CHAPTER 1-1 EVALUATING SIMPLE ALTERNATIVES Analysis of the simplest "maximizing" decisions reveals the bare bones of the choice-making apparatus. It also highlights the information needed to make even these simple decision-choices rationally. (The only less-complex decision hinges upon sheer preference, such as whether to take vanilla or chocolate.) The essence of all business-like decisions, whether made for a firm or an individual or a non-profit organization such as a government, is a) constructing a list of relevant alternatives based on your experience and imagination; b) sensibly estimating the consequences -- the costs and benefits, the incomes and outgoes -- that you expect to follow upon each alternative choice, and c) calculating which alternative will leave you with the largest "profit," that is, the excess of income over outgo. This type of decision is called "maximizing" because the aim of the analysis is to find the alternative that produces the most (or the least) of something. In the first case to come, the quantity to be maximized is profit, and the decision-maker is assumed to be a business. But the decision-making unit could just as well be a non-profit enterprise such as a hospital or an airport. The cases we shall take up here are simple because they all take place entirely within a single short time-period -- a year, say, or even a day. Activities that fit this description include promoting a concert or a symphony tour, and selling baseball hats outside a stadium. But in most business situations, a decision today will have consequences many years into the future, either through long-lived investment in buildings and equipment, or through the goodwill created in long-term customers. This complication of multi-periodicity will be dealt with later. Also unlike most business situations, here we assume that we know with reasonable certainty what will happen following upon the decision we make, rather than being uncertain about the results. (Chapter 3 tackles the fascinating issues that arise when we must explicitly grapple with the uncertainty that pervades most human decision-making situations.) Analyses outside of business -- and for many situations within business, too -- have the added complication that there are multiple goals rather than the simple goal of maximizing profit. Another non-profit complication is that the results may not be measurable in a single index such as money. In later chapters we will grapple with these complexities. Even in a short-run no-uncertainty situation, however, there may arise the difficulty of choosing the best combination of variables within our control -- price, quality, location, production method, advertising, service, and so on. Developing our technique that far is the subject of this chapter. HOW TO PRICE WHAT YOU SELL An enterprise must decide the price to charge for its product when it goes into the market. And an individual must decide what price to set on his or her services when the person looks for work. How should you go about it? You are promoting a basketball game in Bloomington, Iowa, an off-season exhibition featuring a team of professional players playing against a team of recent all-star college graduates. You have rented the 12,000 seat arena for $16,000, and you are committed to pay the teams $2,000. If you charge just one price for all tickets with no reserved seating, what price should you set? Assume that you can expect to sell the following numbers of tickets at the prices shown. Table 1-1-1 Price Tickets Expected to Be Sold $ 14 11,200 16 10,000 20 7,900 24 6,200 28 5,400 32 4,000 Assume also that your expenditures for non-playing labor and other purchases will depend on the number of tickets that you sell, and will be as follows: Table 1-1-2 Attendance Expected Expenditures 4,000 - 5,999 $4,000 6,000 - 7,999 3,400 8,000 - 9,999 6,800 10,000 - 12,000 8,000 You want to "make" as much money as possible from this operation. That is, you would like to maximize the amount left over after you pay all the expenses. Therefore, it is straightforward common sense to put all your costs and revenues into a table like this one: Table 1-1-3 Sales Price Quantity Revenue Expenditures PV _____ ________ __________ __________ __________ $14 11200 $156,800 $56,000 $100,800 $16 10000 $160,000 $56,000 $104,000* $20 7900 $158,000 $54,000 $104,000* $24 6200 $148,800 $54,000 $ 94,800 $28 5400 $151,200 $52,000 $ 99,200 $32 4000 $128,000 $52,000 $ 76,000 From the table you conclude that your profit will be greatest at a ticket price of either $16 or $20. We might also note that expenses will be somewhat less at a price of $20 and an attendance of 7900 than at a price of $16 and an attendance of 10,000, and hence this more refined analysis suggests $20 is better. The conclusion is only as sound as your estimates of the numbers used in the table. Part Two sets forth methods for making sound estimates. You might now consider whether there is some price between $16 and $20 which would produce even more profit. Therefore, supplement the existing table with an analysis of, say, $18. You could also refine the analysis by considering even finer gradations of prices, but practical decision-makers are usually satisfied with the analysis of a few round-number prices. When I first began to study business, a mathematics instructor asked what I was learning. I mentioned this topic of setting a price so as to maximize profit in the simplest possible situation. He then asked me if the correct answer could not be arrived at by simply looking for the price with the biggest difference between income and outgo. I said yes, that's true in a simple situation, but in a more complex situation you need the more powerful intellectual machinery of the "marginal analysis," a name which conjures respect and even fear from those who have encountered it in Economics 1. My response was wrong. The marginal analysis using higher mathematics is not helpful in complex price-setting problems any more than it is necessary -- or even useful -- in the simple case we're dealing with at the moment. Hard as it may be for some readers to believe, the simple table we constructed above cannot be excelled by any other method of calculation. And extension of the same sort of common-sense table will produce the best possible decision in all other business situations, too, as we shall see. Indeed, the marginal analysis, even using calculus rather than just tables, cannot handle complex problems nearly as well as can this