each price and splitting the totals Note that the market supply curve lies farther from the origin and is flatter than the individual producers’ supply curves The entry of more producers will shift the market supply curve farther outward and lower its slope even more (More will be said about cost and supply in later chapters.) MANAGER’S CORNER: Cutting Health Insurance Costs The cost of doing business is a constant worry for all firms At times, those business costs feed major policy debates in the nation’s capital As is so often the case, the infamous “healthcare crisis” in the United States amounts to nothing more than costs for Chapter Production Costs and Business Decisions 14 a particular service – healthcare responding to the market forces of supply and demand Unfortunately, the forces have been distorted by legal and political factors that have gotten the incentives wrong In our view, the “crisis” is more a matter of political rhetoric than economics Political grandstanding alone will hardly solve whatever healthcare problem exists Careful reflection by policy makers and managers on the exact sources of the problem might The current distortion presents a possibility for managers to benefit both their firms and its workers by policies that get the incentives right FIGURE 9.7 Market Supply Curve The market supply curve (S A+B ) is obtained by adding together the amount producers A and B are willing to offer each at each and every price, as shown by the individual supply curves S A and S B (The individual supply curves are obtained from the upward sloping portions of the firms’ marginal cost curve.) If private firms and Washington-based politicians want to reform the system and temper cost increases, they can so by working with the forces of supply and demand, which means, fundamentally, changing people’s incentives to provide and consume healthcare services Granted, healthcare costs, and the insurance premiums that finance a major share of healthcare expenditures, have risen faster than the prices of other goods over the last couple of decades.1 Indeed, the cost of health insurance provided by firms was escalating at double-digit rates in the late 1980s and the very early 1990s when increases in the consumer price index, a broad measure of the cost of living, were falling.2 In the mid1990s, healthcare cost increases slowed, but they were, at this writing, still increasing at a rate that was over 50 percent higher than the rate of increase in the general cost of living See Paul J Feldstein Health Policy Issues: An Economic Perspective on Health Reform (Arlington, Va : AUPHA Press; Ann Arbor, Mich.: Health Administration Press, 1994); and Paul J Feldstein, The Politics of Health Legislation: An Economic Perspective, 2nd ed (Chicago, Ill.: Health Administration Press, 1996) Put another way, the consumer price index was increasing at decreasing rates, which means that the rate of inflation was gradually but irregularly decreasing for most of the 1980s and 1990s Chapter Production Costs and Business Decisions 15 In order to understand the problem of insurance cost increases, we need first to consider the market forces that have been at work driving up healthcare costs What are those forces? Consider the following list of factors affecting the supply and demand of healthcare: Doctors have been subject to a growing degree of litigation They have been sued with growing frequency partly because they have made mistakes, but also because they are now being held responsible for problems over which they may have no control Patients have found that they can make money by blaming doctors for almost any problem that emerges when they are being treated Fearful that they will be sued for delivering incomplete or misguided care, doctors have been covering their financial and professional backsides by ordering tests that may be only marginally valuable from a medical perspective but can help them defend themselves in the event they are sued when problems emerge They have also been trying to acquire legal protection and to spread the risk of lawsuits by increasing referrals to specialists Federal expenditures on Medicare for older patients and Medicaid for low-income patients have increased the demand for healthcare services since the late 1960s, which has tended to boost prices and forced many younger and lower-income patients out of the health insurance market Medical care has become technologically more sophisticated, and doctors have applied the new technology for offensive reasons (to keep patients alive longer) and for defensive reasons (they don’t want to be accused of negligence for failing to employ the latest life-saving technology) The extensive use of the latest and best technology may have saved and prolonged lives, but medical care costs have been driven up in the process The healthcare industry has always been plagued by the problem of “asymmetric information,” or the doctors knowing more about many patients’ medical conditions and what will remedy their problems than the patients themselves As a consequence, doctors have always been in a position to induce patients to buy more medical care than the patients