# Some evidence on the Alchian and Allen theorem: the third law of demand?

I. INTRODUCTION

The Alchian and Allen theorem first appeared in writing more than twenty-five years ago in University Economics. Since then the theorem has grown to be standard pedagogy in many microtheory courses and the topic of several clarifying journal articles.(1) Despite the widespread use of the theorem, little scientific evidence has been brought to bear on its validity.(2) Perhaps this is due to the fact that the result is so transparent and intuitively pleasing that hardly anyone requires evidence on the subject. Furthermore, there are a large number of ad hoc examples of the principle in practice. And finally, the very nature of the proposition makes it difficult to test directly. We have overcome the last hurdle with an unusual dataset, and thus we are now in position to subject the theorem to a systematic examination.

We have acquired data on all season ticket purchases to Clemson University home football games for the 1986 and 1987 seasons. This encompasses 23,440 buyers of 95,958 tickets. We can identify the name and address of each purchaser along with the quantity and quality of tickets bought. This allows us to inquire whether those individuals traveling farther choose to purchase higher-quality tickets.

The paper proceeds as follows. In the next section we briefly summarize and criticize the literature on the Alchian and Allen theorem. After that we describe our data and present a test of the proposition. We close with a summary and conclusions.

II. THE LITERATURE

Alchian and Allen first presented their analysis in 1964:(3)

Suppose that grapes are grown in California and that it costs 5 cents a pound to ship grapes to New York whether the grapes are "choice" or "standard" (poorer) and that the total production of grapes is 50 percent "choice" and 50 percent "standard." Suppose further that in California the "choice" grapes sell for 10 cents a pound and the standard for 5 cents a pound; that is in California 2 pounds of "standard" and 1 pound of "choice" grapes sell for the same price. If grapes are shipped to New York, the shipping costs will raise the costs of "choice" grapes to 15 cents and of "standard" grapes to 10 cents. In New York the costs of "choice" grapes are lower relative to "standard" grapes (1.5 to 1) than in California (2 to 1). To buy 1 pound of "choice" grapes in New York would mean a sacrifice of 1.5 pounds of "standard" whereas in California it would cost 2 pounds of "standard." According to our law of demand, New Yorkers faced with a lower price of "choice" grapes relative to "standard" will consume relatively more "choice" grapes than Californians will. In California where "standard" grapes are cheaper relative to "choice" grapes a larger fraction of "standard" grapes will be consumed--and this is what actually happens.

Since the succinct original statement of the transportation cost theorem several others have offered remarks attempting to clarify, extend, and even correct the analysis. First, Gould and Segall |1969~ introduced a third good into the analysis in an attempt to demonstrate that the theory does not hold in general. Borcherding and Silberberg |1978~ pointed out that Gould and Segall's comment, though technically correct, was misleading and that the nature of substitution effects probably made the theorem hold. Umbeck |1980~ clarified the conditions necessary for the proposition to hold, specifically that the transportation or fixed charges had to be non-productive, that is, yielding no utility in and of themselves. According to his argument, meat consumed in a restaurant will not be higher in quality than meat consumed at home because of the services supplied by a waiter, because table-busing charges are neither fixed nor unproductive.(4)

Besides their comment on Gould and Segall's point, Borcherding and Silberberg point out that transportation can be undertaken by the consumer as well as the producer. In their example, tourists visiting Boston eat better lobster than the locals. In this analogy, the transportation undertaken by the consumer must be an unproductive and fixed charge in the Umbeck sense. However, transportation of people to lobsters, on the one hand, and lobsters to people, on the other, is different. When a lobster is shipped, the transportation charge is bundled with the quality charge. But, when the consumer travels, transportation and quality are purchased sequentially, not bundled as in the first case. This raises the theoretical sticking point of whether rational consumers will ignore the sunk costs of travel at the moment they make the quality choice.(5)

Consider the example of the husband and wife who travel from Chicago to Miami for a vacation cruise through the Caribbean. One might be tempted to argue that once they arrive at the dock, the air and cab fares, tips, and time cost of travel are sunk. Thus, when choosing between the first-class staterooms and the inside, low-deck steerage with upper and lower berths, the couple will ignore the costs of travel and make their decision based solely on relative prices posted by the cruise liner.

This approach fails to incorporate the fundamental insight provided by Becker |1971~ and Lancaster |1971~ in their renovation of consumer theory. In the modern theory of consumer behavior, consumers do not demand goods, but instead goods are inputs used with time and human capital in the production of commodities that directly enter the consumer's preference function. In this view, people do not buy airplane tickets, cab rides, and staterooms in cruise ships; they go on vacation. The whole trip, in their eyes and in their economic calculation, is one thing comprising many inputs. Thus, the Becker-Lancaster approach says that consumers make their choices bundled, and the larger the travel component, the lower the relative cost of high-quality staterooms.

When the couple from Chicago plans a Caribbean cruise vacation, there are no fixed costs. The couple sees the travel costs as a component of the overall vacation. That is, rational consumers have foresight. For the sake of pedagogy, let the first-class stateroom cost $8000 per week while the inside, low-deck berth is only $2000 per week. The relative price of quality at the dock is four. But from the point of view of the couple still in Chicago, air travel to Miami adds $1000 to the price of either ship accommodation, reducing the price of high quality to three. This makes the couple more inclined to high-quality accommodations, ceteris paribus. Suppose they decide to travel first-class while on the boat. They will choose other accommodations to match this decision. If they were to divert to cheaper, less luxurious quarters when they arrive in Miami, the bundle of other goods already purchased or contracted for would be inefficient in producing the pre-designed vacation. The marginal products of the household production inputs, relative to their prices, would no longer be equal across all inputs. Thus, in the household production framework, the couple will not change rooms.

The consumer's utility function is determined not by the goods, x, consumed, but rather by the flow of services, z, yielded by the goods and the time, t, necessary to convert the goods into services. Each of the zs, say |z.sub.i~, is produced by a set of goods, |x.sub.i~, and times, |t.sub.i~. So |z.sub.i~ is the ith service and |x.sub.i~ is a vector of n goods used in the production of |z.sub.i~. Also |t.sub.i~ is a vector of various amounts of time used in the production of |z.sub.i~. In sum:

|z.sub.i~ = |z.sub.i~(|x.sub.i~, |t.sub.i~).

