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Shaked Sutton (1982) - Relaxing Price Competition Through Product Differentiation (view source)
Revision as of 19:15, 29 September 2020
, 19:15, 29 September 2020no edit summary
{{Article
|Has page=Shaked Sutton (1982) - Relaxing Price Competition Through Product Differentiation
|Has bibtex key=
|Has article title=Relaxing Price Competition Through Product Differentiation
|Has author=Shaked Sutton
|Has year=1982
|In journal=
|In volume=
|In number=
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*This page is referenced in [[BPP Field Exam Papers]]
*Shaked, A. and J. Sutton (1982), "Relaxing price competition through product differentiation", Review of Economic Studies 49, 3-13. [http://www.edegan.com/pdfs/Shaked%20Sutton%20(1982)%20-%20Relaxing%20price%20competition%20through%20product%20differentiation.pdf pdf]
@article{shaked1982relaxing,
title={Relaxing price competition through product differentiation},
author={Shaked, A. and Sutton, J.},
journal={The Review of Economic Studies},
pages={3--13},
year={1982},
publisher={JSTOR}
}
The objective function for firm <math>k\,</math> is:
:<math>\pi_k - = (t_{k+1}-t_k)\cdot p_k = (\frac{\Delta p_{k+1}}{\Delta q_{k+1}} - \frac{\Delta p_{k}}{\Delta q_{k}})\cdot p_k\,</math>
Likewise for firm <math>n\,</math>:
:<math>\pi_k - pi_n = (t''-t_n)\cdot p_n = (\frac{t'' - \Delta p_{n}}{\Delta q_{n}})\cdot p_n\,</math>
Firm 2 maximizes:
:<math>\max_{p_2} (t'' - t_2)\cdot p_2 = (t'' - \frac{\Delta p_2}{\Delta q_2})\cdot p_2\,</math>
:<math>\therefore p_2 = \frac{t'' \Delta q_2 +p_1}{2}\,</math>
Likewise firm 1 maximizes:
:<math>\max_{p_1} (t_2 - t')\cdot p_1 = (\frac{\Delta p_2}{\Delta q_2} - t')\cdot p_2\,</math>
:<math>\therefore p_1 = \frac{p_2 - t' \Delta q_2}{2}\,</math>
Clearly both would like to pick the high quality, unless it has already been picked, in which case they want to pick the lowest possible quality. Quality choice is therefore a coordination game with lopsided payoffs. Presumably perturbation to timing will allow one to pick first.
==Conclusion==
Vertical differentiation is not isomorphic to horizontal differentiation. In horizontal differentiation, competitors with two equal prices have local market power. Here lower quality firms are driven out, and only high quality firms exploit some market power. However, quality and price competition with many firms will be too fierce, so even under free entry conditions we will get a finite number of firms, quality differentiation and positive profits.
