Estimating Economies of Scope Using Profit Function: A Dual Approach of the Normalized Quadratic Profit Function

Theoretical relationships between the parameters of the normalized quadratic cost and profit functions were derived. The cost function was recovered from an estimated profit function, and thus economies of scope (EOS) were calculated using a profit function. An empirical example showed that the parameters in the true cost function could be precisely recovered using the estimated profit function. Estimating economies of scope measures using profit function have several merits over that using cost function, which include easier imposition of curvature, avoiding calculating EOS off the production frontier and capturing the inefficiency in the allocation of output quantities. The EOS calculated using profit function was based on the traditional concept of EOS can be easily compared with the EOS that was computed using cost function.