Monopolies that advertise with recyclable free samples: beware of professors selling gifts? Reply.

Conclusions generated by any economic theory depend on the underlying assumptions. The growth in the economic literature documents the pursuit of determining how robust a result is with different assumptions. For example, in a note recently published in this Journal, Michael Mazur and I [1] show that a monopolistic publisher reduces the price of its textbook if a larger percentage of the examination copies given to professors are recycled as used books. This result depends on the assumption that examination copies act as advertising which shifts the demand curve for new textbooks out parallel to the right.

The previous comment regarding our model makes two important points. First, it confirms our result. Second, the comment shows that a different assumption may result in a different conclusion. The comment assumes that, rather than shifting the demand curve outward in a parallel fashion, an increase in examination copies causes the demand curve to rotate outward from the same vertical intercept. With this assumption, which the comment claims is more plausible than our assumption of a parallel shift, an increase in the percentage of examination copies recycled as used books has an indeterminate effect on the price of new textbooks. The comment agrees with our caveat that the effect of recycling examination copies on the price of new textbooks needs the harsh scrutiny of empirical investigation.

Given its assumptions, the comment's analysis is correct. After several pages of algebraic manipulation and substitutions, I could not derive an unambiguous result using the information contained in the first-order and second-order conditions of the profit-maximization problem. Therefore, the impact of recycling examination copies on the price of new textbooks is sensitive to how advertising affects the demand for textbooks. If an increase in examination copies causes the demand curve to shift outward, parallel to the right, an increase in the percentage of examination copies resold as used books always causes the publisher to lower the price of its new textbooks. On the other hand, if advertising causes the demand curve to rotate outward from the same vertical intercept, an increase in the percentage of examination copies recycled as secondhand books could cause the publisher to raise prices.

However, with the addition of another equally plausible assumption, I show that a publisher always lowers its price in response to a larger percentage of examination copies recycled as used books regardless of how advertising affects the demand curve for new textbooks. If the elasticity of demand with respect to advertising is inversely related to the amount of examination copies issued, a monopolistic publisher will lower the price of its product if more of its advertising - the free examination copies - are recycled as used books. It seems intuitive that, at the profit-maximizing level of advertising, the sensitivity of new textbooks sold in response to issuing more examination copies diminishes with successive increases in the number of examination copies.

But first, the previous comment brings up an interesting point in the literature that needs more theoretical and empirical investigation. How does advertising affect a demand curve? Does advertising cause the demand curve to shift out parallel to the right? Or does advertising cause the demand curve to rotate outward? If advertising causes the demand curve to shift parallel to the right, then demand is less elastic at every price. On the other hand, if advertising cause the demand curve to rotate outward from the same vertical intercept, then the price elasticity of demand remains the same at every price. The effect of advertising is more complicated in this model. Free examination copies influence the professors' decision whether to adopt a text which, in turn, affects the students' demand for textbooks.

The literature regarding the effect of advertising on demand curves is mixed. In his classic text, Stigler [6, 202] writes that "the purpose of advertising is, of course, to shift the demand curve to the right and upward" [emphasis added]. Current, popular textbooks report claims similar to Carlton and Perloff's [3, 604] that "all advertising is designed to increase the demand for a firm's product" [emphasis added]. In the graph that accompanies their discussion, Carlton and Perloff show a demand curve shifting parallel to the right. Therefore, an increase in advertising that contains persuasive content changes tastes, affects the price elasticity of demand, and is thought to shift the entire demand curve outward. Theoretical articles such as Dixit and Norman's [4] study of the impact of advertising on social welfare, assume that an increase in advertising causes the demand curve for a product to shift outward, parallel to the right.

However, when advertising has purely informational content that informs consumers of the product's existence, the effect of increased advertising upon the demand curve has been modeled as an outward rotation from the same vertical intercept. Shapiro [5] argues that if advertising acts only to inform consumers and doesn't attempt to change tastes, then increased advertising causes the demand curve to rotate. Butters [2] also assumes that the role of advertising is to make consumers aware about the existence of the product and its price, and he models the effect of advertising as a rotation in the demand curve. However, the literature seems confused on this issue as Carlton and Perloff write that "an increase in informative or persuasive advertising . . . causes an outward shift of the demand curve . . . [2,604]." Therefore, claims of more plausibility notwithstanding, the impact of examination copies on the demand for textbooks needs more empirical and theoretical investigation.