In the case at hand, |x.sub.h~ and |x.sub.l~ are two inputs of the same basic type but different quality, two varieties of staterooms if you will. When planning the vacation, efficiency requires that

(|Delta~|z.sub.i~ / |Delta~|x.sub.i~) / (|Delta~|z.sub.i~ / |Delta~|x.sub.j~) = |p.sub.i~/|p.sub.j~

for all i and j where |p.sub.i~ is the price of the ith consumer input. Suppose some inputs are purchased sequentially, first one then another. For instance, air travel must be purchased before meals and lodging. Then, for the optimal vacation, the consumer must forecast or plan the quality and quantity levels of all the other inputs to assure the necessary equilibrium condition. Thus, having made the basic vacation decision, the choice of room quality, having already traveled to the vacation site, remains relevant. Borcherding and Silberberg's insight that the Alchian and Allen theorem holds for travelers as well as shipped goods is on a firm theoretical foundation.(6)

In spite of all the theoretical inquiry into the topic, the empirical validity of the Alchian and Allen theorem rests primarily on a large volume of anecdotes and ad hoc evidence. Therein lies the point of our paper. We have acquired an unusual set of data through which we can identify, at the customer level the quantity and quality purchased and the distance traveled. Moreover, in the case at hand, the consumers travel to the market. This allows, in our eyes, the nearly perfect experimental setting to test the travel cost theorem. That is where we now turn our attention.

III. THE EMPIRICAL ANALYSIS

Clemson University plays several football games at home each fall. The seats to view these games are sold via a complicated two-part pricing scheme.(7) Consumers must pay a fixed fee to obtain the right to buy season tickets. A variety of fixed-fee plans are available to customers. Over the period of our data, there were six different quality categories ranging in price from a low of $30 to a high of $2000. Table I reports the distribution of demand across the six quality categories. Category III is the largest with 27 percent of the total. The distribution of fees paid is skewed toward the high-quality classes.

Associated with each fixed-fee category is a package of goods. The fixed fees do not include the prices of the season tickets themselves, which cost approximately $100 apiece. In category I at the bottom of the quality spectrum, two end-zone tickets and little else are available. As the fee increases, so does quality. The purchaser gets better football tickets, closer to mid-field, high or low, depending on preference. The higher the fixed fee, the greater accommodation to such requests. In addition, reserved parking is available, with larger payments getting the prime slots. In the highest categories, buyers can group large numbers of tickets together, an option unavailable in the low categories. For instance, in category V, eight tickets can be purchased together at the fixed fee of $1000. Alternatively, eight tickets can be purchased in pairs by paying the category I fee four times for a total fixed-fee payment of only $120. However, when a single buyer chooses this option, the eight category I tickets are spread throughout the stadium in pairs. Category III purchasers have the option of four tickets together, category IV can get six en masse, and so on. The maximum number of tickets that can be grouped together is ten in category VI. Other perquisites are also available as the buyer moves to higher categories, but the primary quality distinction involves the location of seats in the stadium, the number of seats together, and the proximity and number of reserved parking slots. Choosing to pay a high fixed fee is choosing a high-quality football experience.

We have data on all season ticket purchasers for the 1986 and 1987 years.(8) We know the fixed-fee level chosen and the number of years that each buyer has previously bought tickets. In addition, we know the address of each purchaser and the number of tickets bought. For each zip code we have the Census Bureau estimates of population and income per capita.(9) The latitude and longitude of each zip code are used to compute the distance between the buyer and the football stadium.(10) Table II reports some summary statistics on our data base. The average fan paid a fixed fee of about $340 for the right to buy season tickets and then bought around four. This corresponds to a modal fan in the level III category who gives $250 and buys four tickets.

The full unit-price of these tickets includes their face value, the value of the time to travel to the stadium, and the direct expenses of traveling. We estimate these in the following way. Assume the fan travels to the games via car, at an average speed of 50 miles per hour. In addition, assume that the cost per mile driven is $.20. To compute the hourly value of time, take the zip-code-average, annual income per capita and divide it by 2000 (40 hours per week times 50 weeks per year). For our sample, this gives an average distance of around 100 miles and an average cost of travel time of $35 one way.

Thus, in addition to the money price of the ticket, the full price includes the two parts of travel costs, that is, (i) two times the distance between home and the stadium, divided by 50, times the individual's hourly income, plus (ii) the distance times .2. For the season ticket package then, the full season price, |p.sub.ij~, for the ith buyer in the jth year is

|n.sub.j~ |center dot~ 2 |center dot~ |(|D.sub.i~/50) |center dot~ |w.sub.ij~ + .2 |center dot~ |D.sub.i~~ + |n.sub.j~ |center dot~ |t.sub.j~,

where |n.sub.j~ is the number of games in the jth season, |D.sub.i~ is the distance between the stadium and home of the ith person, |w.sub.ij~ is the hourly income of the ith person in the jth year, and |t.sub.j~ is the money price of tickets in the jth year.(11) The full unit-price of a ticket averaged $407 in 1986 and $751 in 1987, the primary difference being the number of home games (eight in 1987).(12)

We subject these data to two inquiries. By the first law of demand, since the travel component of cost is higher, we expect that fans living farther away will buy fewer tickets. By the Alchian and Allen theorem, as transportation costs increase, the relative price of high quality declines. Accordingly, our second proposition is that consumers of football tickets will purchase higher-quality tickets the farther they live from the stadium. Indeed the Alchian and Allen theorem is a joint hypothesis: travel costs reduce quantity, TABULAR DATA OMITTED holding quality constant, and increase quality, holding quantity constant.

Our first statistical test estimates the demand for tickets as a function of the full price, income, number of consecutive years purchasing, population density, intensity of demand, the number of home games per season (five in 1986 or eight in 1987), and the quality category chosen (measured by the fixed fee paid). These are all self explanatory except for intensity. To measure intensity, we computed the total number of buyers in each zip code and then normalized it by the population of that zip code. There are two countervailing forces at work here. When the density of buyers is high, acquiring tickets from friends or neighbors is easier; therefore, the demand to buy season tickets from the original source is lower. At the same time, when the density of buyers is high, there is a commonality of interests that may increase demand via shared consumption, a synergy effect. We do not guess which effect dominates.

The ordinary-least-squares estimates of the quantity equation are reported in Table III. The top half of the table uses the logs of the variables, while the lower portion uses the levels. Overall, both specifications have their strong points, but the log model explains a greater portion of the variation in the dependent variable.(13) Since quantity and quality are jointly determined, ordinary-least-squares estimation of either may be biased. We jointly estimated the quantity and quality equations using the technique of three-stage-least squares, but the differences are so slight as to be ignored.

The demand for tickets succumbs to the first law; the coefficient is significant at the 2 percent level in the log specification and at the .1 percent level in the linear specification. We note that demand is quite price inelastic and that income and quantity are negatively linked. The magnitude and sign of these elasticities are tied to the two-part pricing scheme.(14) The longer buyers have been purchasing, the more tickets they buy. Densely populated areas have larger demand, ceteris paribus. The evidence on intensity of demanders, that is, areas with many buyers, is specification dependent. In the levels version, the number of buyers in the area who purchase tickets is linked with smaller number of tickets purchased by any one buyer. In the log model, however, this result reverses, begging further inquiry.(15) Consumption is lower when there are more home games.(16) Also note that these results are not driven by the difference in the number of home games in each season; the results replicate for each year cross sectionally. Finally, fans who purchase high quality also buy many tickets.

