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

• Author: Cheung, Francis K.
• Position: Comment on article by D. Brummer and M. Mazur, Southern Economic Journal, p. 803, 1993

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...