Monopolists that advertise with recyclable free samples: beware of professors selling gifts?I. Introduction Publishers of college textbooks face an interesting dilemma. To increase sales, publishers give professors free examination copies of textbooks, but many of these books will be sold to secondhand book buyers. These former examination copies compete against the publishers' product. Claiming the sale of examination copies forces them to charge higher prices, several companies print warnings on their examination copies urging professors not to sell their free books. For example, McGraw-Hill examination copies state "the selling of free textbooks contributes to higher book prices to students and denies authors their royalties." The model presented in this paper shows publishers reduce prices if a larger percentage of examination copies are resold as used books. Used books are substitutes for new textbooks, and if the supply of used books increases, a publisher must lower its price to meet the competition. Attempts by colleges, academic departments, or faculty to reduce the number of examination copies recycled as used books leads to higher, not lower, textbook prices for students. II. The Economic Intuition intuition, in philosophy, way of knowing directly; immediate apprehension. The Greeks understood intuition to be the grasp of universal principles by the intelligence (nous), as distinguished from the fleeting impressions of the senses. Behind the Model Free examination copies act like advertising. Publishers recognize complementary copies increases demand, and makes demand less elastic elastic Of or relating to the demand for a good or service when the quantity purchased varies significantly in response to price changes in the good or service. . Using Nelson's jargon jargon, pejorative term applied to speech or writing that is considered meaningless, unintelligible, or ugly. In one sense the term is applied to the special language of a profession, which may be unnecessarily complicated, e.g., "medical jargon. |7~, textbooks have search and experience characteristics. By providing free examination copies, publishers reduce the search cost in selecting a book, and increase the probability their text will be chosen. Brand loyalty to a given text is established after the book has been successfully used in class. Publishers combat brand loyalty with free examination copies. While free examination copies advertise the publisher's product, they can be recycled as used books which directly compete against the publisher's output. Friedman |3~, Gaskins gas·kin n. 1. The part of the hind leg of a horse or related animal between the stifle and the hock. 2. gaskins Obsolete Galligaskins. [Probably short for galligaskins.] |4~, Swan |9~, and Martin |5~ have analyzed an·a·lyze tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es 1. To examine methodically by separating into parts and studying their interrelations. 2. Chemistry To make a chemical analysis of. 3. the effect of recycling recycling, the process of recovering and reusing waste products—from household use, manufacturing, agriculture, and business—and thereby reducing their burden on the environment. on a monopolist that produces a durable, recyclable re·cy·cle tr.v. re·cy·cled, re·cy·cling, re·cy·cles 1. To put or pass through a cycle again, as for further treatment. 2. To start a different cycle in. 3. a. product. Friedman |3, 278-79~ argues the presence of a competitive recycling industry forces the monopolist to behave like a perfectly competitive firm, and the monopolist charges a price equal to the marginal cost Marginal cost The increase or decrease in a firm's total cost of production as a result of changing production by one unit. marginal cost The additional cost needed to produce or purchase one more unit of a good or service. of its output. Gaskins reaches the opposite conclusion as he shows a competitive second-hand market does not lower the monopolist's long-run price and "it makes things worse in the short-run |4, 255~." Swan offers some support for Friedman's views as he finds conditions where a competitive second-hand market results in the monopolist charging a price equal to its marginal cost. Martin analyzes five different cases, and although he finds consumers always benefit from the existence of an independent recycling sector, he also concludes the monopolist always earns economic profits. He finds "monopoly rents are reduced by technological improvement in scrap recovery and scrap conversion |5, 412~." If a greater percentage of free examination copies are sold to second-hand book buyers, the supply of used textbooks increases. This is similar to an improvement in scrap recovery. As more professors sell their examination copies, publisher's profits decline; it is not surprising publishers discourage the resale of their examination copies. The interaction between the new and second-hand book markets has not been ignored by economists. Miller |6~ investigated whether a monopolist publishes a new edition only to destroy the competition from used