might really buy, if they had the information and knowledge at the disposal of the doctors Medical technology has drastically lowered the cost of many medical procedures and has, as a consequence, lowered the cost of extending the lives of patients by some varying and uncertain number of months and years For example, less than four decades ago, heart and kidney transplants and heart bypass operations were impossible No one knew how to them Then, the costs of those procedures were infinite Their prices may now remain high in absolute dollar terms, running into the tens, if not hundreds, of thousands of dollars However, those high prices also represent lower prices And the lower prices for those procedures have, no doubt, increased the number of patients who have been willing and able to pay for the procedures (as well as insurers who have helped with the payments) Although the issue has not been statistically evaluated to date, the lower prices for many medical procedures have probably increased total medical expenditures in Chapter Production Costs and Business Decisions 16 absolute dollar terms and as a percentage of national income Hence, some of the so-called healthcare “crisis” probably mirrors, to a degree, the success of the healthcare industry in lowering the cost of prolonging life The cost of employer-provided medical insurance is tax deductible, which means that its price has been artificially lowered, causing more consumers to buy more complete insurance coverage and to demand more medical services (than they otherwise would) The greater demand has enabled medical professionals to boost their prices As tax rates rose in the 1960s and 1970s, workers naturally had growing incentive to take more of their income in tax-deductible fringe benefits and less of an incentive to take their income in taxable money wages The higher tax rates spurred demand for health insurance and healthcare – and added to pressure on healthcare costs Employers have typically bought insurance policies with very low deductibles, for example, $200 a year This means that after the first $200 of medical care expenditures in any one year, the cost of additional medical services to the insured patient is often close to zero This feature of insurance policies has encouraged excessive use of healthcare services, which, in turn, has driven up employees’ insurance premiums and caused some workers to forgo health insurance altogether.3 The growth in social problems crimes involving bodily injury, the use of street drugs, and teenage pregnancy has also contributed to the demand for medical services, which has driven up their prices as well as the price of insurance The unwillingness or inability of medical professionals to deny services to people who cannot pay for the services has also increased the number of people seeking services Social attitudes favoring universal medical care coverage have reduced the cost of irresponsible behavior, increasing the demand on the healthcare industry and inflating costs Without question, if the grocery industry were operated the way the healthcare industry operates, then we would likely have a “crisis” in the grocery business The reason is simple: People would pay a fixed sum each month (their grocery premium) through their employer that would entitle them to virtually unlimited access to the grocery store shelves (after they have covered the $200 annual deductible) at zero, or very low, cost Under such an arrangement, we should not be surprised if people consumed significantly more and better food, some of which would have limited value We should also not be surprised if the shoppers’ grocery premiums went through the roof as everyone allowed their tastes to run wild, with many low-income shoppers forced out of the grocery policies by the inflated premiums As you may recall from our study of consumer behavior in the last chapter, a working rule of consumer maximizing behavior is that the consumer will continue to buy units of any good or service until the point at which the marginal cost of the last unit consumed just equals the marginal value of the last unit If the person consumes more than that amount, the additional cost of any additional units will exceed their additional value By “excessive” consumption, we mean that patients are induced to go beyond the point where the marginal value is, while still positive, less than the marginal cost The reason for this excessive consumption is that the individual consumer isn’t paying the entire cost of additional medical care Chapter Production Costs and Business Decisions 17 How can the so-called “crisis” be solved, at least partially? We don’t intend to offer a detailed set of public policy solutions here Other specialists in the field have done that.4 We only point out here that many of the supply and demand forces listed above are beyond the control of individual businesses There is simply not much most individual businesses can to affect the broad sweep of social attitudes and government tax and expenditure policies We only note, however, that the demand for healthcare services can be lowered by reducing, at least marginally, government subsidies