A Direct Test of the Alchian and Allen Theorem

To investigate the main thesis of the Alchian and Allen theorem, we estimate a model of quality choice. We assume that the quality category chosen depends on income, the number of tickets purchased, the number of consecutive years purchasing, population density in the local neighborhood, the same measure of intensity as before (the relative portion of the local population who also purchase tickets), and number of home games (which is perfectly collinear with year). We explore the Alchian and Allen thesis by including the transportation costs paid by the buyers. Table IV reports the ordinary-least-squares estimates of the quality equation for six different specifications using two different measures of travel costs--the one-way distance traveled and the one-way time cost of traveling.(17)

The results conform to the predictions of the theorem. The farther fans travel, the higher the quality category they choose. We discuss the dimensions of the transportation cost theorem in more detail after we review the estimates of the other coefficients. We find that quality is a normal good; recall that quantity and income were negatively related. Furthermore, the quality of tickets purchased and the number bought are positively associated. We attribute these effects to the two-part pricing scheme in place. People who have bought for many years consecutively buy better tickets. Population density and quality are negatively linked. The intensity variable also has a negative coefficient. When people have many neighbors who also buy tickets, they tend to buy lower-quality ones themselves.(18) Buyers choose better tickets when there are more home games, and most importantly, whether measured in distance traveled or the income cost of travel time, the more distant buyers choose better tickets.

The results reported in the first column of Table IV support the theorem. Our evidence is not the result of a peculiarity of either season; the results hold for the two years separately. However, there are reasons to believe that these estimates are imprecise. First, a few buyers live a long way from the stadium, too far to believe that they travel by car; one buyer lives in Pearl City, Hawaii. To investigate the seriousness of this problem we delete from the sample all buyers living more than 500 miles from the stadium. This eliminates 356 purchasers (1.5 percent) over the two-year period. Then we reestimate the quality model. These results are reported in the second column of Table IV. Deleting the buyers who must travel extreme distances may improve the estimates, as their travel costs are harder to estimate. In addition, these people may be buying tickets to give them away.

TABULAR DATA OMITTED

One other possibility worth pursuing is that some buyers, those with very intense demand, have permanently relocated near the stadium because of their desired consumption. If this is true, then these individuals will buy the best tickets, although they live close to the stadium, and our distance measure does not accurately reflect their true travel costs. For these people, transportation costs involve lost consumption opportunities at their alternative location, for now they either forego the amenities they would enjoy at the next best homesite or they must travel to those markets. In effect, some people living close by may have high transportation costs disguised by their location. To eliminate this potential source of bias, we constructed a second reduced sample, first deleting those people living more than 500 miles away, and, second, arbitrarily omitting those who live in Clemson or within 15 miles. This second cut eliminates 2224 more buyers over two years, reducing the sample size to 20,860. The results of estimating the quality equation over this sample are reported in the third column of Table IV. Here the impact of distance on quality chosen is estimated to be substantially higher than in the other samples. We interpret this to mean that some close-in buyers would actually live elsewhere were it not for the opportunity to enjoy football and the associated activities. In sum, we believe that the estimates in the third column of Table IV are probably the most accurate.(19)

One way to assess the economic magnitude of the Alchian and Allen theorem applied in this context is to consider the predicted behavior of a person who moves. Using these last estimates (from the truncated sample), we can forecast the impact of distance on quality. The average buyer in our reduced sample lives 94.5 miles from the stadium. The standard deviation is 73.4 miles. Assume a buyer, living one standard deviation below the mean, moves one standard deviation past the mean--from 21.1 miles away to 167.9 miles away, a 696 percent increase. The estimated distance elasticity of quality is 0.085. Thus, this move would be associated with a .085 |center dot~ 6.96 = 59.2 percent increase in fixed fees paid. The mode fee paid is $250. The increase in expenditures on quality is estimated to be $148 per consumer per year, from $250 to $398. Alternatively, think of the problem this way. Clemson University is located in the northwest corner of South Carolina, approximately 250 miles from the coast. Our model says that if a football fan living just outside Clemson and buying tickets in the level III category ($250) moves to Charleston, which is on the coast, he will double his choice of quality and jump from level III to level IV.

In our minds, this evidence, based on a large sample, is very nearly the perfect experimental setting to test the Alchian and Allen theorem. And it is so: the good tickets are shipped out.

IV. CONCLUSIONS

The subject of considerable theoretical debate as to its economic content, the insightful application of the first law of demand to quality proposed by Alchian and Allen has been widely accepted in the profession. Many examples of the principle in practice have worked their way into our oral tradition. Using season ticket sales to Clemson University home football games, we have put the principle to the test, and it performs well.

We find that fans who travel the farthest, choose to buy the best tickets. This confirms the theorem as well as the conjecture of Borcherding and Silberberg who say that "it does not matter if the goods are shipped to the consumers or the consumers are shipped to the goods." This suggests that the wide variety of ad hoc versions of the theorem--that couples hiring babysitters will enjoy nicer restaurants; that tourists will choose more elegant rooms the farther they travel; that out-of-towners will select the best theater seats; that cigarettes tend to be made of better grades of tobacco as taxes increase; and that more motorists choose premium gasoline over regular as the tax per gallon increases--are all sound pedagogical devices that would withstand systematic analysis were they so tested.

The Alchian and Allen theorem consistently provides a theoretical explanation for apparently anomalous behavior. Consider the following two cases. There is casual evidence that the consumption of certain brands of whiskey increases when liquor taxes go up. And, it appears that the quality of telephone service is now lower with deregulation and competition than it was in the regulated monopoly period. The theorem explains both outcomes without resort to public choice theory.(20) In our minds, the Alchian and Allen theorem is one of those rare insights, simple on the surface, yet, in application, so full of fury that we are inclined to label it the third law of demand.

1. See Gould and Segall |1969~, Borcherding and Silberberg |1978~, and Umbeck |1980~.

2. There are at least two papers with empirical content: Kaempfer and Brastow |1985~ and Umbeck and Staten |1989~. See also Cowen, Taborrok, and Poitras |1990~.

3. Alchian and Allen |1964, 75~.

4. For a broad discussion of this literature, see Silberberg |1990, 385-89~. In addition, Kaempfer and Brastow |1985~ argue that in the case of unit consumption, such as a parking lot, the imposition of a fixed fee does not alter relative prices.

5. Cowen, Taborrok, and Poitras |1990~ contend that since shipping fees amount to a sunk cost, when customers travel to the market, the proposition does not work, for consumers will (rationally) ignore the past cost of transportation.

