Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

Published in: Dynamic Games and Applications 2/2022

09-11-2021

Asymmetric Information and Differentiated Durable Goods Monopoly: Intra-Period Versus Intertemporal Discrimination

Authors: Didier Laussel, Ngo Van Long, Joana Resende

Published in: Dynamic Games and Applications | Issue 2/2022

Login to get access
share
SHARE

Abstract

A durable good monopolist faces a continuum of heterogeneous customers who make purchase decisions by comparing present and expected price-quality offers. The monopolist designs a sequence of price-quality menus to segment the market. We consider the Markov perfect equilibrium (MPE) of a game where the monopolist is unable to commit to future price-quality menus. We obtain the novel results that: (a) under certain conditions, the monopolist covers the whole market in the first period (even when a static Mussa–Rosen monopolist would not cover the whole market), because this is a strategic means to convince customers that lower prices would not be offered in future periods and that (b) this can happen only under the stage-wise Stackelberg leadership assumption (whereby consumers base their expectations on the value of the state variable at the end of the period). Conditions under which MPE necessarily involves sequentially trading are also derived.

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 69.000 Bücher
  • über 500 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Testen Sie jetzt 15 Tage kostenlos.

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 50.000 Bücher
  • über 380 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




Testen Sie jetzt 15 Tage kostenlos.

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 58.000 Bücher
  • über 300 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Testen Sie jetzt 15 Tage kostenlos.

Appendix
Available only for authorised users
Footnotes
1
p.156.
 
2
Technically, as noticed by Inderst [9],“while the real time in which the market is served goes to zero as the time between periods shrinks, the number of periods it takes to clear the market also increases”.
 
3
More precisely, consumers may use the Tesla online platform (https://​www.​tesla.​com/​en_​GB/​models/​design#battery) to parametrize a wide range of characteristics of the car (including the personalized dashboard). At the end, different consumers may end up getting differentiated variants of their cars.
 
4
See Laussel et al. [18] for a model in which a monopolist firm producing a non-durable good gets full information on customers’ preferences after their first purchase, using such information to make personalized price-quality offers (first-degree price discrimination). Laussel et al. [19] also look at the case of non-durable goods. Their setup departs from the present model (and also from [18]) since there, the monopolist is unable to adjust the specification of the product (quality) when it gets information on customers’ tastes (after the customers’ first purchase).
 
5
We are grateful to an anonymous referee for drawing our attention to this point.
 
6
For example, McKinsey [24] argues that “Personalization is teetering on the edge of the buzzword precipice. But companies that can figure out what it really means and how to take advantage of it are already outstripping their competition.” For more information, visit https://​www.​mckinsey.​com/​business-functions/​marketing-and-sales/​our-insights/​perspectives-on-personalization-at-scale [Access date: 25 February 2020] .
 
7
In the Gap case the price tends instantaneously toward the lowest type’s valuation. The profit is substantially eroded but not entirely dissipated. Immediate full market-coverage still holds.
 
8
Laussel et al. [20] show that the standard results for Coasian dynamics must be modified when the durable-good monopolist participates in two distinct markets with consumption network effects (the primary market and the aftermarket).
 
9
In static settings, the issue of optimal product design has been widely studied, following the seminal work of Mussa and Rosen [26]. Some recent contributions include Deneckere and McAfee [3] and Johnson and Myatt [11]. Johnson and Myatt [10] look at the problem of optimal product design in a competitive setup.
 
10
The outside option may be, for instance, the possibility of buying another product.
 
11
The customer base is “super strong” if the lowest type customers’ maximum net surplus (gross surplus minus production cost) is strictly positive, i.e., if a benevolent social planer would always strictly prefer to supply them.
 
12
That does not mean that this consumption does not yield permanent per period benefits.
 
13
For instance, Kumar ([15], p. 900), wrote that “Each consumer is in the market for only one unit of the good and exits after making the purchase” . Inderst ([9], p. 174) stated that “Consumers want to buy at most a single good”. ([28], p. 6) wrote that “In the baseline setting, buyers have unit-demand for the product and exit the market upon purchasing either of the two varieties.” On the contrary, for a model where upgrading is possible, see Takeyama [30].
 
14
They remark that “after all, in these models, durability simply amounts to sales permanently depleting the demand for the good.
 
15
For instance, one may think of a cataract operation, or a removal of an internal organ such as “Appendix” or the tonsil.
 
16
The quality level being selected according to equation (2) so as to maximize the social surplus of each consumer’s type.
 
17
See below for more details.
 
18
Note that \(h(\theta )\frac{1}{r}q(\theta )\) is not the information rent \( U(\theta )\) of type \(\theta \).
 
19
With the uniform distribution, \(h(\theta )={\overline{\theta }}-\theta \), and \( \theta -h(\theta )=2\theta -{\overline{\theta }}\), which is positive iff \( \theta \ge {\overline{\theta }}/2\).
 
