 # The Theory of Limit Pricing

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The theory of limit pricing suggests that an incumbent firm may be able to make it unprofitable for a potential entrant to enter the industry. The argument is that the incumbent firm can produce a certain output before entry, and threaten to continue producing that output even if entry occurs. If the potential entrant believes the claim, he will decide it is unprofitable to enter.

Later economists were critical of "limit pricing" theory, except when the incumbent firm can impose restrictions on itself to make its threat credible.

The example below explores limit pricing theory. (You will have to look at the textbook (page 361) for the graph of this model).

Assume market demand is P = 100 – Q. There is one incumbent firm in the industry (a monopoly), and its output is designated by qi. There is a potential entrant to this industry and its output is designated by the symbol qe.

Both firms have the same costs of production: TC = 400 + 10q, and therefore AC = (400/q) + 10.

The incumbent firm knows that there is a potential entrant, and believes that the potential entrant believes that the incumbent will not change its output even if the potential entrant decides to enter. The incumbent firm therefore wants to choose qi so that entry will be unprofitable. In fact, the incumbent knows that the potential entrant will not enter unless it earns a positive profit (∏e > 0), so the incumbent will choose qi to make the entrant's profit equal to zero. This will happen if the residual demand curve of the potential entrant just touches (is tangent to) its AC curve but does not rise above it anywhere.

To find the tangency point, take dAC/dq = -400q-2 and set this equal to the slope of the residual demand curve dP/dq = -1. Therefore, -400q-2 = -1 or q = 20. When q = 20, AC = (400/20) + 10 = \$30. This means that the residual demand curve must pass through the point q =20, P = \$30 and have a slope of –1. The general equation for this residual demand curve will be P = X - qe (where X is the vertical intercept), and at the point of tangency, this equation will satisfy 30 = X – 20. Therefore, X = 50, and the residual demand curve which just touches the AC curve will have the equation, P = 50 – qe.

The market demand curve is P = 100 – Q or P = 100 - qi – qe. To leave the appropriate residual demand curve, qi must = 50. This is the entry-deterring output for the incumbent firm. Given the beliefs of the potential entrant, it will calculate its best output this way: P = 50 – qe, therefore MRe = 50 – 2qe. Setting this equal to MC, we have 50 – 2qe = 10, or qe = 20. Therefore Pe = 50 – 20 = \$30. At this price and quantity, profit for the entrant is:

∏e = (30 x 20) – [400 + (10 x 20)] = \$0. Given this calculation, the potential entrant

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