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### Long-run and short-run cost curves

Cost curves form a staple part of the curriculum of undergraduate microeconomics. Their presentation across textbooks is fairly uniform and has not varied much over the years since Marshallian partial equilibrium analysis was first codified in a set of diagrams. The uniformity and stability of the presentation of the curves belies their controversial beginnings in the 1920s and 30s, as economists struggled to contain Marshall’s realistic descriptive insights and biological analogies into a logically coherent static equilibrium model. In the battle that played out between descriptive realism and neat formalisms, the latter won out for center stage in textbook studies of cost.

Cost curves are drawn with the quantity of a specific product along the horizontal axis and money cost on the vertical. For an analysis of perfect competition, the assumption is that each firm faces identical input prices and choices of technology. Under this assumption, the curves can be interpreted to correspond either to the industry as a whole, or to a representative firm.

They can represent the total cost of the quantity, the average (per unit) cost, or the marginal cost. For the short-run, total and average costs can be broken down into the portion reflecting the amount spent on factors of production whose quantities can be varied, and the portion reflecting the sunk costs of the fixed factors of production. Further, one can consider long-run cost curves drawn under the assumption that the quantities of all factors can be varied. Drawn together on one diagram, cost curves can appear daunting to students of economics, and even their teachers can have difficulty disentangling them in a comprehensible way. Evidence of the difficulty can be seen in three pedagogical articles on cost curves that have appeared in the Journal of Economic Education in recent years.

In the case of constant returns to scale, the most common assumption for production functions, the LRAC curve is horizontal. If it is the case that a larger scale of production is obtained through increasing the number of identical plants, then the long-run cost curve approaches a horizontal line as the number of plants increases (Joseph 1933); that is, the production function will exhibit “asymptotic-first-degree-homogeneity” (Samuelson 1967, p. 131). Long-run average cost curves that are everywhere decreasing will arise in industries with a large fixed cost and constant variable costs. Traditionally, decreasing long-run cost curves have been associated with natural monopolies. More generally, the LRAC curve can be drawn as a U-shape displaying increasing returns at lower levels of output and decreasing returns at higher levels.

The long-run marginal cost curve is usually omitted in introductory treatments. If it is included, it is drawn so that it lies above the short-run marginal cost curve to the left of their intersection point, and below to the right. Understanding the relationship between the short-run and long-run marginal cost curves can be challenging, and may require conjuring up additional diagrams. Sexton, Graves and Lee (1993) couch their explanation using isocosts and isoquants; whereas Boyd and Boyd (1994) show how the relationship can be explained using the total cost curves.