Microeconomics for MBAs - Chapter 3 ppt

CHAPTER 3 Principles of Rational Behavior at Work in Society and Business We are not ready to suspect any person of being defective in selfishness. Adam Smith ith this chapter we begin a detailed examination of key issues in microeconomics, namely the study of how prices are determined in individual markets. Prices are important – or, rather, should be important – to managers because of their unavoidable impact on the decisions of managers within individual firms. We have already seen how the forces of supply and demand determine prices (Chapter 2). Now we will explore the determinants of the supply and demand for goods, services, and resources. Microeconomics rests on certain assumptions about individual behavior. One is that people are capable of envisioning various ways of improving their position in life. This chapter reviews and extends the discussion begun in Chapter 1 of how people – business people included go about choosing among those alternatives. According to microeconomic theory, consumers and producers make choices rationally, so as to maximize their own welfare and their firms’ profits. This seemingly innocuous basic premise about human behavior will allow us to deduce an amazing variety of implications for business and every other area of human endeavor. Rationality: A Basis for Exploring Human Behavior People’s wants are ever expanding. We can never satisfy all our wants because we will always conceive of new ones. The best we can do is to maximize our satisfaction, or utility, in the face of scarcity. Utility is the satisfaction a person receives from the consumption of a good or service or from participation in an activity. Happiness, joy, contentment, or pleasure might all be substituted for satisfaction in the definition of utility. Economists attempt to capture in one word—utility—the many contributions made to our well being when we wear, drink, eat, or play something. The ultimate assumption behind this theory is that people act with a purpose. In the words of von Mises, they act because they are “dissatisfied with the state of affairs as it prevails.” 1 1 Ludwig von Mises, The Ultimate Foundations of Economic Science: An Essay on Method (Princeton, N.J.: D. Van Nostrad, 1962), pp. 2—3. W Chapter 3 Principles of Rational Behavior at Work in Society and Business 2 The Acting Individual If people act in order to satisfy their consciously perceived wants, their behavior must be self directed rather than externally controlled. However, there is no way to prove this assertion. Economists simply presume that individuals, as opposed to groups, perform actions. It is the individual who has wants and desires, and looks for the means to fulfill them. It is the individual who attempts to render his or her state “less unsatisfactory.” Group action, when it occurs, results from the actions of the individuals in the group. Social values, for instance, draw their meaning from the values held collectively by individuals. Economists would even say that group action cannot be distinguished from individual action. Although economists do not deny the existence of group psychology, they leave the study of social groups to others. Thus to understand group behavior, the economist looks to the individual. Of course individuals in a group affect one another’s behavior. In fact, the size and structure of a group can have a dramatic effect on individual behavior. When economists speak of a competitive market, they are actually talking about the influence that other competitors have on the individual consumer or firm. Rational Behavior When individuals act to satisfy their wants, they behave rationally. Rational behavior is consistent behavior that maximizes an individual’s satisfaction. The notion of rational behavior rests on three assumptions: • First the individual has a preference and can identify, within limits, what he or she wants. • Second, the individual is capable of ordering his or her wants consistently, from most preferred to least preferred. • Third, the individual will choose consistently from these ordered preferences to maximize his or her satisfaction. Even though the individual cannot fully satisfy all her wants, she will always choose more of what she wants rather than less. Furthermore, she will always choose less rather than more of what she does not want. In short, the rational individual always stands ready to further her own interests. Some readers will find these assertions obvious and acceptable. To others, they may seem narrow and uninspiring. Later in the chapter we will examine some possible objections to the concept of rational behavior, but first we must examine its logical consequences. Chapter 3 Principles of Rational Behavior at Work in Society and Business 3 Rational Decisions in a Constrained Environment Several important conclusions flow from the economist’s presumption of rational behavior. First, the individual makes choices from an array of alternatives. Second, in making each choice, a person must forgo one or more things for something else. All rational behavior involves a cost, which is the value of the most preferred alternative forgone. Third, in striving to maximize his or her welfare, the individual will take those actions whose benefits exceed their costs. Choice We assume that the individual can evaluate the available alternatives and select the one that maximizes his utility. Nothing in the economic definition of rational behavior suggests that the individual is completely free to do as he wishes. Whenever we talk about individual choices, we are actually talking about constrained choices—choices that