Replacement cycles, income distribution and dynamic price discrimination

Abstract

This article analyses how income distribution, Intellectual Property Rights and other regulatory policies such as minimum quality standards determine pricing strategies in a dynamic context where a monopolist periodically introduces new generations or upgrades of a durable good. Discrimination through quality and screening in this article takes place in a context where consumers buy several versions of the durable good during their lifetime, instead of a single version as in Inderst’s (2008) or Koh’s (2006). It also differs from Glass (2001) in that an equilibrium may emerge in which different consumer types replace their durable generations with different frequencies. Our modelling is motivated by stylized facts from the last Brazilian POF (household budget survey).

Keywords:

• intertemporal price discrimination
• durable good monopoly
• optimal pricing strategy
• minimum quality standards
• imitation

JEL Classification:

• D42
• D92

Acknowledgements

The authors would like to thank CPP-Insper for the assistance with POF database.

Notes

¹ Truly, any quality upgrade generates a temporary monopoly. In our model, furthermore, we have the same firm (monopolist) introducing all the successive quality upgrades. This may happen because innovation is a process with memory, giving a firm that has already innovated an advantage to bring forth the next quality upgrade.

² Waldman (2003) offers an excellent review of the theory, with many ‘real world’ aspects and applications.

³ But we must acknowledge that maybe this is so because we do not model an intertemporal budget constraint for our consumer types.

⁴ See the fourth piece of evidence in Section III and footnote 25 below.

⁵ Glass (2001) is a ‘quality ladder’ model where the good that is innovated/upgraded is nondurable. In quality ladder models with two consumer types, a successful innovator becomes the top firm (selling the latest generation of the product), the previous top firm becomes the trailing firm (selling a one-generation old version of the product) and the previous trailing firm is priced out of the market. R&D is never directed to the current top firm, so it will never become a monopolist for more than one period. In such a competitive setting, at every period there will exist a trailing firm ready to sell its lower quality (older generation) product to low valuation consumers, if the price charged for the latest generation happens to be too high.

⁶ For the same reason, MQS may also reduce entry in the industry.

⁷ POF’s sample is stratified by income and geographic region, so as to be representative of the whole Brazilian population. In the last two versions (2002–2003 and 2008–2009), around 50 000 households were interviewed. For details, see http://www.ibge.gov.br/home/estatistica/populacao/condicaodevida/pof/defaulttab.shtm

⁸ We excluded from the complete POF sample some cheap goods like combs, toothbrushes, etc., and idiosyncratic beauty, personal care articles. Also, we exclude purchases on credit and used goods, because in this article, we will model neither a credit market, nor a secondary market for durable goods. For this reason, some important goods like automobiles do not feature in our sample – at least for the 50% lower bound of the income distribution, they are always bought on credit.

⁹ Throughout our analysis, we consider the per capita income of the households in the survey, and not their total (joint) income. Notice that for each durable good, we have a different subsample of households that made acquisitions, and thus a different pair of indexes (income variability, price variability).

¹⁰ So the figures in the fifth column are obtained by dividing those in the 4th column (% of rich households that are buyers) by those in the 3rd column (% of poor households that are buyers).

¹¹ Correia de Souza and Moita (2011) calculated both Lerner and Hinferdahl–Hirschman indexes for 3-digit industries/sectors of the Brazilian economy. The Hinferdahl–Hirschman index for home appliances is around 0.51, placing the sector as the 34th most concentrated out of 232 sectors.

¹² Of course, this approximation is the more valid, the less purchasing the new generation of durable good is a burden on the consumer’s budget (income).

¹³ Later, this will be proved to result from an optimal pricing strategy of the durable producer’s.

¹⁴ Our idea of an upper bound to the price charged by the monopolist is essentially the same as in Fishman and Rob (2000): ‘If old models in the consumer’s possession continue to be functional after a new model appears, the monopolist can only charge for the incremental flow of services the new model provides.’ (p. 3).

¹⁵ Put another way, imitators do not run independent projects, and i is already the aggregate probability of imitation.

¹⁶ Sales to poor consumers remain constant because if the price is reduced to, say, a half, then the number of poor consumers that in one period will replace their durables’ generation is exactly doubled. This follows from the already known fact that $r_p=\gamma$.

¹⁷ See expression 4 above.

¹⁸ Two generations may be for sale at the same time in Glass’s (2001) model, but not in Inderst’s (2008) or Koh’s (2006) because in their setups, there exists only one ‘new generation’ and the consumer buys it at most once in a lifetime.

¹⁹ ‘Old’ in the sense of being an old model, not in the sense of second hand products.

²⁰ On the right side of expression 12, the factor (1 – i) appears raised to the power α + 1 (plus 1) for the same reason why the expected cost of not waiting on the left side appears multiplied by (1 – i): as before, we assume there exists a probability of instantaneous imitation, so that if I wait, say, 5 periods to buy a generation invented 5 periods ago, there are actually 6 instances in which imitation can take place.

²¹ Since a successful imitation in any of the r_{pd –} δ periods, the poor consumer waits would frustrate a paid generation renewal.

²² In Fig. A1 below, we plot V´ as a function of γ for several sets of parameters values.

²³ Actually, γ* will always be maximal (equal to y) in those cases, as can be inferred by the shape of Vʹ schedule, depicted in Fig. A1 below.

²⁴ Actually, Graph 1 is V_dʹ plotted for i = 0,1, β = 0,8, y = 8, α = 1, s_r = 0,1.

²⁵ This brings us back to Prince’s (2009) conjecture about the correlation between quality choice and replacement frequency (see Section II above) and to the fourth piece of evidence from Brazilian POF in Section III. Under the 2nd scenario, our model delivers the result that rich consumers both acquire higher quality goods and make more frequent replacements/acquisitions. However, we should take this with a grain of salt: in real world situations, there may be many other reasons (some of them purely technological) besides MQS that explain why a durable good monopoly is not able to sell very old generations.

²⁶ See, also, the discussion on pages 32–33.