for the healthcare of many Americans This can be accomplished by lowering Medicare and Medicaid expenditures and by eliminating all or a part of the tax deductibility of health insurance The cost of healthcare can also be lowered by reducing the rewards from suing doctors or by giving patients the right (to a greater or lesser degree) to absolve doctors of liability for problems that they may encounter while the patients are in the doctors’ care Frankly, making those recommendations is much easier than getting them passed They are too politically painful for voters (although we suggest that voters should also consider the gains to everyone from getting healthcare costs under control) Barring changes in public policies, what can businesses themselves to ameliorate their own healthcare costs? Many businesses have done what has come naturally: they have tried to select workers who are not likely to have medical problems and, therefore, drive up the firms’ insurance costs This is, we remind you, a solution that can benefit both owners and many workers, given that healthier workers can mean lower labor costs for firms and lower health insurance premiums While people might object to this solution on fairness grounds, we stress that it is the type of discriminatory hiring policy that is likely to emerge when health insurance costs have been distorted by political factors, such as the ones included in the list above Another private policy solution can emerge if employers and employees recognize that low deductibles on health insurance policies are very expensive because they encourage workers to spend someone else’s money, which motivates excessive demand for healthcare and high insurance premiums With a deductible of $5,000, the price of an additional dollar of insurance coverage for a forty-year old male is measured as a tiny fraction of a cent (actually, 06 of a cent) However, when the deductible is $500, the price escalates to 55 cents When the deductible is as low as $100, the price of an additional dollar of coverage rises to $2.14, a poor bargain for owners and their employees.5 There is an obvious solution to the health insurance problem that has the potential of not only introducing greater efficiency into the healthcare business but also improving the fairness of the system, without any policy change in Washington This solution seeks to lower the private demand for healthcare by changing the incentives a firm’s workers have to consume healthcare services See John C Goodman and Gerald L Musgrave, Patient Power: Solving America’s Health Care Crisis (Washington, D.C : Cato Institute, 1992) As reported by Goodman and Musgrave (Ibid.) Chapter Production Costs and Business Decisions 18 As we indicated above, most firms that offer their workers health insurance provide “Cadillac policies,” ones with small deductibles and broad coverage for just about everything that can go wrong with a person, regardless of whether the person is responsible, through destructive behaviors, for the problems encountered Each worker has little incentive not to use healthcare services for the slightest problem Each worker has less incentive to incur the costs that might be required to eliminate or reduce their destructive behaviors Each worker can reason that if he or she were to cut back on personal usage of this or that healthcare service, the company’s health insurance costs would not be materially affected Certainly, the individual’s health insurance premiums would not fall by the full value of the healthcare services not utilized The savings from non-use by any one individual, if the savings are detectable at all, will be spread over the entire group of workers through slightly lower premiums for everyone In short, the individual gains precious little from personal restraint in consumption of healthcare services.6 Hence, the individual has little incentive to curb consumption Granted, if everyone in a firm were to cut back on healthcare usage, then everyone could possibly gain in terms of reduced insurance premiums The amount of savings could be substantial, and everyone would share in the savings of everyone else However, as is so often true in business and, for that matter, all group settings, getting everyone to what is in their best collective interest comes up against the prisoners’ dilemma discussed earlier If everyone else cuts back, there is still no necessary and compelling reason for any one person to cut back The one person’s reduction is, again, inconsequential regardless of what all others And, we must add, as we have throughout the book, the larger the group, the more difficult the problem in bringing about collective cohesiveness of purpose.7 The basic problem for the firm should be seen as one of finding a means of giving all workers an incentive to cut their consumption This can be done by raising the price of healthcare usage But how can the price of healthcare be raised by the firm? Economist John Goodman, head of the National Center for Policy Analysis, recommends what appears to us to be a ingenious and practical solution, one that firms can, as some already have, institute on their own to the benefit of the