A commodity is indivisible if it has a minimum size below which it is unavailable, at least without significant qualitative change. Indivisible inputs yield economies of scale and scope. But even where indivisibilities impose large fixed costs, if they are not sunk, potential competition can impose behaviour upon incumbents that is consistent with economic efficiency. Perhaps the most significant way in which indivisibilities can impede efficiency in pricing is the existence of indivisible input–output vectors that are efficient but which are not profit maximizing at any positive scalar prices. Integer programming is naturally suited to optimality analysis involving indivisibilities.
KeywordsBarriers to entry Circular flow Economies of scale Economies of scope Euler’s theorem Fixed costs Indivisibilities Integer programming Marginal cost pricing Natural monopoly Non-convexity Ramsey pricing Sunk costs
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