Now, turning to the analysis of the previous comment, the quantity of textbooks sold is the product of two functions - a function of price, P, and a function of Y, the number of examination copies - or Q = f(P)g(Y). The price elasticity of demand, [[Epsilon].sub.P], equals Pf[prime](P)/f(P) and, as the previous comment notes, it is independent of Y at any given price. Similarly, the elasticity of demand with respect to advertising, [[Epsilon].sub.Y], equals Yg[prime](Y)/g(Y), and it is not affected by changes in P.

Given the assumptions of the previous comment, the objective function of the profit-maximizing problem becomes [Pi] = kPf(P)g(Y) - [Theta]PY/(1 + r). After some algebraic manipulation, the first-order conditions of this optimization problem are

kf(P)g(Y)(1 - [[Epsilon].sub.P]) = [Theta]Y/(1 + r) (1)

and

kf(P)g[prime](Y) = [Theta]/(1 + r). (2)

Equation (1) and the assumptions of the model imply [[Epsilon].sub.P] [less than] 1; therefore, the monopolistic publisher always produces in the inelastic portion of its demand curve - a surprising and unusual result.

Combining equations (1) and (2), the elasticity of demand with respect to price and advertising must sum to one or

[[Epsilon].sub.P] + [[Epsilon].sub.Y] = 1. (3)

Assume the solutions to this profit-maximizing problem are [P.sup.*] and [Y.sup.*]. Differentiating equation (3) with respect to [Theta], the exogenous percentage of examination copies recycled as used books, results in

[Mathematical Expression Omitted].

Since [Delta][[Epsilon].sub.P]/[Delta][P.sup.*] is positive, and it can be shown, even with the different assumptions of the previous comment, that [Delta][Y.sup.*]/[Delta][Theta] is negative, equation (4) implies that [Delta][P.sup.*]/[Delta][Theta] and [Delta][[Epsilon].sub.Y]/[Delta][Y.sup.*] are of the same sign.

Therefore, if the monopolistic publisher increases price in response to a larger percentage of examination copies being resold as used books, the advertising elasticity of demand increases as more examination copies are issued. This result may strike some as counterintuitive and paradoxical as why would a monopolist stop advertising at an alleged profit-maximizing level as the responsiveness to that advertising is increasing? As pointed out in the previous comment, if [[Epsilon].sub.Y] is constant, then an increase in the percentage of examination copies resold on the secondhand market does not affect the price of new textbooks. Finally, if [[Epsilon].sub.Y] and Y are inversely related at the profit-maximizing level of Y, a result which I argue is more plausible, then a larger percentage of examination copies recycled as used books means the monopolist lowers the price of its new textbooks.

Dale S. Bremmer Rose-Hulman Institute of Technology Terre Haute, Indiana 

This paper was written while I was on sabbatical and employed by the Indiana Office of Utility Consumer Counselor. I am indebted to the helpful comments of Randy Kesselring and John Conant. But as always, I am responsible for any opinions, errors or omissions contained in the paper.

References

1. Bremmer, Dale and Michael Mazur, "Monopolists That Advertise with Recyclable Free Samples: Beware of Professors Selling Gifts?" Southern Economic Journal, April 1993, 803-807.

2. Butters, G., "Equilibrium Distributions of Sales and Advertising Prices." Review of Economic Studies, October 1977, 465-91.

3. Carlton, Dennis and Jeffrey Perloff. Modern Industrial Organization. New York: HarperCollins College Publishers, 1994.

4. Dixit, Avinash and Victor Norman, "Advertising and Welfare." Bell Journal of Economics, Spring 1978, 1-17.

5. Shapiro, Carl, "Advertising and Welfare: Comment." Bell Journal of Economics, Autumn 1980, 749-752.

6. Stigler, George. The Theory of Price. New York: Macmillan Publishing Co., 1966.