are limited by outside forces. For example, you as a student find yourself in a certain social and physical environment and have certain physical and mental abilities. These environmental and personal factors influence the options open to you. You may have neither the money, the time, nor the stomach to become a surgeon, or your career goal may not allow you the luxury of taking many of the electives listed in your college catalog. Although your range of choices may not be wide, choices do exist. At this moment you could be doing any number of things instead of reading this book. You could be studying some other subject, or going out on a date, or playing with your son or daughter. You could have chosen to go shopping, to engage in intramural spots, or to jog around the block. You may not be capable of playing varsity sports, but you have other choices. Although your options are limited, or constrained—you are not completely free to do as you please—you can still choose what you want to do. In fact, you must choose. Suppose that you have an exam tomorrow in economics and that there are exactly two things you can do within the next 12 hours. You can study economics, or you can play your favorite video game. These two options are represented in Figure 3.1. Suppose you spend the entire 12 hours studying economics. In our example, the most you can study is four chapters, or E 1 . At the other extreme, you could do nothing but play games—but again, there is a limit: eight games or G 1 . Neither extreme is likely to be acceptable. Assuming that you aim both to pass your exam and to have fun, what combination of games and study should you choose? The available options are represented by the straight line E 1 G 1 , the production possibilities curve for study and play and the area underneath it. If you want to maximize your production, you will choose some point on E 1 G 1 , such as a: two chapters of economics and four games. You might yearn for five games and the same amount of study, but that point is above the curve and beyond your capabilities. If you settle for less—say one chapter and three games, or point x—you will be doing less than you are capable of doing and will not be maximizing your utility. The combination you actually choose will depend on your preference. Chapter 3 Principles of Rational Behavior at Work in Society and Business 4 Changes in your environment or your physical capabilities can affect your opportunities and consequently the choices you make. For example, if you improve your study skills, your production rate for chapters studied will rise. You might then be able to study eight units of economics in 12 hours in which case your production possibilities curve would expand outward. Even if your ability to play Amazons from Outer space remained the same, your greater proficiency in studying would enable you to increase the number of games played. Your new set of production possibilities would be E 2 G 1 in Figure 3.2. Again, you can choose any point along this curve or in the area below it. You may decide against further games and opt instead for four chapters of economics (point c). You could move to point b, in which case you would still be learning more economics—three chapters instead of two—but would also be playing more games. The important point is that you are able to choose from a range of opportunities. The option you take is not predetermined. FIGURE 3.1 Constrained Choice With a given amount of time and other resources, you can produce any combination of study and games along the curve E 1 G 1 . The particular combination you choose will depend on your personal preferences for those two goods. You will not choose point x, because it represents less than you are capable of achieving—and as a rational person, you will strive to maximize your utility. Because of constraints on your time and resources, you cannot achieve a point above E 1 G 1 . FIGURE 3.2 Change in Constraints If your study skills improve and your ability at the game remains constant, your production possibilities curve will shift from E 1 G 1 to E 2 G .1 . Both the number of chapters you can study and the number of games you can play will increase. On your old curve, E 1 G 1 , you could study two chapters and play four games (point a). On your new curve E 2 G 1 , you can study three chapters and play five games (point b). Chapter 3 Principles of Rational Behavior at Work in Society and Business 5 Cost The fact that choices exist implies that some alternative must be forgone when another is taken. If A and B represent two mutually exclusive opportunities, to choose A is simultaneously to not choose B. In the presence of choice—a situation in which no more than one alternative can be taken at a time—a cost must be incurred. Cost (or more precisely, opportunity cost) is the value of the most highly preferred alternative not taken. Put another way, it is the value the individual places on the most favored alternative not taken at the time the choice is made. For example, suppose that you have decided to spend half an hour watching old television programs. The two programs you most want to watch are M.A.S.H. and Gilligan’s Island. If you choose Gilligan’s Island, the cost is the pleasure you sacrifice by not watching M.A.S.H. Notice that cost is not defined in terms of money. Money is a useful measure because it reduces all costs to one common denominator. Money is only the means of measuring cost, however; it is not cost itself. The shoes you are wearing may have cost you $50 (a money cost), but the real cost (the opportunity cost) is the value of what you could have purchased instead. Money cost