Examples for economists with DERIVE: long- and short-run costs

The relations between long- and short-run average, marginal and total costs have been a standard topic in elementary economics since Viner's (1931) account. As is well known, Viner's original account contains an error which his draughtsman Y. K. Wong attempted unsuccessfully to prevent. Viner (1950) corrects this error, which relates to the property that the long-run average cost is the lower envelope of the family of short-run average cost curves. The purpose of this note is to use DERIVE 3 to illustrate the whole topic for an arbitrary well-behaved technology. In particular, we can use DERIVE to illustrate a point that is not usually brought out in elementary accounts. There is a much more specific relation between long-run and short-run average and total cost curves beyond the property noted above. In particular, the functional form of short-run cost is intimately related to the functional form of long-run cost.