Production Function Geometry With "Knightian" Total Product

Abstract

Abstract: Authors of principles and price theory textbooks generally illustrate short-run production using a total product curve that displays first increasing and then diminishing marginal returns to employment of the variable input(s). Although it seems reasonable that a temporary range of increasing returns to variable inputs will likely occur as variable inputs are added to a set of fixed ones. This proposition implies an isoquant diagram that is not a familiar one in text-books. The authors examine a linearly homogeneous production function conforming to the textbook case and construct its isoquant diagram. They then use a geometrical proof attributable to Geoffrey Jehle (2002) to demonstrate that, in general, isoquants must have, outside the traditional ridge lines, a range where they are convex toward those (MP = 0) ridge lines and another range where they are concave toward them if there are short-run increasing, then diminishing, marginal returns. The authors suggest how this issue might be presented to students.

Keywords:

• isoquants
• Knightian total product
• production function