is a monetary measure of the benefits forgone when a choice is made. The real cost is the actual benefits given up from the most preferred alternative not taken when a choice is made. When economists use the term cost, they mean real, or opportunity, cost. You could have bought dozens of soft drinks or deposited the $50 in a savings account for future use. Either option would be a legitimate alternative to purchasing shoes. The point is that the cost of the shoes to you is the value of the most attractive option not taken, whether it is the soft drinks or the future use of the money. As long as you have alternative uses for your time and other resources, there is no such thing as a free lunch. Nothing can be free if other opportunities are available. One goal of economics courses is to help you recognize this very simple principle and to train you to search for hidden costs. There is a cost to writing a poem, to watching a sunset, to extending a common courtesy, if only to open a door for someone. Although money is not always involved in choices, the opportunity to do to other things is. A cost is incurred in every choice. Maximizing Satisfaction: Cost-benefit Analysis An individual who behaves rationally will choose an option only when its benefits are greater than or equal to its costs. Furthermore, individuals will try to maximize their satisfaction by choosing the most favorable option available. That is, they will produce or consume those goods and services whose benefits exceed the benefits of the most favored opportunity not taken. This restatement of the maximizing principle, as it is called, explains individual choice in terms of cost. In Figure 3.1, the choices along curve E 1 G 1 represent various Chapter 3 Principles of Rational Behavior at Work in Society and Business 6 cost-benefit tradeoffs. If you choose point a, we must assume that you prefer a to any other combination because it yields the most favorable ratio of benefits to costs. A change in cost will produce a change in behavior. Suppose you and a friend set a date to play checkers, but at the last moment he received a lucrative job offer for the day of the match. Most likely the contest will be rescheduled. The job offer will change your friend’s opportunities in such a way that what otherwise would have been a rational act (playing checkers) becomes one that is no longer rational. The cost of playing checkers will rise significantly, enough to exceed the benefits of most checkers games. Economists see cost-benefit analysis as the basis of much (but certainly not all) of our behavior. Cost-benefit analysis is the careful calculation of all costs and benefits associated with a given course of action. Why do you attend classes, for example? The obvious answer is that at the time you decide to attend class, you expect the benefits to attending the exceed the costs. The principle applies even to classes you dislike. A particular course may have no intrinsic value, but you may fear that by cutting class, you will miss information that would be useful on the examination. Thus the benefits of attending are a higher grade than you would otherwise expect. Besides, other options open to you on Tuesday morning at 10:00 AM may have so little appeal that the cost of going to class is very slight. Take another example. Americans are known for the amount of waste they pile up. Our gross national garbage is estimated to be more valuable than the gross national output of many other nations. We throw away many things that people in other parts of the world would be glad to have. However morally reprehensible, waste may be seen as the result of economically rational behavior. Wastefulness may be beneficial in a limited personal sense. The food wrappings people throw away are “wasted,” but they do add convenience and freshness to the food. In the individual’s narrow cost-benefit analysis, the benefits of the wrapping can exceed the costs. Is life priceless? Although we like to think so, many of us are not willing to bear the cost that must be paid to preserve it. Several million animals—dogs, opossums, squirrels, and birds—are killed on the highways each year. Most of us make some effort to avoid animal highway deaths. If saving lives were all important, we could drive less but that would bring a significant cost. Even when human beings are involved, we sometimes refuse to bear the cost of preserving life. People avoid helping victims of violent crime, and doctors routinely pass by highway accidents although they might save lives by stopping to help. Indeed, revolutions succeed through people’s willingness to sacrifice lives—both others’ and their one to achieve political or economic goals. The behavior of business people is not materially different from that of drivers or consumers. People in business are constantly concerned with cost-benefit calculations, only the comparisons are often (but not always) made in dollar terms: For example, whether the cost of improving the quality of a product is matched by the benefits of the improvement. Will consumers value the added benefits enough to pay for hem? In assessing the safety of their products, business people must consider whether consumers are willing to pay the cost of any improvements. Chapter 3 Principles of Rational Behavior at Work in Society and Business 7 The Effects of Time and Risk on Costs and Benefits When an individual acts, costs are not necessarily incurred immediately, and benefits are not necessarily received immediately. The decision to have a child is a good example. At turn of the century prices, a college educated couple’s first child can easily cost more than $500,000, from birth through college. 