books. However, his results were inconclusive INCONCLUSIVE. What does not put an end to a thing. Inconclusive presumptions are those which may be overcome by opposing proof; for example, the law presumes that he who possesses personal property is the owner of it, but evidence is allowed to contradict this presumption, and show who is . III. The Model Publishers sell highly differentiated products, and they are modeled as firms with market power. The firm is assumed to be a price-setting monopolist that sets the price of the textbook and sells whatever quantity is demanded at that price. The dynamic model we employ has two periods. Only new textbooks are sold during the first period. However, students buy either new or used textbooks during the second period. Used textbooks come from two different sources. Some new textbooks bought in the first period are resold as used books in the second period as are some of the former examination copies. The market for the current textbook is destroyed at the end of the second period when the publisher markets a new edition. Because institutional restrictions or menu costs prohibit pro·hib·it tr.v. pro·hib·it·ed, pro·hib·it·ing, pro·hib·its 1. To forbid by authority: Smoking is prohibited in most theaters. See Synonyms at forbid. 2. price changes, the publisher charges the same price in both periods. Since used books experience some wear and tear, they are sold at a lower price than new books. The model assumes enough students view used and new textbooks as acceptable substitutes so that all second-hand books are sold. The demand for the higher priced new textbooks is the difference between the total demand for textbooks and the supply of used books. Let |Q.sub.1~ = |Q.sub.1~(P, Y) and |Q.sub.2~ = |Q.sub.2~(P, Y) denote de·note tr.v. de·not·ed, de·not·ing, de·notes 1. To mark; indicate: a frown that denoted increasing impatience. 2. the demand for textbooks in period 1 and period 2, respectively. The quantity of books demanded each period is negatively related to P, the price the publisher charges in both periods, and positively related to Y, the amount of free examination copies issued in period 1. These assumptions imply |Delta~|Q.sub.i~/|Delta~P |is less than~ 0 and |Delta~|Q.sub.i~/|Delta~Y |is greater than~ 0 for i = 1, 2. To simplify the comparative statics Comparative statics is the comparison of two different equilibrium states, before and after a change in some underlying exogenous parameter. As a study of statics it compares two different unchanging points, after they have changed. , we assume the demand curves in both periods are linear or ||Delta~.sup.2~|Q.sub.i~/|Delta~|P.sup.2~ = 0 for i = 1, 2. We also assume free examination copies shift each period's demand curve parallel to the right. This implies ||Delta~.sup.2~|Q.sub.i~/|Delta~P|Delta~Y = 0 for i = 1, 2. In addition, diminishing returns to advertising is assumed as subsequent increases in quantity demanded becomes smaller as the number of free examination copies given away increases or ||Delta~.sup.2~|Q.sub.i~/|Delta~|Y.sup.2~ |is less than~ 0 for i = 1, 2. The publisher maximizes the discounted stream of profits from both periods. At the beginning of period 1, the monopolist must choose a level of P and Y that maximizes the following objective function: |Pi~(P,Y)=P|Q.sub.1~(P,Y) - c|Q.sub.1~(P,Y) - cY + (P - c)||Q.sub.2~(P,Y) - |Lambda~|Q.sub.1~(P,Y) - |Theta~Y~/(1 + r). (1) The first three terms on the right-hand side right-hand side n → derecha right-hand side right n → rechte Seite f right-hand side n → lato destro equation (1) denotes the profits the publisher earns in period 1. The last term on the right-hand side of the above equation is the present value of the profits the publisher receives during period 2. r denotes the discount rate, |Lambda~ represents the fraction of books bought in the first period sold as used books in the second period, and |Theta~ denotes the percentage of free examination copies recycled as used books in the second period. Both the marginal cost of output and examination copies are assumed to equal c. The bracketed term on the right-hand side of equation (1) measures the new books sold during the second period after the supply of used books had been exhausted. Maximizing this objective function requires both ||Pi~.sub.P~ = |Delta~|Pi~(P,Y)/|Delta~P and ||Pi~.sub.Y~ = |Delta~|Pi~(P,Y)/ |Delta~Y to equal zero.