6. The point is easy to see in the context of capital budgeting. A firm is constructing a new corporate headquarters. After the foundation is laid, the structural steel and concrete are in place, the marble facade has been added, and the fine wood paneling nailed to the walls, the firm does not install cheap indoor-outdoor carpeting in the executive suite, thinking to itself, those previous expenditures are now sunk and should be ignored. Since the structure was built to generate cash flows, the components must work together in a matching fashion. We contend that consumer expenditures are the same. People go on vacation, not only to enjoy the moment, but, as Jimmy Buffet has been known to croon, for the stories they can tell. Vacations produce value in the future, and no matter whether we examine the expenditures at the beginning, looking forward, or at the end, via retrospect, the bundle of goods creates the experience and, hence, they must match in the quality sense.

7. See Maloney and McCormick |1989~ for a more complete description and analysis of the scheme.

8. The Clemson University Athletic Department made these data available to us.

9. These data were obtained from D&B--Donnelley Demographics, Donnelley Marketing Information Services, Dun & Bradstreet Corp., Stamford, CT.

10. This technique naturally is inaccurate. We compute the straightline distance. Roads are seldom so agreeable. Moreover, over long distances, the great globe technique of travel is appropriate. We eschew this more complicated algorithm on the grounds that road curvature did not warrant the extra precision afforded by spherical trigonometry.

11. Our method of calculating travel costs is quite similar to that used in the recreational demand literature. For further discussion of the travel costs facing demanders of distant goods see Morey |1981~ and Morey, Shaw, and Rowe |1991~.

12. The income data are not available for all zip codes, and, hence, in Table II the sample size is reduced for the cost of travel time and the full price of season tickets in both years.

13. The |R.sup.2~s cannot be compared directly. We use the log model parameter estimates to forecast the dependent variable and compute |R.sup.2~ from this.

14. For a general discussion of multi-part tariffs, see Oi |1971~. For a more detailed discussion on this particular point see Maloney and McCormick |1989~.

15. As an alternative measure of intensity, we compute the number of season ticket purchasers per Clemson alumnus. However, the alumni data are only available at the county level of aggregation. Estimates of the demand function using this alternative measure of intensity are similar to the ones we report, and they are available from us.

16. Recall that there were five home games in 1986 but eight in 1987. Moreover, in even-numbered years, the home schedule features games with the three biggest long-term rivals. In odd-numbered years, there are no rival games at home.

17. All variables in Table IV are measured in logs. We also estimate the equation in levels. The levels estimates support the theory, but we deem them inferior to the log versions on the basis of goodness of fit. They can be obtained from us.

18. One interpretation of this variable is a selection effect. Buyers from regions with a small Clemson following are by definition intense demanders, and this is revealed in the negative sign. When these people buy at all, they buy good tickets. While this variable acts as a control, some might argue that the quality-distance tradeoff is only a selection effect. However, demand for quantity and quality are not necessarily linked. Big eaters are rarely gourmets. In its purest form, the theorem predicts that as people travel farther, they choose less quantity and more quality. Empirically this is exactly what we find.

19. Since quality cannot be negative, ordinary-least-squares estimates of the quality equation stand to be inefficient. The data are censored at zero. Maximum likelihood estimates of the quality equation compare with the results in Table IV.

20. Consider two brands of whiskey--six-year-old Scotch and twelve-year-old Scotch--that are relatively close substitutes. Suppose a tax is imposed on whiskey regardless of its quality. The price level of both Scotches will increase, but the relative price of the more expensive, longer-aged variety will decline relative to the lower-quality six-year-old swill. By the first law of demand, the overall consumption of whiskey will decline, but this, by itself, does not imply that the amounts consumed of both grades separately will decrease. If the substitution effect of the relative price decline between high and low grade dominates the own-price effect, the consumption of the high-quality, longer-aged whiskey can increase. See Silberberg |1990, 388-89~ for the proof of this proposition.

Regulation implies high prices, competition low ones. The higher prices of regulation are, under the appropriate assumptions, the analogue to the fixed transportation charges in the theorem. Thus, demanders seek lower quality under competition than they desired under regulation. It can be shown that the relative price of high quality declines when an industry shifts from competitive to monopoly pricing.

REFERENCES

Alchian, Armen, and William Allen. University Economics. Belmont, CA: Wadsworth Publishing Co., 1964.

Becker, Gary. Economic Theory. New York: Alfred Knopf, 1971.

Borcherding, Thomas E., and Eugene Silberberg. "Shipping the Good Apples Out: The Alchian and Allen Theorem Reconsidered." Journal of Political Economy, February 1978, 131-38.

Cowen, Tyler, Alex Taborrok, and Mark Poitras. "Good Grapes and Bad Lobsters: The Alchian and Allen Theorem Revisited." Working paper, George Mason University, 1990.

Gould, John P., and Joel Segall. "The Substitution Effects of Transportation Costs." Journal of Political Economy, January/February 1969, 130-37.

Kaempfer, William H., and Raymond T. Brastow. "The Effect of Unit Fees on the Consumption of Quality." Economic Inquiry, April 1985, 341-48.

Lancaster, Kelvin. Consumer Demand: A New Approach. New York: Columbia University Press, 1971.

Maloney, Michael T., and Robert McCormick. "Block Pricing and the Distribution of Demand." Working paper, Clemson University, 1989.

Morey, Edward R. "The Demand for Site-Specific Recreational Activities: A Characteristics Approach." Journal of Environmental Economics and Management, December 1981, 345-71.

Morey, Edward R., W. Douglas Shaw, and Robert D. Rowe. "A Discrete-Choice Model of Recreational Participation, Site Choice, and Activity Valuation When Complete Trip Data Are Not Available." Journal of Environmental Economics and Management, March 1991, 181-201.

Oi, Walter. "A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly." Quarterly Journal of Economics, February 1971, 77-96.

Silberberg, Eugene. The Structure of Economics: A Mathematical Analysis, 2d ed. New York: McGraw-Hill, 1990.

Umbeck, John R. "Shipping the Good Apples Out: Some Ambiguities in the Interpretation of 'Fixed Charge'." Journal of Political Economy, February 1980, 199-208.

Umbeck, John R., and Michael Staten. "Shipping the Good Students Out: The Effect of a Fixed Charge on Student Enrollments." Journal of Economic Education, Spring 1989, 165-71.

The Alchian and Allen theorem first appeared in writing more than twenty-five years ago in University Economics. Since then the theorem has grown to be standard pedagogy in many microtheory courses and the topic of several clarifying journal articles.(1) Despite the widespread use of the theorem, little scientific evidence has been brought to bear on its validity.(2) Perhaps this is due to the fact that the result is so transparent and intuitively pleasing that hardly anyone requires evidence on the subject. Furthermore, there are a large number of ad hoc examples of the principle in practice. And finally, the very nature of the proposition makes it difficult to test directly. We have overcome the last hurdle with an unusual dataset, and thus we are now in position to subject the theorem to a systematic examination.