2 Fortunately this high cost is incurred over a relatively long period of time (or people would rarely become parents!). Benefits received in the future must also be compared with present benefits. If you had a choice between receiving $10,000 now and $10,000 one year from now, you would take $10,000 today. You could put the money in a bank, if nothing else, where it would earn interest, or you could avoid the effects of future inflation by spending the money now. In other words, future benefits must be greater than present benefits to be more attractive than present benefits. To compare future costs and benefits on an equal footing with costs and benefits realized today, we must adjust them to their present value. Present value is the value of future costs and benefits in terms of current dollars. The usual procedure for calculating present value a process called discounting involves an adjustment for the interest that could be earned (or would have to be paid) if the money were received (or due) today rather than in the future. 3 If there is any uncertainty about whether future benefits or costs will actually be received or paid, further adjustments must be made. Without such adjustments, perfectly rational act may appear to be quite irrational. For example, not all business ventures can be expected to succeed. Some will be less profitable than expected or may collapse altogether. The average fast-food franchise may earn a yearly profit of $1 million, but, but only nine out of ten franchises may survive their first year (because the average profits is distorted by the considerable earnings of one franchise). Thus the estimated profits for such a franchise must be discounted, or multiplied by 0.90. If 10 percent of such ventures can be expected to fail, on average each will earn $900,000 ($1 million x .90). The entrepreneur who starts a single business venture runs the risk that it may be the one out of ten that fails. In that case profit will be zero. To avoid putting all their eggs in one basket, many entrepreneurs prefer to avoid putting all their “eggs” in the 2 For rough estimates of the cost of rearing children by expenditure, see U.S. Department of Commerce, Statistical Abstract of the United States: 1998 (Washington, D.C.: U.S. Government Printing Office, 1998), table 732. To obtain the total cost of childcare, you must then estimate the value of parental time. 3 The mathematical formula for computing the present value of future costs or benefits received one year from now is PV = [1/(1 + r)] f, where PV stands for present value, r for the rater of interest, and f for future costs or benefits. The interest rate used in this formula is the rate at which we discount future costs and benefits. Chapter 3 Principles of Rational Behavior at Work in Society and Business 8 proverbial one basket by initiating several new ventures, thereby spreading the risk of doing business. In the same way, investors spread their risk by investing in a wide variety of companies, and firms spread their risk by producing a number of products. To give another example, criminal behavior may appear irrational if only the raw costs and benefits are considered. A burglar who nets $1,500 from the sale of stolen property may have to spend a year in jail if caught, prosecuted, and convicted. He could lose the annual income from his legitimate job, perhaps $10,000. That is a high cost to pay for a $1,500 profit on stolen property, but he pays that cost only if he is caught, prosecuted, convicted, and sentenced. The police cannot be everywhere at all times; prosecutors may be reluctant to prosecute; and suspended sentences are commonplace. All in all, even an inept burglar may have no more than a 10 percent chance of spending a year in jail. 4 To estimate the actual cost faced by the burglar who is caught, sentenced, and sent to jail for a year, we might multiply the cost if caught, $10,000, by 0.10. That calculation indicates that to a burglar who is sent to jail for an average of one out of ten burglaries, the cost of any one burglary is only $1,000 ($10,000 x 0.10). Thus the actual cost of the burglary is less than the benefits received, $1,500. Although it may be morally reprehensible, the criminal act can conceivably be a rational one. Surveys of criminal activities and their rewards tend to support such a conclusion. A study of burglary and grand larceny cases in Norfolk, Virginia, showed that for the unusual criminal who committed just one crime and was caught in the act, crime did not pay. The typical criminal, however, convicted the average number of times and sentenced to the average number of years in prison, more than tripled the lifetime income he could have earned from a regular salaried job—even allowing for one or more years of unsalaried incarceration. 5 When this study was replicated in Minnesota, the results were not quite as dramatic, but the criminal’s lifetime income still doubled. 6 For criminals who are never caught, crime pays even more handsomely. The same logical process of discounting can be applied to your life as a student. When you signed up for your MBA program, you actually had limited information on how it would work out for you. (Admit it, it was a gamble!) Similarly, when you sign up for courses, you usually have only a very rough idea of how difficult and time 4 This is not an unreasonably low figure. Gregory Krohm “concluded that the chance of an ‘adult’ (seventeen or older) burglar being sent to prison for any single offense is .0024. . . For juveniles. . . the risk was much lower, .0015.” “The Pecuniary Incentives of Property Crime,” in The Economics of Crime and Punishment, ed. Simon Rottenberg (Washington, D.C.: American Enterprise Institute for Public Research, 1973), p. 33. 