(1) After rearranging terms, the necessary first order conditions(2) can be written as: ||Pi~.sub.P~ = (1 + r - |Lambda~)|(P - c)(|Delta~|Q.sub.1~/(|Delta~P) + |(P - c)(|Delta~|Q.sub.2~/|Delta~P) + |Q.sub.2~ - |Theta~Y = 0 (2) ||Pi~.sub.Y~ = (1 + r - |Lambda~)(P - c)(|Delta~|Q.sub.1~/|Delta~Y) + (P - c)|(|Delta~|Q.sub.2~/|Delta~Y) - |Theta~~ - c(1 + r) = 0. (3) Equation (2) implies the monopolist sets price such that the discounted marginal revenue Marginal revenue The change in total revenue as a result of producing one additional unit of output. marginal revenue The extra revenue generated by selling one additional unit of a good or service. of selling one more new book is equal to the discounted marginal cost of producing one more new book. This condition is similar to the one found by Martin |5, 409~ and Tirole |10, 80~. Equation (3) is essentially the Dorfman-Steiner |2~ condition for the optimal level of advertising intensity that equates the discounted marginal benefits of increased advertising to the discounted marginal cost of giving away one more free examination copy. The second order conditions ensure P - c |is greater than~ 0. Although the monopolist faces potential competition in the form of a competitive recycling industry, it still possesses market power as the price of a new textbooks exceeds marginal cost. This result confirms similar findings by Martin |5, 406~. Given the second order conditions, the necessary Jacobian needed to invoke To activate a program, routine, function or process. the implicit function theorem In the branch of mathematics called multivariable calculus, the implicit function theorem is a tool which allows relations to be converted to functions. It does this by representing the relation as the graph of a function. exists; hence, P and Y can be solved in terms of the model's parameters: c, r, |Lambda~, and |Theta~. Defining P* and Y* as the optimal levels of P and Y that maximize the discounted stream of profits, then P* = P*(c, r, |Lambda~, |Theta~) and Y* = Y*(c, r, |Lambda~, |Theta~). The indirect profit function, |Pi~*, is the objective function evaluated at the optimal solutions or |Pi~* = |Pi~*(P*,Y*) = |Pi~*|P*(c, r, |Lambda~, |Theta~), Y*(c, r, |Lambda~, |Theta~)~. (4) Using the envelope theorem The envelope theorem is a basic theorem used to solve maximization problems in microeconomics. It may be used to prove Hotelling's lemma, Shephard's lemma, and Roy's identity. |8, 195-98~, the indirect profit function is partially differentiated with respect to |Theta~ to obtain |Delta~|Pi~*/|Delta~|Theta~ = -(P* - c)Y*/(1 + r) |is less than~ 0. (5) Equation (5) shows higher percentages of examination copies resold mean publisher's maximum profits decline. A straightforward exercise in comparative statics shows the publisher lowers price if more examination copies are resold. Totally differentiating the first order conditions, and using Cramer's rule Cramer's rule is a theorem in linear algebra, which gives the solution of a system of linear equations in terms of determinants. It is named after Gabriel Cramer (1704 - 1752). to solve for |Delta~P*/|Delta~|Theta~ and |Delta~Y*/|Delta~|Theta~, it can be shown that |Mathematical Expression A group of characters or symbols representing a quantity or an operation. See arithmetic expression. Omitted~ |Mathematical Expression Omitted~ D is the 2 x 2 Jacobian of the objective function in equation (1). The signs of the partial derivatives partial derivative In differential calculus, the derivative of a function of several variables with respect to change in just one of its variables. Partial derivatives are useful in analyzing surfaces for maximum and minimum points and give rise to partial differential in equations (6) and (7) are denoted by the + and - symbols above each term. Second order conditions require both ||Pi~.sub.PP~ and ||Pi~.sub.YY~ to be negative and D to be positive. It can also be shown that both ||Pi~.sup.P|Theta~~ and ||Pi~.sub.Y|Theta~~ are negative, while one can prove ||Pi~.sub.PY~ is positive. The denominators in equations (6) and (7) are unambiguously positive, while the numerators in the two equations are unambiguously negative. Therefore, both P* and Y* are inversely in·verse adj. 1. Reversed in order, nature, or effect. 2. Mathematics Of or relating to an inverse or an inverse function. 3. Archaic Turned upside down; inverted. n. 1. related to |Theta~. Equation (6) states the publisher charges a lower price if a larger percentage of the examination copies are recycled as used books. Consequently, selling complementary books does not cause a publisher to raise price; rather, the sale of examination copies and the increased competition from the used book market lowers price. If there is an increase in the percentage of examination copies sold to second-hand book buyers, equation (7) implies the monopolist advertises less intensively, and distributes fewer free examination copies. IV. Conclusions We have analyzed how free examination copies affect the textbook market. Free examination copies act as advertising that increases the demand for the publisher's product. On the other hand, if the examination copies are recycled as used books, the demand for the publisher's output declines. If a larger percentage of the examination copies are sold to second-hand book buyers for recycling, holding everything else constant, the publisher's profit-maximizing price is lower. Our results confirm similar findings in the second-hand market literature. Like Martin, we find that even though the publisher possesses market power, consumers benefit from the used book market because it forces the publisher to charge lower prices. If there are more used books, the publisher's profits decline, and the publisher lowers price. Given these