workers and the firm To see how Goodman’s proposal might work, let us start with a few observations and assumptions Many firms spend upwards of $4,500 annually per worker on health insurance, partly because, with the small deductible, workers have an incentive to consume a lot of healthcare Let us assume that a basic catastrophic health insurance policy, one with a very large deductible of about $3,000 (meaning the insurance covers Of course, the extent to which the individual’s actions can be detected depends on the size of the employment group In small groups of workers, it would be easier to detect the impact of what one individual does or does not One of the more serious problems in having government provide health insurance is that the relevant group is really large, extending to the boundaries of the country, which means people may have absolutely no incentives to curb their consumption of healthcare services The benefits of doing so are spread ever so thinly over too many people Chapter Production Costs and Business Decisions 19 only major medical problems), can be purchased for each employee for a premium of $1,200 per year (which is, we are told, in the ballpark of the actual cost for a group policy) Suppose also that the employer agrees to provide this catastrophic insurance policy and, at the same time, agrees to place in a bank reserve account (what Goodman prefers to call a “Medical Savings Account” or “MSA”) a sum of $3,000 each year per employee The employer tells the employees that they can draw on that account for any medical “need” (with “need” being defined broadly) The workers can use the account, for example, to pay for visits to doctors, to cover the cost of hospital stays not covered by insurance, or to pay for a membership in a fitness center (given that exercise can prevent the need for some medical care) Finally, suppose that the workers are also told that the balance remaining in the account at the end of the year can be applied to their individual retirement accounts, or even withdrawn at the end of the year for any purpose that the workers choose.8 This proposal has a chance of lowering the employees’ healthcare consumption because it requires that people pay for most routine medical care with their own money Under common insurance arrangements, the additional cost of medical procedures (other than the patients’ time) approximates zero (after the low deductible is met) Under the MSA proposal, the cost to the employee of the first $3,000 of medical care is exactly equal to the cost of the service This is because the employee is made the residual claimant on the balance at the end of the year Hence, we should expect that workers will more carefully evaluate their usage of medical services and cut back After all, under the old system, the workers were probably consuming “too much,” given the low cost (close to zero) that they incurred We would expect that the gains from this new MSA system could be shared by both the workers and their firm We have already developed the example in a way that obviously benefits the firm The firm was paying $4,500 a year for the insurance of each worker Now, it must pay $1,200 for the insurance and $3,000 for the MSA, for a total of $4,200 The firm saves $300 per worker The workers, however, can also gain Under the old arrangement, the workers were getting “paid” with insurance, not money Under the MSA system, they are given a pot of money, $3,000, that they can use, if they choose, to buy insurance that would cover the first $3,000 of care But many would not likely that They can self-insure just by holding onto the money and paying the first $3,000 in medical bills However, they can, conceivably, also buy a variety of other things, from new televisions to education programs to additional days of vacation Accordingly, the additional money should enable workers to be better off by allocating the sum to higher valued uses The particulars of the Medical Savings Accounts are not important here The important characteristic is broad discretion on the part of the worker, which will likely mean that the worker has a sum of money that is set aside to cover the large deductible under a catastrophic medical insurance policy and that can be used by the employee when it is not spent for medical purposes Any actual MSA program might for political reasons have restrictions on the range of goods and services that the workers can buy with any MSA balance remaining at the end of the year For example, one MSAtype proposal would require that the balance go into a worker’s retirement account Chapter Production Costs and Business Decisions 20 Both workers and their employers can also gain because the new insurance arrangement can be expected to lower the worker’s demand for use of the health insurance provided by their employers Many workers will want to be careful not to use up their $3,000 account, as they become more careful shoppers of medical care Workers will make use of the catastrophic insurance only in those situations when they have serious problems and little choice but to make use of medical care, which explains why the premiums for catastrophic insurance are