Some Propositions on Cost Functions

The interaction between returns to scale and learning is investigated using a homogeneous production function. A cost function for the problem of production to customer order is derived. In this situation, several exceptions to previously derived propositions concerning the form of the resulting cost function were uncovered. Specifically, Alchian's assertion that, with volume of output fixed, marginal costs increase with production rate was found to require that the production function exhibit substantial decreasing returns to scale if there were possibilities for input substitution. Alchian's ''conjectural proposition'' that marginal costs decrease with volume, only holds in the presence of input substitution and substantial learning. In the presence of learning, exceptions were also found to Hirshleifer's proposition that marginal costs rise with production rate when the length of the program is fixed.