|Has page=Shapiro (2001) - Navigating The Patent Thicket
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|Has article title=Navigating The Patent Thicket
|Has author=Shapiro
|Has year=2001
|In journal=
|In volume=
|In number=
|Has pages=
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}}
*This page is referenced in the [[Patent Thicket Literature Review]]
*This page is listed on the [[PTLR Core Papers]] page
===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:
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.
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.