so low By providing catastrophic health insurance coupled with a medical savings account, a firm can attract better workers by providing them with a more valuable compensation package at lower cost Overall, we would expect the firms that adopt this type of insurance system would be more productive and competitive However, we hasten to add that our simple example does not reflect the full complexity of employment conditions most firms face The problem managers will have in developing acceptance of the MSA is the cross-subsidies that are embedded in current insurance programs Low-risk workers typically subsidize high-risk workers Hence, we doubt that the firm’s deposit into workers’ MSA accounts would equal the insurance deductible, as we have assumed in our example The reason is that many healthy (typically younger) workers are fortunate in that they often don’t go to the doctor or hospital in any given year, and other workers have only modest medical expenditures in most years They are subsidizing the unhealthy (typically older) workers who make extensive use of medical care If the MSA deposit equaled the deductible, this crosssubsidy would be wiped out, and the insurance company would very likely be hit with high bills from the high-risk workers without the payments from the low-risk workers To make the MSA system work, the deposit would have to be limited, with the workers themselves sharing in some of the gains in the event they have limited expenses but also sharing in some of the risks if their expenses exceed their MSA deposits Therein lies the rub, which will rule out many firms from instituting the deal However, some firms will still be able to find a reasonable compromise Managers must also be mindful of the possibility that MSAs can set up perverse incentives for some workers for some types of healthcare Knowing that they will have to draw down their MSA account in order to cover annual physical examinations (and other preventive healthcare measures), workers can reason that MSAs increase the immediate cost of physical examinations But that doesn’t mean that the “cost” of physicals goes up for all workers For some cost will rise; for others the cost will fall Some employees, no doubt, will be more inclined to get physicals, given that physicals can be paying propositions (or will have a lower net cost to them) That is to say, the employees can reason that the current outlay from their MSA for a physical can be more than offset by the reduction in MSA outlays in the future, given that current physicals can “nip” health problems when they are minor Thus, current physicals can lower the workers’ healthcare expenditures from their MSA account over the long run However, we suspect that it’s also a safe bet that some employees will not be able, or will not be willing, to make the required careful calculations or can properly assess the current and future benefits of physicals Other workers may reason that most of their later healthcare expenditures for “major” problems that go undetected will be Chapter Production Costs and Business Decisions 21 covered as the catastrophic health insurance kicks in To accommodate these potential problems, employers can consider covering a portion of the current cost of physicals and other preventive measures The employers can cover the added cost of subsidizing the physicals and preventive care with any reduction in their insurance premiums they get from encouraging preventive care If there are no insurance savings from the subsidy, then it seems reasonable to conclude that either the problem of employees skipping preventive care is not a problem or it is such a minor problem that the insurance companies see no need to reduce the insurance premiums of firms that encourage preventive care The main point is that managers must be tread carefully in trying to accommodate problems with “preventive care.” The problem is that “preventive care” can include not only physicals, but also an array of tests that have little useful medical value If “preventive care” is defined too broadly and the subsidies are high, managers can be back in the prisoner’s dilemma trap that results in excessive healthcare and healthcare insurance expenditures, the net effect of which is healthcare benefits that are not worth the costs to the workers Has the MSA concept been tried and has it worked? Yes, on both counts, although the trials to date not correspond exactly with our example above One of the problems is that Medical Savings Accounts are not tax deductible, which means that a part of the added cost that must be overridden with benefits is the greater tax payments workers and firms must pay Nevertheless, several firms have already tried the system with beneficial effects: • • Forbes magazine encourages its employees to curb medical care expenditures with a variation of the MSA, by paying workers $2 for every $1 of medical costs not incurred up to $1,000 This means that if a Forbes employee incurs medical costs of only $300 in a given year, the employee is rewarded with a check of $1,400 at the end of the year [2 x ($1,000 - $300)] The magazine’s healthcare costs fell 17 percent in 1992 and 12 