20
To compute the optimal cutoff, we use the condition \(\frac{1}{r}(2\theta ^{*opt}-{\overline{\theta }})\left[ q^{m}(\theta ^{*})\right] -B-\frac{1}{2}\left[ q^{m}(\theta ^{*opt})\right] ^{2}=0=>\frac{1}{r^{2}}(2\theta ^{*opt}-{\overline{\theta }})^{2}-B-\frac{1 }{2r^{2}}(2\theta ^{*opt}-{\overline{\theta }})^{2}=0,\)implying: \(\theta ^{*opt}=\frac{{\overline{\theta }}+r\sqrt{2B}}{2}=\frac{2 \underline{\theta }+{\widehat{\theta }}}{2}>\underline{\theta }.\)
 
21
Function \({\widetilde{v}}(.)\) is defined in Lemma 1 by Eq. (11).
 
22
See Laussel et al. [18], Claim 1, for a proof of this result (in “Appendix”) in a different context (a model with non-durable goods, where the monopolist gets full information on consumers’ type \(\theta \) after their first purchase).
 
23
A similar condition has been obtained in Laussel et al. [18] for the case of a monopolist that sells non-durable goods (and gets full information on consumers’ preferences after their first purchase).
 
24
See, e.g., Long [21] for an exposition of the concept of stage-wise Stackelberg leadership and for a review of that literature.
 
25
This follows from Eq. (28), where \(\theta _{n+1}\) is replaced with \(\underline{\theta }\), and where \(U(\underline{\theta })=0\).
 
26
The first case (Case A) arises when \(\Theta (n+1)\) is such that \( q^{m}(\Theta (n+1)|\Theta (n))>\beta q^{se}(\Theta (n+1)),\) whereas the second case (Case B) arises when \(\Theta (n+1)\) is such that \(q^{m}(\Theta (n+1)|\Theta (n))<\beta q^{se}(\Theta (n+1)).\)
 
27
It should be noticed in addition that this occurs here in one period (the initial one) while in the standard durable model it takes (in the limit, as the duration of each period becomes infinitesimal) an infinite number of periods.
 
28
The proof is analogous to the proof of Lemma 1.
 
29
Notice that the numerator is positive since \(\underline{\theta }\ge \frac{ {\overline{\theta }}+r\sqrt{2B}}{2}\) (full market coverage by the static MR monopolist) and the denominator is positive as well since the market is strong.
 
30
Note that by Assumption A4 and \(h({\overline{\theta }})=0\), we have \(v\left( {\overline{\theta }}\right) >0\).
 
31
Notice that \(q^{se}(\theta )=\arg \underset{q}{\max }\frac{\theta }{r} q-c(q).\)
 
32
Notice that the strict monotonicity of \(q^{m}(\theta |\Theta (n))\) with respect to \(\theta \) (which follows from our assumptions) ensures that the solution is unique.
 
33
Notice that this condition is weaker than the condition \({\overline{\theta }} \le \underline{\theta }\left[ (2-\beta )-\sqrt{(4-\beta )({\overline{\beta }} -\beta )}\right] ;\).
 
