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Loury (1979) - Market Structure And Innovation (view source)
Revision as of 19:15, 29 September 2020
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{{Article
|Has page=Loury (1979) - Market Structure And Innovation
|Has bibtex key=
|Has article title=Market Structure And Innovation
|Has author=Loury
|Has year=1979
|In journal=
|In volume=
|In number=
|Has pages=
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*This page is referenced in [[PHDBA602 (Innovation Models)]]
==Reference(s)==
*Loury G.C.(1979), "Market structure and innovation", Quarterly Journal of Economics, 93, pp. 395-410. [http://www.edegan.com/pdfs/Loury%20(1979)%20-%20Market%20structure%20and%20innovation.pdf (pdf)]
@article{loury1979market,
title={Market structure and innovation},
author={Loury, G.C.},
journal={The Quarterly Journal of Economics},
pages={395--410},
year={1979},
publisher={JSTOR}
}
==Abstract==
:<math>a_i= \sum_{j\ne i} h(x_j)\; </math>
The firm discounts the future reciepts at a rate <math>r\;</math> (note that using continuous compounding, <math>PV = FV \cdot e^{-rt})\;</math>, but apparently this paper values the future price at <math>\frac{V}{r}\;</math>).
The firm wins the prize at time <math>t\;</math> with probability:
With an initial range of increasing returns to scale then returns can go to zero with a finite number of firms. To see this we examine the change in profit with respect the number of firms, remembering that the expenditure each firm will make will depend upon the total number of competitors.
:<math>\frac{\d \Pi}{d n} = \frac{\partial \pi }{\frac \partial a}\cdot (h(x^*) + (n-1)h'(x^*)) + \frac{\partial \Pi}{\frac \partial x} \frac{\partial x}{\frac \partial n} < 0\;</math>
Given a fixed market structure, social welfare is maximized with a choice <math>x^{**}\;</math> characterized by:
:<math>\frac{\partial \pi}{\frac \partial x}((n-1)h(x),x) + (n-1)h'(x) \cdot \frac{\partial \pi}{\frac \partial a}((n-1)h(x),x) = 0\;</math>
Whereas the individual firms choose an <math>x^*\;</math> characterized by:
:<math>\frac{\partial \pi}{\frac \partial x}((n-1)h(x),x)= 0\;</math>
Since <math>\frac{\partial \pi}{\frac \partial a} < 0\;</math> it follows that <math>x^*(n) > x^{**}(n)\;</math>.
The second inefficiency is that there are too many firms. If <math>\overline{x}\;</math> (the point where increasing returns to scale stop) is at zero then infinite firms enter the competitive race. If <math>\overline{x} > 0\;</math> a finite firms enter, but continue to enter until all profits are dissipated.