percent in 1993, years during which other firms’ insurance costs were rising • The utility holding company Dominion Resources gives each worker who chooses a $3,000 deductible on the company’s health insurance policy a deposit of $1,650 a year Since 1989, its insurance premiums have not risen, while the insurance premiums of other companies have risen by an average of 13 percent a year • 10 After Quaker Oats put $300 in each worker’s Medical Saving Account, the company’s healthcare costs grew 6.3 percent a year However, this was during a period when the healthcare costs of the rest of the country were growing at double-digit rates Golden Rule Insurance Company gives each worker a $2,000 deposit if they select a deductible of $3,000 In 1993, its health insurance costs were 40 percent lower than they would have otherwise been.10 See “Answering the Critics of Medical Savings Accounts,” Brief Analysis (NCPA, September 16, 1994), p Chapter Production Costs and Business Decisions 22 We don’t propose to tell firms what to in their own particular circumstances for a very good reason: Frankly, we obviously don’t know the details of the individual circumstances of what we hope will be a multitude of business readers of this book We can use our incentive-based approach to explore the types of business policies managers should consider and then adjust to fit the particulars of their circumstances Moreover, our focus on health insurance is only illustrative of insights that are relevant across a firm’s entire fringe benefit package The important point of this discussion is by now an old one for this book: Incentives matter One of the several important reasons many workers pay high health insurance premiums is that they don’t have much of an incentive to carefully evaluate their healthcare purchases The best way of ensuring that workers get the most out of their healthcare benefits is one that is as old as business itself: make the buyer pay a price that reflects the true cost of their decision Medical Savings Accounts are simply a means (perhaps one of many that have not yet been devised) of making workers potentially better off by making everyone pay a price for what they consume This solution may not work for all businesses Some worker groups may not want to be bothered with considering the costs of their behaviors However, it appears that many firms and their workers have not considered policies like Medical Savings Accounts because they have not realized that they harbor the potential of making everyone better off These are the types of policies all managers should examine Such policies can raise their workers’ welfare, their firm’s stock prices, and the compensation of managers Again, we return to what is by now an old point of the book: firms can make money not only by selling more of their product or service, but also by creatively restructuring incentives in mutually beneficial ways Concluding Comments Cost plays a pivotal role in a producer’s choices Costs change with the quantity produced The pattern of those changes determines the limit of a producer’s activity— from the production of salable goods and services to the employment of leisure time The individual will produce a good or service, or engage in an activity, until marginal cost equals marginal benefit (marginal revenue) Graphically, this is the point where the supply and demand curves for the individual’s behavior intersect At this point, although additional benefits might be obtained by producing additional units of the good, service, or activity, the additional costs that would be incurred discourage further production Costs will not affect an individual’s behavior unless he or she perceives them as costs For this reason the economist looks for hidden, implicit costs in all choices Such costs, if uncovered, will affect choices that remain to be made Implicit costs can also be helpful in explaining those choices that have already been made Review Questions Evaluate the adages “haste makes waste” and “a stitch in time saves nine” from an economic point of view Chapter Production Costs and Business Decisions 23 If executives’ time is as valuable as they claim, why are they frequently found reading the advertisements in airline magazines en route to a business meeting? The price of a one-minute long distance call on a cell phone is several times the cost of a call on any other phone Does that mean that the introduction of cell phones has increased the cost of long distance calling? In discussing accident prevention, we assumed an increasing marginal cost Suppose instead that the marginal cost of preventing accidents remains constant How will that assumption affect the analysis? Using the analysis of accident prevention, develop an analysis of pollution control Using demand and supply curves for clean air, determine the efficient level of pollution control People take some measures to avoid becoming victims of crime Can the probability of becoming a victim be reduced to (virtually) zero? If so, why don’t people eliminate that probability? What does the underlying logic of your answer suggest about the cost of committing crimes and the crime rate? If the