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Shapiro (2001) - Navigating The Patent Thicket (view source)
Revision as of 19:15, 29 September 2020
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|Has article title=Navigating The Patent Thicket
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|Has year=2001
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*This page is referenced in the [[Patent Thicket Literature Review]]
*This page is listed on the [[PTLR Core Papers]] page
==Reference==
*Shapiro, C. (2001), "Navigating the patent thicket: Cross licenses, patent pools, and standard setting", , pp.119--150
@incollection{shapiro2001navigating,
title={Navigating the patent thicket: Cross licenses, patent pools, and standard setting},
author={Shapiro, C.},
booktitle={Innovation Policy and the Economy, Volume 1},
pages={119--150},
year={2001},
abstract={},
discipline={Econ},
research_type={Discussion, Theory},
industry={},
thicket_stance={},
thicket_stance_extract={},
thicket_def={},
thicket_def_extract={},
tags={},
filename={Shapiro (2001) - Navigating The Patent Thicket.pdf}
}
==File(s)==
*[[Media:Shapiro (2001) - Navigating The Patent Thicket.pdf|Download the PDF]]
*[[:Image:Shapiro (2001) - Navigating The Patent Thicket.pdf|Repository record]]
==Abstract==
Each of these is discussed in turn.
===Model===
<math>N\;</math> firms own patents on complementary inputs, with costs of producing a unit of <math>c_i\;</math>, charging a price <math>p_i\;</math>. The price of the product itself will be <math>p\;</math>, and assembling a unit will cost <math>\alpha\;</math>.
Competition at the assembly level ensures that:
:<math>p=\alpha + \sum_i p_i\;</math>
Demand for the product is <math>D(p)\;</math>, and the price elasticity of demand is therefore:
:<math>\epsilon = - \frac{D'(p)\cdot p}{ D(p)}\;</math>
The <math>N\;</math> firms set their component prices independently and non-cooperatively. That is the model assumes that each firm is a monopolist so it sets price (quantity) to maximize profits.
:<math>\pi_i = D(p)(p_i-c)\;</math>
Therefore the FOC is:
:<math>\frac{d \pi_i}{d p_i} = D(p) + D'(p)(p_i - c_i) = 0\;</math>
Summing across all <math>i\;</math>:
:<math>D(p)N + D'(p)\sum_i(p_i - c_i) = 0\;</math>
:<math>\therefore \frac{\sum_i(p_i - c_i)}{p} = \frac{D(p) N}{p D'(p)}\;</math>
Subbing in <math>\sum_i p_i = p - \alpha\;</math>:
:<math>\frac{p - \overbrace{\alpha - \sum_i c_i}^{c}}{p} = \frac{N}{\epsilon}\;</math>
With a single firm, <math>N=1\;</math>, the Lerner index is <math>\frac{1}{\epsilon}\;</math>, so with <math>N\;</math> firms the mark-up is <math>N\;</math> times the standard monopoly mark-up.
===Hold-up===