Literature
1.
go back to reference Board S, Pycia M (2014) Outside options and the failure of the Coase conjecture. Am Econ Rev 104(2):656–71 CrossRef Board S, Pycia M (2014) Outside options and the failure of the Coase conjecture. Am Econ Rev 104(2):656–71 CrossRef
3.
go back to reference Deneckere RJ, McAfee PR (1996) Damaged goods. J Econ Manag Strategy 5(2):149–174 CrossRef Deneckere RJ, McAfee PR (1996) Damaged goods. J Econ Manag Strategy 5(2):149–174 CrossRef
4.
go back to reference Fudenberg D, Tirole J (1991) Game theory. Massachusetts, Cambridge MATH Fudenberg D, Tirole J (1991) Game theory. Massachusetts, Cambridge MATH
5.
go back to reference Golosov M, Troskin M, Tsyvinski A (2016a) Redistribution and social insurance. Am Econ Rev 106(2):359–386 CrossRef Golosov M, Troskin M, Tsyvinski A (2016a) Redistribution and social insurance. Am Econ Rev 106(2):359–386 CrossRef
6.
go back to reference Golosov M, Tsyvinski A,Werquin N (2016b) A variational approach to the analysis of tax systems.” Update of NBER Working Paper No. 20780 Golosov M, Tsyvinski A,Werquin N (2016b) A variational approach to the analysis of tax systems.” Update of NBER Working Paper No. 20780
7.
go back to reference Gul F, Sonnenschein H, Wilson R (1986) Foundations of dynamic monopoly and the Coase conjecture. J Econ Theory 39(1):155–190 MathSciNetCrossRef Gul F, Sonnenschein H, Wilson R (1986) Foundations of dynamic monopoly and the Coase conjecture. J Econ Theory 39(1):155–190 MathSciNetCrossRef
8.
go back to reference Holmstrom B (1977) On incentives and control in organizations. Ph.D. Thesis, Standford University Holmstrom B (1977) On incentives and control in organizations. Ph.D. Thesis, Standford University
10.
go back to reference Johnson JP, Myatt DP (2018) The determinants of product lines. Rand J Econ 49(3):541–573 CrossRef Johnson JP, Myatt DP (2018) The determinants of product lines. Rand J Econ 49(3):541–573 CrossRef
11.
go back to reference Johnson JP, Myatt DP (2003) Multiproduct quality competition: fighting brands and product line pruning. Am Econ Rev 93(3):748–774 CrossRef Johnson JP, Myatt DP (2003) Multiproduct quality competition: fighting brands and product line pruning. Am Econ Rev 93(3):748–774 CrossRef
12.
go back to reference Karp L (1996) Depreciation erodes the Coase conjecture. Eur Econ Rev 40:473–490 CrossRef Karp L (1996) Depreciation erodes the Coase conjecture. Eur Econ Rev 40:473–490 CrossRef
13.
go back to reference Kahn C (1987) The durable goods monopolist and consistency with increasing costs. Econometrica 54:274–294 MathSciNet Kahn C (1987) The durable goods monopolist and consistency with increasing costs. Econometrica 54:274–294 MathSciNet
14.
go back to reference Kocherlakota N (2005) Zero expected wealth taxes: a Mirrlees approach to dynamic optimal taxation. Econometrica 73(5):1587–1621 MathSciNetCrossRef Kocherlakota N (2005) Zero expected wealth taxes: a Mirrlees approach to dynamic optimal taxation. Econometrica 73(5):1587–1621 MathSciNetCrossRef
15.
go back to reference Kumar P (2006) Intertemporal price–quality discrimination and the Coase conjecture. J Math Econ 42(7–8):896–940 MathSciNetCrossRef Kumar P (2006) Intertemporal price–quality discrimination and the Coase conjecture. J Math Econ 42(7–8):896–940 MathSciNetCrossRef
17.
go back to reference Laffont J-J, Martimort D (2002) The theory of incentives: the principal-agent model. Princeton University Press, Princeton CrossRef Laffont J-J, Martimort D (2002) The theory of incentives: the principal-agent model. Princeton University Press, Princeton CrossRef
19.
go back to reference Laussel D, Long NV, Resende J (2020) The curse of knowledge: having access to customer information can be detrimental to monopoly’s profit. RAND Journal of Economics (Forthcoming) Laussel D, Long NV, Resende J (2020) The curse of knowledge: having access to customer information can be detrimental to monopoly’s profit. RAND Journal of Economics (Forthcoming)
20.
go back to reference Laussel D, Long NV, Resende J (2015) Network effects, aftermarkets and the Coase conjecture. Int J Ind Organ 41:84–96 CrossRef Laussel D, Long NV, Resende J (2015) Network effects, aftermarkets and the Coase conjecture. Int J Ind Organ 41:84–96 CrossRef
21.
go back to reference Lederer JP, Hurter AP (1986) Competition of firms: discriminatory pricing and location. Econometrica 54(3):623–640 MathSciNetCrossRef Lederer JP, Hurter AP (1986) Competition of firms: discriminatory pricing and location. Econometrica 54(3):623–640 MathSciNetCrossRef
22.
go back to reference Martimort D (2006) Multi-contracting mechanism design. In: Advances in economics and econometrics, Vol. 1., Cambridge University Press: 57-101 Martimort D (2006) Multi-contracting mechanism design. In: Advances in economics and econometrics, Vol. 1., Cambridge University Press: 57-101
23.
go back to reference Mason R (2000) Network externalities and the Coase conjecture. Eur Econ Rev 44:1981–1992 CrossRef Mason R (2000) Network externalities and the Coase conjecture. Eur Econ Rev 44:1981–1992 CrossRef
25.
go back to reference Mirrlees JA (1971) An exploration in the theory of optimum income taxation. Rev Econ Stud 38:175–208 CrossRef Mirrlees JA (1971) An exploration in the theory of optimum income taxation. Rev Econ Stud 38:175–208 CrossRef
28.
go back to reference Nava F, Schiraldi P (2019) Differentiated durable goods monopoly: a robust Coase conjecture. Am Econ Rev 109(5):1930–68 CrossRef Nava F, Schiraldi P (2019) Differentiated durable goods monopoly: a robust Coase conjecture. Am Econ Rev 109(5):1930–68 CrossRef
29.
go back to reference Stantcheva S (2017) Optimal taxation and human capital policies over life cycle. J Polit Econ 125(6):1931–1190 CrossRef Stantcheva S (2017) Optimal taxation and human capital policies over life cycle. J Polit Econ 125(6):1931–1190 CrossRef
30.
go back to reference Takeyama LN (2002) Strategic vertical differentiation and durable goods monopoly. J Ind Econ 50(1):43–56 CrossRef Takeyama LN (2002) Strategic vertical differentiation and durable goods monopoly. J Ind Econ 50(1):43–56 CrossRef
Metadata
Title
Asymmetric Information and Differentiated Durable Goods Monopoly: Intra-Period Versus Intertemporal Discrimination
Authors
Didier Laussel
Ngo Van Long
Joana Resende
Publication date
09-11-2021
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 2/2022
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-021-00405-z

Other articles of this Issue 2/2022

Dynamic Games and Applications 2/2022 Go to the issue

Premium Partner