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Loury (1979) - Market Structure And Innovation (view source)
Revision as of 19:43, 17 November 2010
, 19:43, 17 November 2010no edit summary
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>
