Abstract
This chapter develops the long-run supply curve for a competitive industry. It begins with the simplest case, in which the industry consists of identical firms whose cost curves are not affected by the number of firms. Next it allows for these identical firms’ costs to be influenced by the number of firms. Then it analyzes the case in which each firm has unique cost curves. Finally, it addresses the implication of allocative efficiency.
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- 1.
The economist does not “determine” the number of firms in any industry, of course. Rather, economic analysis analyzes the forces that determine the number of firms. The material below shows the number of firms given the information contained in the illustrative functions. No analyst could ever have this much information.
- 2.
A fourth case, in which each firm has a unique cost structure and that structure depends on the number of firms, is not illustrated. The illustration would be more complex than that of the third case, but it would yield qualitatively similar results.
- 3.
The number of firms does not affect the cost curves of member firms if changes in the number of firms do not affect input prices and if the number of firms does not directly affect member firms’ production functions (no technical externalities).
- 4.
The constant term could be interpreted as follows. Suppose that if the firm produces even the smallest positive amount, it must incur a cost of a, but if it shuts down entirely (x = 0), this term vanishes, as does the firm itself. With this interpretation, \(a + b {\ast} {x}^{2}\) is the cost curve for all but the smallest positive values, and ltc = 0 for x = 0.
- 5.
This is less restrictive than it appears. In an industry of price takers, production always occurs in a range such that the marginal cost curve is increasing, so having it increase from the beginning does not constitute a serious restriction.
- 6.
Analogously, in the short run, price must be at least as high as the minimum average variable cost.
- 7.
Part of that statement involves the quote-quote (’’) operator, which activates the expression in parentheses for use in function calls.
- 8.
The makelist command now contains four arguments: 10*i multiplies the value of i by 10, i identifies the variable, and the final two terms define the endpoints.
- 9.
The arguments of the function are not included in the map command. The expression must be a function of a single variable so that Maxima treats the values in plist as the values for the function’s argument.
- 10.
Some authors refer to the move from one long-run equilibrium to another as dynamic. In some sense this is correct, but we avoid this usage. Speaking of dynamics suggests a time path than can be discovered. Such a discernible path is not likely to exist, however, for if it did traders would exploit it and in the process change it.
- 11.
The increased demand eventually causes a shift in the short-run supply curve, but a movement along the (relevant) long-run supply curve. In the short-run, the increased demand causes a movement along the (relevant) short run supply curve.
- 12.
According to [1], the market for dynamic random access memory (DRAM) chips is an example of this type of industry, where cost-saving discoveries made by any one firm are quickly adopted by other firms.
- 13.
A more flexible functional form would allow a and b to be multiplied by different functions of n. This generalization would increase computational complexity with little gain.
- 14.
The cost curves could be constructed so that the lowest average cost occurs at different output levels for different firms. This change would have no effect of consequence. In a market of price-taking firms, entry will occur until the marginal firm earns an economic profit of zero.
- 15.
We do not develop the firms’ short-run cost curves. We could do so, following the approach developed in the preceding section. The result would be similar to that above: The long-run industry supply curve would be more elastic than the short-run industry supply curves.
- 16.
Actually, it is not quite necessary for all firms to have identical costs for this result to hold. It will hold if all firms have the same minimum lac even if the common value does not occur at the same quantity for every firm.
References
McAfee RP (2006) Introduction to economic analysis. Available at www.introecon.com
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Hammock, M.R., Mixon, J.W. (2013). Long-Run Supply. In: Microeconomic Theory and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9417-1_9
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DOI: https://doi.org/10.1007/978-1-4614-9417-1_9
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