We have acquired data on all season ticket purchases to Clemson University home football games for the 1986 and 1987 seasons. This encompasses 23,440 buyers of 95,958 tickets. We can identify the name and address of each purchaser along with the quantity and quality of tickets bought. This allows us to inquire whether those individuals traveling farther choose to purchase higher-quality tickets.

The paper proceeds as follows. In the next section we briefly summarize and criticize the literature on the Alchian and Allen theorem. After that we describe our data and present a test of the proposition. We close with a summary and conclusions.

II. THE LITERATURE

Alchian and Allen first presented their analysis in 1964:(3)

Suppose that grapes are grown in California and that it costs 5 cents a pound to ship grapes to New York whether the grapes are "choice" or "standard" (poorer) and that the total production of grapes is 50 percent "choice" and 50 percent "standard." Suppose further that in California the "choice" grapes sell for 10 cents a pound and the standard for 5 cents a pound; that is in California 2 pounds of "standard" and 1 pound of "choice" grapes sell for the same price. If grapes are shipped to New York, the shipping costs will raise the costs of "choice" grapes to 15 cents and of "standard" grapes to 10 cents. In New York the costs of "choice" grapes are lower relative to "standard" grapes (1.5 to 1) than in California (2 to 1). To buy 1 pound of "choice" grapes in New York would mean a sacrifice of 1.5 pounds of "standard" whereas in California it would cost 2 pounds of "standard." According to our law of demand, New Yorkers faced with a lower price of "choice" grapes relative to "standard" will consume relatively more "choice" grapes than Californians will. In California where "standard" grapes are cheaper relative to "choice" grapes a larger fraction of "standard" grapes will be consumed--and this is what actually happens.

Since the succinct original statement of the transportation cost theorem several others have offered remarks attempting to clarify, extend, and even correct the analysis. First, Gould and Segall |1969~ introduced a third good into the analysis in an attempt to demonstrate that the theory does not hold in general. Borcherding and Silberberg |1978~ pointed out that Gould and Segall's comment, though technically correct, was misleading and that the nature of substitution effects probably made the theorem hold. Umbeck |1980~ clarified the conditions necessary for the proposition to hold, specifically that the transportation or fixed charges had to be non-productive, that is, yielding no utility in and of themselves. According to his argument, meat consumed in a restaurant will not be higher in quality than meat consumed at home because of the services supplied by a waiter, because table-busing charges are neither fixed nor unproductive.(4)

Besides their comment on Gould and Segall's point, Borcherding and Silberberg point out that transportation can be undertaken by the consumer as well as the producer. In their example, tourists visiting Boston eat better lobster than the locals. In this analogy, the transportation undertaken by the consumer must be an unproductive and fixed charge in the Umbeck sense. However, transportation of people to lobsters, on the one hand, and lobsters to people, on the other, is different. When a lobster is shipped, the transportation charge is bundled with the quality charge. But, when the consumer travels, transportation and quality are purchased sequentially, not bundled as in the first case. This raises the theoretical sticking point of whether rational consumers will ignore the sunk costs of travel at the moment they make the quality choice.(5)

Consider the example of the husband and wife who travel from Chicago to Miami for a vacation cruise through the Caribbean. One might be tempted to argue that once they arrive at the dock, the air and cab fares, tips, and time cost of travel are sunk. Thus, when choosing between the first-class staterooms and the inside, low-deck steerage with upper and lower berths, the couple will ignore the costs of travel and make their decision based solely on relative prices posted by the cruise liner.

This approach fails to incorporate the fundamental insight provided by Becker |1971~ and Lancaster |1971~ in their renovation of consumer theory. In the modern theory of consumer behavior, consumers do not demand goods, but instead goods are inputs used with time and human capital in the production of commodities that directly enter the consumer's preference function. In this view, people do not buy airplane tickets, cab rides, and staterooms in cruise ships; they go on vacation. The whole trip, in their eyes and in their economic calculation, is one thing comprising many inputs. Thus, the Becker-Lancaster approach says that consumers make their choices bundled, and the larger the travel component, the lower the relative cost of high-quality staterooms.

When the couple from Chicago plans a Caribbean cruise vacation, there are no fixed costs. The couple sees the travel costs as a component of the overall vacation. That is, rational consumers have foresight. For the sake of pedagogy, let the first-class stateroom cost $8000 per week while the inside, low-deck berth is only $2000 per week. The relative price of quality at the dock is four. But from the point of view of the couple still in Chicago, air travel to Miami adds $1000 to the price of either ship accommodation, reducing the price of high quality to three. This makes the couple more inclined to high-quality accommodations, ceteris paribus. Suppose they decide to travel first-class while on the boat. They will choose other accommodations to match this decision. If they were to divert to cheaper, less luxurious quarters when they arrive in Miami, the bundle of other goods already purchased or contracted for would be inefficient in producing the pre-designed vacation. The marginal products of the household production inputs, relative to their prices, would no longer be equal across all inputs. Thus, in the household production framework, the couple will not change rooms.

The consumer's utility function is determined not by the goods, x, consumed, but rather by the flow of services, z, yielded by the goods and the time, t, necessary to convert the goods into services. Each of the zs, say |z.sub.i~, is produced by a set of goods, |x.sub.i~, and times, |t.sub.i~. So |z.sub.i~ is the ith service and |x.sub.i~ is a vector of n goods used in the production of |z.sub.i~. Also |t.sub.i~ is a vector of various amounts of time used in the production of |z.sub.i~. In sum:

|z.sub.i~ = |z.sub.i~(|x.sub.i~, |t.sub.i~).

In the case at hand, |x.sub.h~ and |x.sub.l~ are two inputs of the same basic type but different quality, two varieties of staterooms if you will. When planning the vacation, efficiency requires that

(|Delta~|z.sub.i~ / |Delta~|x.sub.i~) / (|Delta~|z.sub.i~ / |Delta~|x.sub.j~) = |p.sub.i~/|p.sub.j~

for all i and j where |p.sub.i~ is the price of the ith consumer input. Suppose some inputs are purchased sequentially, first one then another. For instance, air travel must be purchased before meals and lodging. Then, for the optimal vacation, the consumer must forecast or plan the quality and quantity levels of all the other inputs to assure the necessary equilibrium condition. Thus, having made the basic vacation decision, the choice of room quality, having already traveled to the vacation site, remains relevant. Borcherding and Silberberg's insight that the Alchian and Allen theorem holds for travelers as well as shipped goods is on a firm theoretical foundation.(6)

In spite of all the theoretical inquiry into the topic, the empirical validity of the Alchian and Allen theorem rests primarily on a large volume of anecdotes and ad hoc evidence. Therein lies the point of our paper. We have acquired an unusual set of data through which we can identify, at the customer level the quantity and quality purchased and the distance traveled. Moreover, in the case at hand, the consumers travel to the market. This allows, in our eyes, the nearly perfect experimental setting to test the travel cost theorem. That is where we now turn our attention.

