Isoquants of the Cubic Production Function
James A. Yunker
Western Illinois University - Department of Economics
March 25, 2008
The one-input cubic production function displays a range of increasing returns to a factor, followed by a range of decreasing returns, followed by a range of negative returns. If this situation holds with respect to two factors, it generates a natural intuition that the total product function in 3-dimensional space is represented by a sort of hill or protuberance with a well defined peak at the maximum value of /TP/ with respect to the two factors, with the consequence that the production isoquants are closed oblongs. However, the explicit mathematical function typically shown in textbooks as the two-input cubic production function (designated herein the "usual" function) does not have these properties. Rather the 3-dimensional total product function rises to a ridge curve before descending. The isoquants on either side of the ridge curve isoquant are not closed oblongs but rather convex downward-sloping configurations that converge in the limit but do not join. Two alternatives to the usual cubic production function are proposed: the additive and the multiplicative cubic production functions. Both of these have the expected properties: the 3-dimensional surface is depicted as a hill with a unique peak, and the isoquants are closed oblongs.
Number of Pages in PDF File: 19
JEL Classification: D24
Date posted: April 9, 2008