Upgrading, Degrading, and Intertemporal Price Discrimination

Abstract

The paper studies monopoly pricing of a vertically differentiated durable good in a two-period model. It provides an explanation for seemingly unusual practice of a firm selling a "degraded good," arguing that the presence of Coasian dynamics may lead to the sale of the degraded good that is not less costly to produce than a high-quality good. The main finding is that when the firm can identify previous customers only if they voluntarily reveal their past purchases, it sells the degraded good along with the high-quality good in the first period. When the firm sells an upgrade of the degraded good, the price of the high-quality good cannot be "too low" in the second period, since otherwise the upgrading customers would pretend to be new customers. Thus the firm can enhance first-period sales while mitigating consumers' incentive to wait until the next period.

Optimal collusion with internal contracting

“…To clarify the exposition, consider the case where α = α * (δ) for any δ. 26 Define a vector z(α) 24 The derivation of (9) is included in the proof of Lemma 3 in the Appendix. 25 The length given by the RHS of (9) satisfies the required length for the segment to exist.…”

“…If On-IC i H is not binding (say, slack), then the width on the RHS is not long enough. 26 In the Appendix, we show that for any α ≥ α * (δ) for a given δ, there exist z(α) ∈ Z IC (V (α)) that establishes such that (i) prices are fixed at ρ, (ii) market shares are allocated by the criterion of productive efficiency with q 1 LL = q 1 HH = 0 and (iii) continuation values are…”

“…A simplification shows that On-IC i H becomes ρ ≥ ρ. Thus, as indicated by (26), this constraint is slack (binding) if…”

“…If α rises, then the LHS falls, but the RHS rises because the price ρ in (26) rises. This inequality is thus reduced to α ≥ α * (δ) ≡ max…”

“…Using an principal-agent setting, Dewatripont and Maskin (1995) show that the contracting parties may find it desirable to deliberately restrict the observability of principal. Lee (2003) argues that the scope of intertemporal price discrimination may diminish if a monopolist has more information as to consumers' past purchasing history. 10 Vickers (1985), Fershtman and Judd (1987), Katz (1991), Reitman (1993), Sklivas (1987), Spagnolo (2000), and Kockesen and Ok (2004) show that incentive contracts with delegated agents can serve as a strategic commitment device.…”