MONOPOLISTIC COMPETITION AND OPTIMUM PRODUCT DIVERSITY

Pettengill tests whether there is an excessive number of firms in a monopolistically competitive equilibrium by a device of considerable expository merit. He removes one firm, and redistributes the resources thus released equally over the remaining firms in the sector, to see if welfare can be improved. To do this correctly, we write n, for the equilibrium number of firms and xe for the output of each.

With fixed cost a and constant average variable cost c, removing one firm releases (a + Cxe) of resources, and this enables the output of each of the remaining ( I) firms to be increased (a + c Xe )/(1fl 1)}. The quantity xo of the numeraire good is unaffected by this, and the utility function (equation (31) of our paper) is