III. THE EMPIRICAL ANALYSIS

Clemson University plays several football games at home each fall. The seats to view these games are sold via a complicated two-part pricing scheme.(7) Consumers must pay a fixed fee to obtain the right to buy season tickets. A variety of fixed-fee plans are available to customers. Over the period of our data, there were six different quality categories ranging in price from a low of $30 to a high of $2000. Table I reports the distribution of demand across the six quality categories. Category III is the largest with 27 percent of the total. The distribution of fees paid is skewed toward the high-quality classes.

Associated with each fixed-fee category is a package of goods. The fixed fees do not include the prices of the season tickets themselves, which cost approximately $100 apiece. In category I at the bottom of the quality spectrum, two end-zone tickets and little else are available. As the fee increases, so does quality. The purchaser gets better football tickets, closer to mid-field, high or low, depending on preference. The higher the fixed fee, the greater accommodation to such requests. In addition, reserved parking is available, with larger payments getting the prime slots. In the highest categories, buyers can group large numbers of tickets together, an option unavailable in the low categories. For instance, in category V, eight tickets can be purchased together at the fixed fee of $1000. Alternatively, eight tickets can be purchased in pairs by paying the category I fee four times for a total fixed-fee payment of only $120. However, when a single buyer chooses this option, the eight category I tickets are spread throughout the stadium in pairs. Category III purchasers have the option of four tickets together, category IV can get six en masse, and so on. The maximum number of tickets that can be grouped together is ten in category VI. Other perquisites are also available as the buyer moves to higher categories, but the primary quality distinction involves the location of seats in the stadium, the number of seats together, and the proximity and number of reserved parking slots. Choosing to pay a high fixed fee is choosing a high-quality football experience.

We have data on all season ticket purchasers for the 1986 and 1987 years.(8) We know the fixed-fee level chosen and the number of years that each buyer has previously bought tickets. In addition, we know the address of each purchaser and the number of tickets bought. For each zip code we have the Census Bureau estimates of population and income per capita.(9) The latitude and longitude of each zip code are used to compute the distance between the buyer and the football stadium.(10) Table II reports some summary statistics on our data base. The average fan paid a fixed fee of about $340 for the right to buy season tickets and then bought around four. This corresponds to a modal fan in the level III category who gives $250 and buys four tickets.

TABLE I Quality Categories Category Fixed Number of Demanders Fee 1986 1987 I $ 30 2239 2542 II 100 3204 3520 III 250 3280 3769 IV 500 2041 2443 V 1000 1018 1325 VI 2000 409 539

The full unit-price of these tickets includes their face value, the value of the time to travel to the stadium, and the direct expenses of traveling. We estimate these in the following way. Assume the fan travels to the games via car, at an average speed of 50 miles per hour. In addition, assume that the cost per mile driven is $.20. To compute the hourly value of time, take the zip-code-average, annual income per capita and divide it by 2000 (40 hours per week times 50 weeks per year). For our sample, this gives an average distance of around 100 miles and an average cost of travel time of $35 one way.

Thus, in addition to the money price of the ticket, the full price includes the two parts of travel costs, that is, (i) two times the distance between home and the stadium, divided by 50, times the individual's hourly income, plus (ii) the distance times .2. For the season ticket package then, the full season price, |p.sub.ij~, for the ith buyer in the jth year is

|n.sub.j~ |center dot~ 2 |center dot~ |(|D.sub.i~/50) |center dot~ |w.sub.ij~ + .2 |center dot~ |D.sub.i~~ + |n.sub.j~ |center dot~ |t.sub.j~,

where |n.sub.j~ is the number of games in the jth season, |D.sub.i~ is the distance between the stadium and home of the ith person, |w.sub.ij~ is the hourly income of the ith person in the jth year, and |t.sub.j~ is the money price of tickets in the jth year.(11) The full unit-price of a ticket averaged $407 in 1986 and $751 in 1987, the primary difference being the number of home games (eight in 1987).(12)

We subject these data to two inquiries. By the first law of demand, since the travel component of cost is higher, we expect that fans living farther away will buy fewer tickets. By the Alchian and Allen theorem, as transportation costs increase, the relative price of high quality declines. Accordingly, our second proposition is that consumers of football tickets will purchase higher-quality tickets the farther they live from the stadium. Indeed the Alchian and Allen theorem is a joint hypothesis: travel costs reduce quantity, TABULAR DATA OMITTED holding quality constant, and increase quality, holding quantity constant.

Our first statistical test estimates the demand for tickets as a function of the full price, income, number of consecutive years purchasing, population density, intensity of demand, the number of home games per season (five in 1986 or eight in 1987), and the quality category chosen (measured by the fixed fee paid). These are all self explanatory except for intensity. To measure intensity, we computed the total number of buyers in each zip code and then normalized it by the population of that zip code. There are two countervailing forces at work here. When the density of buyers is high, acquiring tickets from friends or neighbors is easier; therefore, the demand to buy season tickets from the original source is lower. At the same time, when the density of buyers is high, there is a commonality of interests that may increase demand via shared consumption, a synergy effect. We do not guess which effect dominates.

The ordinary-least-squares estimates of the quantity equation are reported in Table III. The top half of the table uses the logs of the variables, while the lower portion uses the levels. Overall, both specifications have their strong points, but the log model explains a greater portion of the variation in the dependent variable.(13) Since quantity and quality are jointly determined, ordinary-least-squares estimation of either may be biased. We jointly estimated the quantity and quality equations using the technique of three-stage-least squares, but the differences are so slight as to be ignored.

TABLE III The Demand for Tickets DEPENDENT VARIABLE: Number of Tickets Purchased LOGS F=2256.1 |R.sup.2~ = 0.4026 Sample Size = 23,440 Parameter t ratio Intercept .3853 3.375 Full Price -.0110 -2.139 Income per capita -.0484 -3.693 Number of Years Purchasing .0236 6.439 Population Density .0065 2.519 Intensity .0066 2.436 Number of Home Games -.1232 -10.056 Quality Category ($) .2752 122.046 LEVELS F=972.79 |R.sup.2~ = 0.2252 Sample Size = 23,440 Intercept 3.0758 36.027 Full Price (x1000) -.0831 -4.436 Income per capita (x1000) -.0067 -1.776 Number of Years Purchasing .0067 4.589 Population Density (x1000) .0130 2.263 Intensity -15.1882 -5.258 Number of Home Games -.0811 -7.732 Quality Category ($) .0032 79.871

The demand for tickets succumbs to the first law; the coefficient is significant at the 2 percent level in the log specification and at the .1 percent level in the linear specification. We note that demand is quite price inelastic and that income and quantity are negatively linked. The magnitude and sign of these elasticities are tied to the two-part pricing scheme.(14) The longer buyers have been purchasing, the more tickets they buy. Densely populated areas have larger demand, ceteris paribus. The evidence on intensity of demanders, that is, areas with many buyers, is specification dependent. In the levels version, the number of buyers in the area who purchase tickets is linked with smaller number of tickets purchased by any one buyer. In the log model, however, this result reverses, begging further inquiry.(15) Consumption is lower when there are more home games.(16) Also note that these results are not driven by the difference in the number of home games in each season; the results replicate for each year cross sectionally. Finally, fans who purchase high quality also buy many tickets.

