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Loury (1979) - Market Structure And Innovation (view source)
Revision as of 20:44, 17 November 2010
, 20:44, 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 }{\partial a}\cdot (h(x^*) + (n-1)h'(x^*)) + \frac{\partial \Pi}{\partial x} \frac{\partial x}{\partial n} < 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.
