Measuring the convexity of the cost function

In this paper I argue that, as might be expected, the initial assumption made about the cost function will influence the empirical results obtained regarding the convexity. I show that this expectation is supported empirically by estimating the parameters of two quadratic cost functions. The first is that function which has been traditionally used in the literature. The second is a simplified version of the quadratic cost function where the cost of changing the level of output is dropped since the evidence in the literature suggest that this variable has no significant effect on cost. Using physical product monthly data for 24 industries we find that the conclusion reached regarding the convexity of the cost function depends on the assumption we make regarding the cost function. I further find that the simplified function is consistent with the observed behavior of production and sales while the traditional cost function is inconsistent with that behavior.