A Direct Test of the Alchian and Allen Theorem

To investigate the main thesis of the Alchian and Allen theorem, we estimate a model of quality choice. We assume that the quality category chosen depends on income, the number of tickets purchased, the number of consecutive years purchasing, population density in the local neighborhood, the same measure of intensity as before (the relative portion of the local population who also purchase tickets), and number of home games (which is perfectly collinear with year). We explore the Alchian and Allen thesis by including the transportation costs paid by the buyers. Table IV reports the ordinary-least-squares estimates of the quality equation for six different specifications using two different measures of travel costs--the one-way distance traveled and the one-way time cost of traveling.(17)

The results conform to the predictions of the theorem. The farther fans travel, the higher the quality category they choose. We discuss the dimensions of the transportation cost theorem in more detail after we review the estimates of the other coefficients. We find that quality is a normal good; recall that quantity and income were negatively related. Furthermore, the quality of tickets purchased and the number bought are positively associated. We attribute these effects to the two-part pricing scheme in place. People who have bought for many years consecutively buy better tickets. Population density and quality are negatively linked. The intensity variable also has a negative coefficient. When people have many neighbors who also buy tickets, they tend to buy lower-quality ones themselves.(18) Buyers choose better tickets when there are more home games, and most importantly, whether measured in distance traveled or the income cost of travel time, the more distant buyers choose better tickets.

The results reported in the first column of Table IV support the theorem. Our evidence is not the result of a peculiarity of either season; the results hold for the two years separately. However, there are reasons to believe that these estimates are imprecise. First, a few buyers live a long way from the stadium, too far to believe that they travel by car; one buyer lives in Pearl City, Hawaii. To investigate the seriousness of this problem we delete from the sample all buyers living more than 500 miles from the stadium. This eliminates 356 purchasers (1.5 percent) over the two-year period. Then we reestimate the quality model. These results are reported in the second column of Table IV. Deleting the buyers who must travel extreme distances may improve the estimates, as their travel costs are harder to estimate. In addition, these people may be buying tickets to give them away.

TABULAR DATA OMITTED

One other possibility worth pursuing is that some buyers, those with very intense demand, have permanently relocated near the stadium because of their desired consumption. If this is true, then these individuals will buy the best tickets, although they live close to the stadium, and our distance measure does not accurately reflect their true travel costs. For these people, transportation costs involve lost consumption opportunities at their alternative location, for now they either forego the amenities they would enjoy at the next best homesite or they must travel to those markets. In effect, some people living close by may have high transportation costs disguised by their location. To eliminate this potential source of bias, we constructed a second reduced sample, first deleting those people living more than 500 miles away, and, second, arbitrarily omitting those who live in Clemson or within 15 miles. This second cut eliminates 2224 more buyers over two years, reducing the sample size to 20,860. The results of estimating the quality equation over this sample are reported in the third column of Table IV. Here the impact of distance on quality chosen is estimated to be substantially higher than in the other samples. We interpret this to mean that some close-in buyers would actually live elsewhere were it not for the opportunity to enjoy football and the associated activities. In sum, we believe that the estimates in the third column of Table IV are probably the most accurate.(19)

One way to assess the economic magnitude of the Alchian and Allen theorem applied in this context is to consider the predicted behavior of a person who moves. Using these last estimates (from the truncated sample), we can forecast the impact of distance on quality. The average buyer in our reduced sample lives 94.5 miles from the stadium. The standard deviation is 73.4 miles. Assume a buyer, living one standard deviation below the mean, moves one standard deviation past the mean--from 21.1 miles away to 167.9 miles away, a 696 percent increase. The estimated distance elasticity of quality is 0.085. Thus, this move would be associated with a .085 |center dot~ 6.96 = 59.2 percent increase in fixed fees paid. The mode fee paid is $250. The increase in expenditures on quality is estimated to be $148 per consumer per year, from $250 to $398. Alternatively, think of the problem this way. Clemson University is located in the northwest corner of South Carolina, approximately 250 miles from the coast. Our model says that if a football fan living just outside Clemson and buying tickets in the level III category ($250) moves to Charleston, which is on the coast, he will double his choice of quality and jump from level III to level IV.

In our minds, this evidence, based on a large sample, is very nearly the perfect experimental setting to test the Alchian and Allen theorem. And it is so: the good tickets are shipped out.

IV. CONCLUSIONS

The subject of considerable theoretical debate as to its economic content, the insightful application of the first law of demand to quality proposed by Alchian and Allen has been widely accepted in the profession. Many examples of the principle in practice have worked their way into our oral tradition. Using season ticket sales to Clemson University home football games, we have put the principle to the test, and it performs well.

We find that fans who travel the farthest, choose to buy the best tickets. This confirms the theorem as well as the conjecture of Borcherding and Silberberg who say that "it does not matter if the goods are shipped to the consumers or the consumers are shipped to the goods." This suggests that the wide variety of ad hoc versions of the theorem--that couples hiring babysitters will enjoy nicer restaurants; that tourists will choose more elegant rooms the farther they travel; that out-of-towners will select the best theater seats; that cigarettes tend to be made of better grades of tobacco as taxes increase; and that more motorists choose premium gasoline over regular as the tax per gallon increases--are all sound pedagogical devices that would withstand systematic analysis were they so tested.

The Alchian and Allen theorem consistently provides a theoretical explanation for apparently anomalous behavior. Consider the following two cases. There is casual evidence that the consumption of certain brands of whiskey increases when liquor taxes go up. And, it appears that the quality of telephone service is now lower with deregulation and competition than it was in the regulated monopoly period. The theorem explains both outcomes without resort to public choice theory.(20) In our minds, the Alchian and Allen theorem is one of those rare insights, simple on the surface, yet, in application, so full of fury that we are inclined to label it the third law of demand.

1. See Gould and Segall |1969~, Borcherding and Silberberg |1978~, and Umbeck |1980~.

2. There are at least two papers with empirical content: Kaempfer and Brastow |1985~ and Umbeck and Staten |1989~. See also Cowen, Taborrok, and Poitras |1990~.

3. Alchian and Allen |1964, 75~.

4. For a broad discussion of this literature, see Silberberg |1990, 385-89~. In addition, Kaempfer and Brastow |1985~ argue that in the case of unit consumption, such as a parking lot, the imposition of a fixed fee does not alter relative prices.