money price of a good rises from $5 to $10, the economist can confidently predict that less will be purchased One cannot be equally confident that denying a child a dessert will improve the child’s behavior, however Explain why Consider the information in the production schedule that follows (a) At what output level diminishing returns set in? (b) Assume that each worker receives $8 Fill in the marginal product column, and develop a marginal cost schedule and a marginal cost curve for the production process Number of Workers 10 11 12 13 14 15 16 17 Total Product of All Workers 0.10 0.30 0.60 1.00 1.45 2.00 2.50 2.80 3.00 3.19 3.37 3.54 3.70 3.85 4.00 3.90 3.70 Marginal Product of Each Worker Chapter Production Costs and Business Decisions 24 READING: Sunk Costs in the Railroad Industry Clinton H Whitehurst, Jr., Clemson University Historically, a large part of a railroad’s investment has been in assets with fixed costs—cost that not vary with output in the short run In the early 1900s, fixed costs were estimated to be as much as 75 percent of railroads’ total costs More recently they have been estimated at 40 to 50 percent A significant part of a railroad’s fixed costs is the investment in its right of way—the 75- to 200foot-wide corridors in which its tracks are laid Most railroads purchased that land and paid for its grading many years ago, perhaps in the last century Those costs are considered historical, or sunk To the degree that its costs are fixed, a railroad’s average total cost decreases as its volume increases The more tons it carries per mile, the lower the average total cost of moving a ton of freight The railroad’s fixed costs are simply spread out over more units of freight To use their hauling capacity fully and lower their average total cost, railroads have tended to set their rates low for long hauls In the early days they often generated only enough revenues to cover their variable costs, not their total costs But in many instances they compensated for low rates on long hauls by charging high rates on short hauls In 1887, customer complaints about differences in rates prompted congress to place railroad rates and routes under the regulation of the Interstate Commerce Commission (ICC) Throughout much of its history, the ICC considered rates that did not cover total costs to be unfair or predatory—designed, that is, to drive out competition It insisted that railroads set their rates high enough to cover total costs After the Second World War, the rapidly growing trucking industry became the railroads’ chief competitor Fixed costs were much less significant in trucking than in railroads As much a 90 percent of the total cost of trucking varied with the number of tons carried per mile From the point of view of the trucking industry, then, the ICC’s requirement that rates cover total costs made sense But from the railroads’ perspective, the requirement was disastrous By keeping railroad rates high, the ICC enabled the trucking industry to compete for railroad business and expand its share of the transportation market In 1958, following an extensive lobbying effort by the railroads, Congress amended the Interstate Commerce Act The amendment instructed the ICC that “Rates of a carrier shall not be held up to a particular level to protect the traffic of any other mode of transportation.” Earlier Interstate Commerce Act provisions still barred “unfair or destructive competitive practice,” however Given the ambiguity of the legislation, the ICC continued to insist that rates cover total costs In 1968 the Supreme Court upheld its interpretation Recently railroads have been given considerable freedom to set their own rates under the railroad Revitalization and Regulatory Reform Act (1976) and especially the Staggers Rail Act (1980) Rates that cover only variable costs are no longer considered unfair and are not challenged by the Interstate Commerce Commission Meanwhile, the interstate highways—the right of way for trucks—are becoming more congested Truck delivery, once much faster than railroad delivery, is slowing down But railroad tracks remain underutilized As circumstances change, railroads are putting their century-old investment in their rights of way to good use By ignoring sunk costs and offering lower rates, they have recaptured much of the freight business they lost to trucks after the Second World War Today, one often sees highway trailers riding on railroad flatcars, reflecting the new competitiveness of railroads In fact, hauling trailers is now one of the fastest-growing railroad services  ... insurance provided by firms was escalating at double-digit rates in the late 198 0s and the very early 199 0s when increases in the consumer price index, a broad measure of the cost of living, were... Certainly, the individual’s health insurance premiums would not fall by the full value of the healthcare services not utilized The savings from non-use by any one individual, if the savings are detectable... services See John C Goodman and Gerald L Musgrave, Patient Power: Solving America’s Health Care Crisis (Washington, D.C : Cato Institute, 199 2) As reported by Goodman and Musgrave (Ibid.) Chapter