5 William E. Cobb, “Theft and the Two Hypotheses,” in The Economics of Crime and Punishment, ed. Simon Rottenberg (Washington, D.C.: American Enterprise Institute for Public Policy Research, 1973), pp. 19 30. 6 David L. Johnson, “An Analysis of the Costs and Benefits for Criminals in Theft” (Economics Department, St. Cloud State College, St. Cloud, Minn., May 1974), mimeographed. Chapter 3 Principles of Rational Behavior at Work in Society and Business 9 consuming they will be, and what benefits you will receive from them. In other words, you are rarely certain of their costs and benefits. To make your decision, you will have to discount the raw costs and benefits by the probability of their being realized. Risks are pervasive in human experience, and rational behavior takes those risks into account. What Rational Behavior Does Not Mean The concept of rational behavior often proves bothersome to the noneconomist. Most of the difficulties surrounding this concept arise from a misunderstanding of what rationality means. Common objections include the following: 1. People do many things that do not work out to their benefit. A driver speeds and ends up in the hospital. A student cheats, gets caught, and is expelled from school. Many other examples can be cited. To say that people behave rationally does not mean that they never make mistakes. We can calculate our options with some probability, but we do not have perfect knowledge, nor can we fully control the future. Chances are that we will make a mistake at some point, but as individuals, we base our choices on what we expect to happen, not on what does happen. We speed because we expect not to crash, and we cheat because we expect not to be caught. Both can be rational behaviors. 2. Rational behavior implies that a person is totally self centered, doing only things that are of direct personal benefit. Rational behavior need not be selfish. Altruism can be rational; a person can want to be of service to others, just as he can want to own a new car. Most of us get pleasure from seeing others happy—and particularly when their happiness is the result of our actions. Altruism may not always spring from rational cost-benefit calculations; however, it is not always inconsistent with economic rationality. Self interest, moreover, does not necessarily stop at the individual. For many actions, “self” includes members of one’s family or friends. When a father spends a weekend building a tree house for his children, economists say that he has been engaged in self interested behavior. 3. People’s behavior is subject to psychological quirks, hang ups, habits and impulses. Surely such behavior cannot be considered rational. Human actions are governed by the constraints of our physical and mental makeup. Like our intelligence, our inclination toward aberrant or impulsive behavior is one of those constraints. It makes our decision-making less precise and contributes to our mistakes, but it does not prevent our acting rationally. Moreover, what looks like impulsive or habitual behavior may actually be the product of some prior rational choice. The human mind can handle only so much information and make only so many decisions in one day. Consequently, we may attempt to economize on decision making by reducing some behaviors to habit. Smoking may appear to be totally impulsive, and the physical addition that accompanies it may indeed restrict the smoker’s range of choices. Why might a person pull a cigarette from the pack “without Chapter 3 Principles of Rational Behavior at Work in Society and Business 10 thinking”? Perhaps because she has reasoned earlier that contemplating the pros and cons of smoking each and every time she things of cigarettes is too costly. By allowing smoking to become more or less automatic, the smoker probably increases the number of cigarettes she smokes daily, but she sees the tedium of having to make the decision each and every time she smokes. 4. Rational behavior implies that people know what they want, that they know which alternatives are available, and that they know how to act on that information. People cannot assimilate all the information they need to make rational choices, however. People do lack information, and they could make better choices if information were easier to obtain. However, rational behavior does not require perfect information. People will make choices on the basis of the information they have or can rationally acquire. If they have less than perfect information, they may make mistakes in their choices. The success or failure of their choices must be judged within those constraints. 5. People do not necessarily maximize their satisfaction. For instance, many people do not perform to the limit of their abilities. Satisfaction is a question of personal taste. To some individuals, lounging around is an economic good; by consuming it, they increase their welfare. Criticism of such is tinged with normative value judgments. An observer who equates rational behavior with what he or she considers good will have no trouble demonstrating that such behavior is irrational. Irrational behavior is behavior that is inconsistent or clearly not in the individual’s best interests and that the individual recognizes as such at the time of the behavior. 