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Limit Pricing

An incumbent is limit pricing if it produces more than its optimal quantity, so that there is not sufficient demand for a potential entrant. The lowest price that it sets is the "limit price" that excludes a profitable entry.
A numerical example (based on [1]) illustrates how the profits of both the incumbent and the entrant change with and without limit pricing, for various fixed costs common to both firms. Initially, in the absence of entrant, the incumbent is a monopolist and maximizes its profit (green rectangle). The entrant estimates the residual demand, optimizes its production level, and makes profit (blue rectangle), affecting the profits of the incumbent. To avoid entry, the incumbent must increase its production so that the entrant cannot make profits if it enters. In order to succeed with that, it needs to equate the slope of the residual demand with the slope of average costs. Notice that there are scale economies (decreasing average costs). Consequently, the incumbent's profit is reduced to the gray rectangle while the profits of entrant are zero. Finally, if the entrant exits due to the limit price, the incumbent makes a higher profit (yellow rectangle).

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Reference
[1] D. Carlton and J. Perloff, Modern Industrial Organization, 4th int. ed., Pearson Addison–Wesley, 2005.
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