encouraging results, some important caveats are necessary. Our paper does not prove that a second-hand market prevents the publisher from charging "high" prices. A higher discount rate, ceteris paribus Ceteris Paribus Latin phrase that translates approximately to "holding other things constant" and is usually rendered in English as "all other things being equal". In economics and finance, the term is used as a shorthand for indicating the effect of one economic variable on , causes the publisher to charge higher prices regardless of the used book market. Only an empirical study will determine the impact of second-hand sales on the price of textbooks. The conclusions of this model are probably sensitive to the underlying assumptions about market structure. What would happen if publishers were modelled as oligopolies or as monopolistically competitive firms? How would the firms' pricing and advertising decisions change if more examination copies are resold? Research by Dixit and Norman |1~ indicates that firms with market power advertise excessively from a social viewpoint. Does this result differ in the context of this model? A competitive, oligopolistic publishing industry probably issues too many examination copies. However, since examination copies later compete against industry's output, the incentive to overadvertise is reduced. This model has several interesting extensions which are left for future research. Dale Bremmer Michael Mazur Rose-Hulman Institute of Technology Rose-Hulman Institute of Technology (abbreviated RHIT), formerly Rose Polytechnic Institute, is a small, private, non-sectarian college specializing in teaching engineering, mathematics, and science. RHIT is highly regarded for its undergraduate engineering program. Terre Haute, Indiana Terre Haute (IPA: [ˌtɛ·ɹə ˈhoʊt]) is a city in Vigo County, Indiana near the state's western border with Illinois. 1. In terms of notation notation: see arithmetic and musical notation. How a system of numbers, phrases, words or quantities is written or expressed. Positional notation is the location and value of digits in a numbering system, such as the decimal or binary system. , the following conventions are used throughout the paper. If z = f(x, y) then the first partial derivatives of this function are denoted as |z.sub.x~ = |Delta~z/|Delta~x~ and so on. The notation for the second partial derivatives is similar. For example, |z.sub.xy~ = ||Delta~.sup.2~z/|Delta~x|Delta~y and so on. 2. The calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value. derivations in this paper were verified by the second coauthor co·au·thor or co-au·thor n. A collaborating or joint author. tr.v. co·au·thored, co·au·thor·ing, co·au·thors To be a collaborating or joint author of: "He and a colleague . . . using MAPLE maple, common name for the genus Acer of the Aceraceae, a family of deciduous trees and shrubs of the Northern Hemisphere, found mainly in temperate regions and on tropical mountain slopes. , a computer symbolic algebra algebra, branch of mathematics concerned with operations on sets of numbers or other elements that are often represented by symbols. Algebra is a generalization of arithmetic and gains much of its power from dealing symbolically with elements and operations (such as program. References 1. Dixit, Avinash and Victor Norman, "Advertising and Welfare." Bell Journal of Economics, Spring 1978, 1-17. 2. Dorfman, Robert and Peter Steiner, "Optimal Advertising and Optimal Quality." American Economic Review, December 1954, 826-36. 3. Friedman, Milton Friedman, Milton (frēd`mən), 1912–2006, American economist, b. New York City, Ph.D. Columbia, 1946. Friedman was influential in helping to revive the monetarist school of economic thought (see monetarism). , Price Theory. Chicago: Aldine Publishing Co., 1967. 4. Gaskins, Darius W., "Alcoa Revisited: The Welfare Implications of a Secondhand Market." Journal of Economic Theory, March 1974, 254-71. 5. Martin, Robert E., "Monopoly Power and the Recycling of Raw Materials." The Journal of Industrial Economics, June 1982, 405-19. 6. Miller, H. Laurence, "On Killing Off the Market for Used Textbooks and the Relationship between Markets for New and Secondhand Goods." Journal of Political Economy, May/June 1974, 612-19. 7. Nelson, Phillip, "Advertising as Information." Journal of Political Economy, July/August 1974, 729-54. 8. Silberberg, Eugene, The Structure of Economics: A Mathematical Analysis Analysis has its beginnings in the rigorous formulation of calculus. It is the branch of mathematics most explicitly concerned with the notion of a limit, whether the limit of a sequence or the limit of a function. . New York New York, state, United States New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of : McGraw-Hill, 1990. 9. Swan, Peter L., "Alcoa: The Influence of Recycling on Monopoly Power." Journal of Political Economy, February 1980, 76-99. 10. Tirole, Jean, The Theory of Industrial Organization. Cambridge, MA: The MIT MIT - Massachusetts Institute of Technology Press, 1990. |
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