sort of tabular analysis. Hence, economics teachers have to stick close to this sort of simple case to illustrate the marginal analysis because problems much more complex than this one are too tough to handle with "advanced" methods. But with the simple tabular method we shall do more more complex problems as easily as rolling off a log. This is only the first of several important issues discussed in this book in which the conventional wisdom as widely taught in even the best universities is flatly wrong -- unnecessary, confusing, or even yielding unsound conclusions. (Of course it is prudent to proceed with caution when you come across such a far-out unconventional view. But if you do not at least check it out for yourself, you will close off progress for yourself and for society.) Constructing the above table immediately raises difficult questions such as: How do you judge how many seats you will sell at various ticket prices? How sure can you be of your estimates? Might you make more money by charging different prices for different parts of the arena? And, what about buying some advertising to sell more seats? We will be dealing with these and other questions one by one. For some flavor of the complexities of price-setting -- except that the viewpoint here is that of of the buyer rather than the seller -- here is a vignette from deal-making between television interviewer David Frost and Richard Nixon's agent: I was utterly confident that my interest in the enigma of Richard Nixon would also be reflected by the public's interest in him as well. And, as an independent, I had no corporate bureaucracy to consult. I went ahead and placed the call to Swifty Lazar. I had no corporate bureaucracy to supply any future backup either, of course, but that was not a consideration in my mind at the time -- only the overriding thought of being first in the race to question Richard Nixon about his years in the White House. I was glad that I was dealing with Swifty Lazar. Noted for his legendary ability to enter a revolving door behind you and come out in front, Swifty believed in getting right to the point. He wanted $750,000 for his client for a maximum of four one-hour shows. The main competitors -- later revealed to be NBC -- were currently at $300,000 and on their way to $400,000 for two hours, and would not guarantee more than two hours. That seemed to me to be a heavy rate per hour -- and an underestimate of how much Nixon had to offer, both in terms of information and public interest. Others might not agree, but I was sure there was more -- much more - - than two hours of potentially riveting television in Richard Nixon. I said I was thinking of a maximum of $500,000 for a minimum of four hours. Before returning to the question of a fee, however, I ticked off the points I regarded as mandatory... Within days, the word came back: the response was not unfavorable. Swifty, God bless him, felt "duty- bound" to tell me that the "rival offer" was now $400,000 for two hours, and then returned to his magic figure of $750,000. I said I could not really go beyond my original figure unless I had more time on the air. We compromised at $600,000 plus 20 percent of the profits, if any, for four ninety-minute shows, with $200,000 of that to be paid on signature (1978, pp. 10-12). The key difficulty here is assessing what the other parties will do. Soon we will tackle that difficulty. The same sort of table as used above handles decisions about (say) whether to locate a factory in one city or another, and whether to adopt a new production technique. You need only insert the expected income and outgo for each alternative, and choose that alternative with the highest profit. How Many Alternatives to Consider How many alternatives should you consider? It is impossible even in principle to consider all possibilities. And in most situations it is feasible to consider only a very small number of them. The fact that the pricing table analyses only even-dollar price is not a drawback of the method; it is only a reflection of reality, wherein firms and even countries -- for example, Saudi Arabia when it sets prices for petroleum -- choose among only even-dollar or half-dollar prices. A cost-benefit analysis of the pricing process itself would undoubtedly show that worrying that you might do better with a penny more or less in such a case would not be worth your time -- and indeed, such a cost-benefit analysis is itself not worthwhile (probably). The concept of satisficing was invented by Herbert Simon to refer to this realistic and practical process of aiming for a good-enough decision rather than for a perfect decision -- that is, satisfice rather than try (inevitably unsuccessfully) to maximize. COMBINATION ALTERNATIVES Let's now illustrate the technique with three examples slightly more complex than the basketball pricing case. The tabular method table enables you to easily evaluate the effects of two factors at once. Let's say that you wish to simultaneously choose the best price and the best amount of advertising. First compare the effects of various amounts of advertising at one of the prices to be considered, as in the top panel of Table 1-1-4; then at another of the prices, as in the bottom panel; then choose the best combination of a price and an advertising level from the table as a whole. This technique enables you to compare any sets of combinations you wish to consider, using as many sub-tables as are necessary. Lest you worry that the amount of arithmetic will be inconvenient, the personal computer does all calculations for you in a jiffy with the aid of a "spreadsheet" program. (This is only the first of many ways that the computer enhances our thinking nowadays.) Table 1-1-4 Here The following example of a combination alternative illustrates the power of this method. Setting prices for a "line" of two or more related products has long been thought an intractable problem. The core of the problem is that the price of one product affects the sales of the others. For example, the price of the Postal Service's two-day delivery affects the sales of its overnight service, and vice versa. But the tabular method cracks the problem with ease. Or, for the case of A&P supermarkets' line of three coffees -- Bokar, Red Circle, and Eight O'Clock -- the analysis is shown in Table 1-1-5. The results for each line of three prices are compared to the results for each other alternative line of prices. Simply choose the line with the largest net revenue after