6. But to the economist, the values of the actor, not the observer or the social critic, determine the rationality of an act. Harold, not Jennifer or Max, determines the rationality of Harold’s behavior. Disincentives in Poverty Relief Our discussion of rational behavior can be used to understand one of the biggest policy issues of our time, welfare reform. We can do this by assuming that welfare recipients are tolerably rational. So much of the public discussions about welfare programs, especially cuts in them, assumes that since Congress has the authority to change the programs, it can alter the programs any way it wishes without creating problems. However, as we can easily see, Congress is in something of an economic, if not political, bind on welfare relief, given how incentives change when the program is adjusted. The basic problem is that the practice of scaling down welfare benefits as earned income rises creates an implicit marginal tax on additional earned income that discourages the poor from working. Why not lower the implicit marginal tax rate? Figure 3.3 gives the answer. The 45 degree line that extends out from the origin indicates points of equal distance from each axis—that is, points at which spendable [...]... reputation for honest dealing and to take charge of the contacts 17 Chapter 3 Principles of Rational Behavior at Work in Society and Business Scott Cook, who in 19 83 developed the widely used home-finance software package called “Quicken,” the major product of Cook’s firm, Intuit, Inc., which was courted for a buyout in 1994 by Microsoft Cook eventually agreed to sell Intuit to Microsoft for $1.5 billion... expected of it 23 Chapter 3 Principles of Rational Behavior at Work in Society and Business We have also indicated in this chapter how individual rationality can give rise to a nontrivial problem for managers, the last-period problem, which can make deals costly At the same time, we have indicated how thinking in terms of rational precepts can suggest ways managers can deal with their last-period problems.. .Chapter 3 Principles of Rational Behavior at Work in Society and Business income equals earned income At point y, for example, a poor person earns and can spend $5,000 annually At points above the line, spendable income exceeds earned income For instance, at point x, a poor person earns $5,000 annually and can spend $7,500 He receives a subsidy equal to y – x, or $2,500 FIGURE 3. 3 Policy Tradeoffs... accumulation of relationships that can be counted upon to cushion shock in time and trouble” (ibid., p 164) 13 This explanation for long term contracting has been argued at length by Ronald P Dore, Taking Japan Seriously (Stanford, Calif.: Stanford University Press, 1987) 14 Ibid., p 188 20 Chapter 3 Principles of Rational Behavior at Work in Society and Business creation of long term buyer supplier... to solve a form of the last-period problem of retired workers, especially unionized workers, whose concern for the financial stability of the firm may stop when they get their gold watch Unions often negotiate the retirement payments and fringe benefits for unionized retirees at the same time they negotiate the pay packages for the current workers Even when retirement benefits are fixed for retirees’... Bernard F Lentz, “Entrepreneurial Success and Occupational Inheritance Among Proprietors,” Canadian Journal of Economics, Vol 23, No 3 (August 1990), pp 101 117 9 William Davidow and Michael Malone, The Virtual Corporation, (New York: Harper Collins Publishers, 1992), p 234 18 Chapter 3 Principles of Rational Behavior at Work in Society and Business Firms commonly complain that goods delivered in the last... and provide more motivation for suppliers to keep up honest dealing The Keiretsu As a Solution to the Last-period Problem Japanese firms are renown for organizing themselves into groups of firms called keiretsus Keiretsu members buy from one another, share information, and organize joint ventures to produce goods and services in concert with one another The largest and best-known keiretsu is Mitsubishi,... products The Japanese have demonstrated a knack for bringing new products to market quickly However, we mention the keiretsu organizational form here only because of one of its more unheralded benefits: it is a form of business organization that seeks to solve the last-period problem The integration of the member firms’ purchases and sales and strategic plans for the future is a means by which members can... company by muting (though not always eliminating) the last-period problem The last-period problem extends beyond buyer supplier relationships of the sort we described above involving the purchase of widgets There is clearly a last-period problem for military personnel When officers or enlisted men and women are given 15 Chapter 3 Principles of Rational Behavior at Work in Society and Business their transfer... of the last-period problem Economists Robert Gibbons and Kevin Murphy have found from their econometric studies that as CEOs get closer to retirement age, their compensation tends to become more closely tied to their firm’s stock market performance.7 Another way of solving the last-period problem is through performance payments, which means that payments are made as a project is completed For example, . stands for present value, r for the rater of interest, and f for future costs or benefits. The interest rate used in this formula is the rate at which we discount future costs and benefits. Chapter. Economics, Vol. 23, No. 3 (August 1990), pp. 101 117. 9 William Davidow and Michael Malone, The Virtual Corporation, (New York: Harper Collins Publishers, 1992), p. 234 . Chapter 3 Principles. Government Printing Office, 1998), table 732 . To obtain the total cost of childcare, you must then estimate the value of parental time. 3 The mathematical formula for computing the present value of