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Shapiro (2001) - Navigating The Patent Thicket (view source)
Revision as of 17:13, 27 March 2013
, 17:13, 27 March 2013→Model
Demand for the product is <math>D(p)\;</math>, and the price elasticity of demand is therefore:
:<math>\eta 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.
Subbing in <math>\sum_i p_i = p - \alpha\;</math>:
:<math>\frac{p - \overbrace{\alpha - \sum_i c_i}^{c}}{p} = \frac{N}{\etaepsilon}\;</math>
With a single firm, <math>N=1\;</math>, the Lerner index is <math>\frac{1}{\etaepsilon}\;</math>, so with <math>N\;</math> firms the mark-up is <math>N\;</math> times the standard monopoly mark-up.
===Hold-up===
