Some Conjectures on Increasing Competition and the Ease of Substitution : Implications for Inverting Demand Systems

This paper provides a means for properly comparing demand and inverse demand for a product when the number of firms in the analysis is expanded beyond the duopoly case. To do this, first an index for the ease of substitution was derived for inverse demand systems, and then demand systems, that works when the product is differentiated in some way. Then, the conditions under which the indexes should be equal are explored. The index is used to test if any changes in substitution are detectable when demand systems are inverted and competition is augmented. It is found that unrestricted mathematical inversion does not properly control for ease of substitution when obtaining inverse demand systems from demand systems. This problem is shown to be surprisingly significant. An alternative restricted inversion methodology is reviewed and it was shown to properly control for the ease of substitution when inverting demand systems