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

In a recent article, "Monopolies That Advertise with Recyclable Free Samples: Beware of Professors Selling Gifts?" Bremmer and Mazur [1] argue that if a larger percentage of free examination copies is resold as used books, textbook publishers are forced to lower prices, instead of raising prices

as claimed by textbook publishers and others. This is an interesting result in light of the mixed conclusions on the effects of the second-hand goods market from previous studies (see, for example Miller [2]). The general interest on this issue is also evidenced by the fact that the article is recommended for further reading by Saffran [3].

In Bremmer and Mazur's paper, it is assumed that the demand curve for textbooks shifts parallel to the right as more free examination copies are distributed to professors. In this note, we first observe that this parallel shift assumption, which seems to be a simplifying assumption in their linear model, is actually responsible for their result. We further argue that the institutional arrangement of the textbook market justifies an alternative assumption on the advertisement effect of giving free examination copies on the demand for textbooks. Under this alternative assumption, advertisement by giving free copies has an ambiguous effect on the price of textbooks.

In Bremmer and Mazur's model, the publisher chooses P and Y to maximize the profit

[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),

where P is the price, Y the amount of free samples, [Q.sub.1] and [Q.sub.2] the demands in periods 1 and 2 respectively, c the unit production cost, [Lambda] the fraction of books bought in the first period that are sold as used books in the second period, [Theta] the percentage of free copies recycled as used books in the second period, and r the discount rate. Standard comparative statics give

[Delta][P.sup.*]/[Delta][Theta] = ([[Pi].sub.PY][[Pi].sub.Y[Theta]] - [[Pi].sub.YY][[Pi].sub.P[Theta]])/D, (1)

where [P.sup.*] is the optimal price and D [greater than] 0 is the Jacobian. Since [[Pi].sub.P[Theta]], [[Pi].sub.Y[Theta]] and [[Pi].sub.YY] are all negative, it follows that [Delta][P.sup.*]/[Delta][Theta] [less than] 0 if [[Pi].sub.PY] [greater than or equal to] 0.

Under the parallel shift assumption, the demand functions take the form of [Q.sub.i](P, Y) = [f.sub.i](P) + [g.sub.i](Y)(i = 1, 2), where [f[prime].sub.i] [less than] 0 and [g[prime].sub.i] [greater than] 0. It follows that

[[Pi].sub.PY] = [g[prime].sub.1](Y) + [g[prime].sub.2](Y)/(1 + r) - [Lambda][g[prime].sub.1](Y)/(1 + r) - [Theta]/(1 + r) [greater than or equal to] 0,

where the inequality comes from the first order condition for Y. Thus, the Bremmer and Mazur result is obtained.

An important implication of the parallel shift assumption is that the demand elasticity decreases with an increase in free samples at any given price. In the case of textbooks, professors assign the textbook and students usually can not substitute the assigned textbook by another one. Students can, however, choose to share or copy the assigned textbook or may simply choose not to use the textbook. Thus, advertising the textbook by giving free samples to professors will not affect a student's demand elasticity, although it may affect the number of professors who adopt the textbook and thus may affect the number of students who are assigned the textbook. This means that the market demand for a textbook should swivel outward as more free samples are distributed to professors. More precisely, the market demand functions should take the form of [Q.sub.i](P, Y) = [f.sub.i](P)[g.sub.i](Y). Under this alternative demand specification, the demand elasticity is independent of Y at any given price.

To illustrate that the Bremmer and Mazur result may not hold under the above demand specification, assume that demand is stationary and unit production cost is zero, i.e., [f.sub.i] = f, [g.sub.i] = g and c = 0. Using the first order condition for Y, it is easy to obtain that [[Pi].sub.PY] = kPf[prime](P)g[prime](Y) where k = (2 + r - [Lambda])/(1 + r) [greater than] 0. It follows that [[Pi].sub.PY] [less than] 0. This implies, from (1), that the sign of [Delta][P.sup.*]/[Delta][Theta] is ambiguous. For example, if the elasticity of g with respect to Y is constant, i.e., Yg[prime](Y)/g(Y) = [Alpha](0 [less than] [Alpha] [less than] 1), then simple manipulation of the first order conditions shows that the optimal P is independent of [Theta], implying that [Delta][P.sup.*]/[Delta][Theta] = 0.

It is worthwhile to note that, even if giving free samples to professors not only increases the number of students who are assigned the textbook but also decreases their demand elasticities for the textbook, the Bremmer and Mazur result still may not hold. In this case, the demand functions may take the form of [Q.sup.i](P, Y) = [f.sub.i](P)[h.sub.i](Y) + [g.sub.i](Y), where [f[prime].sub.i] [less than] 0, [h[prime].sub.i] [greater than] 0 and [g[prime].sub.i] [greater than] 0. Simple calculations show that, for the case of stationary demand and zero unit production cost, [[Pi].sub.PY] = kPf[prime](P)h[prime](Y) [less than] 0 and thus the sign of [Delta][P.sup.*]/[Delta][Theta] is, again, ambiguous.

The above analysis suggests that, depending on the specification of the demands and other parameters in the model, selling free samples by professors may have a positive or negative impact on textbook price. Therefore, to decide whether selling free texts by professors will harm or benefit students calls for empirical studies.

While Bremmer and Mazur's analysis addresses one interesting issue of the used textbook problem, some extensions of their model might give additional insights into the more general recyclable capital problem and thus represent topics for future research. First, one could allow the price of a textbook to vary across different periods in the model; this may explain the fact that the price of a textbook may depend on how long it has been out. Second, one could include in a many periods model with multiple editions a signalling effect (on quality) by letting the demands be affected by some characteristics of the book such as the number of editions. This may create behavioral responses on the part of the publishers and the professors and may lead to an equilibrium with reputation effects.(1)

Francis K. Cheung Xinghe Wang University of Missouri Columbia, Missouri

1. In the original paper, Bremmer and Mazur mentioned two other extensions: one involves different market structures and the other relates to the welfare effect of advertising.

References

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

2. 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.

3. Saffran, Bernard, "Recommendations for Further Reading." Journal of Economic Perspectives, Fall 1993, 223-30.