|Has page=Lee,Wilde (1980) - Market Structure And Innovation A Reformulation
|Has bibtex key=
|Has article title=Market Structure And Innovation A Reformulation
|Has author=Lee,Wilde
|Has year=1980
|In journal=
|In volume=
|In number=
|Has pages=
|Has publisher=
}}
*This page is referenced in [[PHDBA602 (Innovation Models)]]
==Reference(s)==
*Lee, T. and L.L. Wilde (1980), "Market structure and innovation: A reformulation", Quarterly Journal of Economics, 94, pp. 429-436. [http://www.edegan.com/pdfs/Lee%20Wilde%20(1980)%20-%20Market%20structure%20and%20innovation%20A%20reformulation.pdf (pdf)]
@article{lee1980market,
title={Market structure and innovation: a reformulation},
author={Lee, T. and Wilde, L.L.},
journal={The Quarterly Journal of Economics},
pages={429--436},
year={1980},
publisher={JSTOR}
}
==Abstract==
iv. When there are initial increasing returns to scale in the R & D technology, competitive entry leads to more than the socially optimal number of firms in the industry.
It turns out that conclusions (i) and (ii) are sensitive to Loury's specification of the costs of R & D. In this paper we investigate the effects of an alternative specification.
==The Model==
===Loury's Model===
The basis for this model is identical to that in [[Loury (1979) - Market Structure And Innovation |Loury (1979)]].
The following are defined the same:
*<math>h(x_i)\;</math>
*<math>F_{\tau}\;</math>, <math>F_{\hat{\tau}}\;</math> and <math>a_i\;</math>
*<math>V\;</math> and <math>r\;</math> (though true continuous discounting in used here, and there seems to be difference in the math)
The expected benefits are (supposed the same as in [[Loury (1979) - Market Structure And Innovation |Loury (1979)]]):
In the full equilibrium, as a result of symmetry, it is the case that:
:<math>a = (n-1)h(\hat{x})\;</math>
Letting the implicit solution to <math>\frac{\partial \mathbb{E}\pi}{\partial x} = 0\;</math> be denoted <math>\hat{x} = H(a)\;</math>, then in the full equilibrium <math>\hat{x} = H((n-1)h(\hat{x}))\;</math>.
We can see the comparative static with respect to <math>n\;</math> is also exactly opposite to that of Loury (providing an analogous stability condition holds):