5. Cowen, Taborrok, and Poitras |1990~ contend that since shipping fees amount to a sunk cost, when customers travel to the market, the proposition does not work, for consumers will (rationally) ignore the past cost of transportation.

6. The point is easy to see in the context of capital budgeting. A firm is constructing a new corporate headquarters. After the foundation is laid, the structural steel and concrete are in place, the marble facade has been added, and the fine wood paneling nailed to the walls, the firm does not install cheap indoor-outdoor carpeting in the executive suite, thinking to itself, those previous expenditures are now sunk and should be ignored. Since the structure was built to generate cash flows, the components must work together in a matching fashion. We contend that consumer expenditures are the same. People go on vacation, not only to enjoy the moment, but, as Jimmy Buffet has been known to croon, for the stories they can tell. Vacations produce value in the future, and no matter whether we examine the expenditures at the beginning, looking forward, or at the end, via retrospect, the bundle of goods creates the experience and, hence, they must match in the quality sense.

7. See Maloney and McCormick |1989~ for a more complete description and analysis of the scheme.

8. The Clemson University Athletic Department made these data available to us.

9. These data were obtained from D&B--Donnelley Demographics, Donnelley Marketing Information Services, Dun & Bradstreet Corp., Stamford, CT.

10. This technique naturally is inaccurate. We compute the straightline distance. Roads are seldom so agreeable. Moreover, over long distances, the great globe technique of travel is appropriate. We eschew this more complicated algorithm on the grounds that road curvature did not warrant the extra precision afforded by spherical trigonometry.

11. Our method of calculating travel costs is quite similar to that used in the recreational demand literature. For further discussion of the travel costs facing demanders of distant goods see Morey |1981~ and Morey, Shaw, and Rowe |1991~.

12. The income data are not available for all zip codes, and, hence, in Table II the sample size is reduced for the cost of travel time and the full price of season tickets in both years.

13. The |R.sup.2~s cannot be compared directly. We use the log model parameter estimates to forecast the dependent variable and compute |R.sup.2~ from this.

14. For a general discussion of multi-part tariffs, see Oi |1971~. For a more detailed discussion on this particular point see Maloney and McCormick |1989~.

15. As an alternative measure of intensity, we compute the number of season ticket purchasers per Clemson alumnus. However, the alumni data are only available at the county level of aggregation. Estimates of the demand function using this alternative measure of intensity are similar to the ones we report, and they are available from us.

16. Recall that there were five home games in 1986 but eight in 1987. Moreover, in even-numbered years, the home schedule features games with the three biggest long-term rivals. In odd-numbered years, there are no rival games at home.

17. All variables in Table IV are measured in logs. We also estimate the equation in levels. The levels estimates support the theory, but we deem them inferior to the log versions on the basis of goodness of fit. They can be obtained from us.

18. One interpretation of this variable is a selection effect. Buyers from regions with a small Clemson following are by definition intense demanders, and this is revealed in the negative sign. When these people buy at all, they buy good tickets. While this variable acts as a control, some might argue that the quality-distance tradeoff is only a selection effect. However, demand for quantity and quality are not necessarily linked. Big eaters are rarely gourmets. In its purest form, the theorem predicts that as people travel farther, they choose less quantity and more quality. Empirically this is exactly what we find.

19. Since quality cannot be negative, ordinary-least-squares estimates of the quality equation stand to be inefficient. The data are censored at zero. Maximum likelihood estimates of the quality equation compare with the results in Table IV.

20. Consider two brands of whiskey--six-year-old Scotch and twelve-year-old Scotch--that are relatively close substitutes. Suppose a tax is imposed on whiskey regardless of its quality. The price level of both Scotches will increase, but the relative price of the more expensive, longer-aged variety will decline relative to the lower-quality six-year-old swill. By the first law of demand, the overall consumption of whiskey will decline, but this, by itself, does not imply that the amounts consumed of both grades separately will decrease. If the substitution effect of the relative price decline between high and low grade dominates the own-price effect, the consumption of the high-quality, longer-aged whiskey can increase. See Silberberg |1990, 388-89~ for the proof of this proposition.

Regulation implies high prices, competition low ones. The higher prices of regulation are, under the appropriate assumptions, the analogue to the fixed transportation charges in the theorem. Thus, demanders seek lower quality under competition than they desired under regulation. It can be shown that the relative price of high quality declines when an industry shifts from competitive to monopoly pricing.

REFERENCES

Alchian, Armen, and William Allen. University Economics. Belmont, CA: Wadsworth Publishing Co., 1964.

Becker, Gary. Economic Theory. New York: Alfred Knopf, 1971.

Borcherding, Thomas E., and Eugene Silberberg. "Shipping the Good Apples Out: The Alchian and Allen Theorem Reconsidered." Journal of Political Economy, February 1978, 131-38.

Cowen, Tyler, Alex Taborrok, and Mark Poitras. "Good Grapes and Bad Lobsters: The Alchian and Allen Theorem Revisited." Working paper, George Mason University, 1990.

Gould, John P., and Joel Segall. "The Substitution Effects of Transportation Costs." Journal of Political Economy, January/February 1969, 130-37.

Kaempfer, William H., and Raymond T. Brastow. "The Effect of Unit Fees on the Consumption of Quality." Economic Inquiry, April 1985, 341-48.

Lancaster, Kelvin. Consumer Demand: A New Approach. New York: Columbia University Press, 1971.

Maloney, Michael T., and Robert McCormick. "Block Pricing and the Distribution of Demand." Working paper, Clemson University, 1989.

Morey, Edward R. "The Demand for Site-Specific Recreational Activities: A Characteristics Approach." Journal of Environmental Economics and Management, December 1981, 345-71.

Morey, Edward R., W. Douglas Shaw, and Robert D. Rowe. "A Discrete-Choice Model of Recreational Participation, Site Choice, and Activity Valuation When Complete Trip Data Are Not Available." Journal of Environmental Economics and Management, March 1991, 181-201.

Oi, Walter. "A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly." Quarterly Journal of Economics, February 1971, 77-96.

Silberberg, Eugene. The Structure of Economics: A Mathematical Analysis, 2d ed. New York: McGraw-Hill, 1990.

Umbeck, John R. "Shipping the Good Apples Out: Some Ambiguities in the Interpretation of 'Fixed Charge'." Journal of Political Economy, February 1980, 199-208.

Umbeck, John R., and Michael Staten. "Shipping the Good Students Out: The Effect of a Fixed Charge on Student Enrollments." Journal of Economic Education, Spring 1989, 165-71.

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Title Annotation: | Armen Alchian and William Allen |
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Author: | Bertonazzi, Eric P.; Maloney, Michael T.; McCormick, Robert E. |

Publication: | Economic Inquiry |

Date: | Jul 1, 1993 |

Words: | 5552 |

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