expenditures have been allowed. The key is not to think separately about the individual elements in a line. Rather, because the sales of each product affect each other's, and because the firm is ultimately interested in its overall profit and not in the individual product's results, we consider the combined results for each alternative. This all-together technique makes simple almost any analysis of several activities which affect each other such as a structure of discounts. Table 1-1-5 After looking at Table 1-1-5 you may conclude that the analysis is indeed simple, but the data to support the analysis may not be easy to come by. Very true. One of the advantages of this tabular method, however, is that it focuses your attention on the needed data, whereas if you get caught up in a complex mathematical analysis of a decision-making situation, your attention is likely to be deflected from the data. In this case, the data are relatively easy to come by, however, once the table makes clear what you are looking for. The supermarket chain need simply conduct experiments with different lines of prices in different store locations. Lest you think that this tabular analysis is small-time stuff, rest assured that exactly this decision method is used for the very biggest business-like decisions -- for example, whether a firm should start an operation in Africa or should instead invest in deep-sea mining of metals, or whether a government should or should not spend billions of dollars for a canal or a supersonic airplane. (The name "cost-benefit analysis" was first used for such public investment decisions.) Such analyses are, of course, more complex than figuring the expenses for the ushers and arena-rental involved in your pro-basketball game, and the table therefore will have entries in it. But the method of analysis is exactly the same. And in such a complex situation not even the bravest economist tries to use fancy mathematical marginal analysis; the formulae just cannot handle the real-life details of a cost-benefit analysis of a dam or deep-sea mining operation. So, if the simple table is good enough for such multi- billion-dollar analyses, should it not be good enough for you in your daily life or business decision-making? You may think that this framework is obvious and uncontroversial for making decisions about price-setting. Incredibly, it is not so. This framework implies that the basic analytical framework of microeconomic decision-making -- the marginal analysis -- is useless and confusing, as it is. But economists are so wedded to that contorted method, because of an interesting series of twists and turns in intellectual history, that they continue to teach it to students of business.1 After we learn about present-value analysis in the next chapter, we can extend the analysis to decisions that cover many years rather than just the immediate period. FOOTNOTES 1Modern economics follows in a line from the English economist Alfred Marshall. The original geometric analysis done by Marshall showed only curves for supply and demand, and the analysis applied to agricultural markets, as wholes. In such cases, the independent variable is the weather, and hence it makes sense to put the quantity supplied on the horizontal axis, and the dependent variable price on the vertical axis. For manufactured goods, however, price is the appropriate independent variable, especially when one is making the analysis for the firm rather than the industry. But economists were stuck with the old tradition. And when they came to add the additional machinery known as the marginal analysis, they found themselves making the analysis with respect to quantity rather than price, which has tied generations of students into knots. The ironic part is that the great French economist Cournot had the analysis quite straight in 1838, but his great book never affected the later mainstream of analysis. (For more details, see Simon, 1981). REFERENCES Cournot, Augustin, Researches into the Mathematical Principles of the Theory of Wealth (Homewood: Irwin, 1838/1963) Simon, Julian L., "Unnecessary, Confusing, and Inadequate: The Marginal Analysis as a Tool for Decision Making", The American Economist, XXV, Spring, 1981, 28-35. Frost, David, I Gave Them a Sword (New York: Ballantine, 1978). ADDITIONAL READING A.M. E., Chapters Calabresi on shelf and floor Rossi, Freeman, Wright on shelf The text I used Herbert Simon, or March EXERCISES Two Prices for a Blue Concert. The basketball game you promoted was so profitable that you want to continue your career as an entertainment promoter with a blue concert in a college town. This time, however, you plan to charge different prices for students and the general public, because students may be more sensitive than the general public to ticket price. You therefore write down your guesses of the numbers of tickets that you will sell to the two classes of customers at each price, as in Table 1-1-6. Next you combine each student price and each general public price into an alternative as in Table 1-1- 6, making sure that the total number of seats is the 6,000-seat capacity. You then calculate the profit for each alternative, and choose the one with the highest alternative. Table 1-1-6 Panel A Student Price General Public Price Total Expectable 3 4 3 5 3 6 3 7 Panel B 4 4 4 5 4 6 4 7 This illustrates the general strategy for choosing the best alternative under any set of business circumstances: 1) Write down all the distinct combinations of possibilities, that is, each alternative that you wish to consider. 2) Estimate all the incomes and outgoes that are expected with each alternative. 3) Choose that alternative with the highest residual of income over outgo. For example, if you want to consider a variety of prices -- $99.95, $119.95 and $129.95 -- as well as a variety of discounts (2% off for payment within 30 days, or 3% off for payment within 30 days, or 3% off for payment within 60 days), examine each separate combination -- say, $99.95 and 2%-30 days. Of course, you might find it laborious to examine each combination that you could dream up. But good business sense will almost always allow you to narrow down the alternative to a manageable few. About the only situations in which this is not true are some technical decision such as how to split crude oil refining into auto gasoline, airplane gasoline, heating oil and so on, and advanced mathematical techniques are available to aid such decisions. Page # thinking smpcb11% 3-3-4d