The choice of the number of varieties : justifying simple mechanisms

We study a mechanism designerís trade-off between the complexity level and optimality level of a mechanism. While our techniques apply to a much larger class of mechanism design problems, we restrict our presentation to Mussa and Rosen (1978) quality di§erentiation in which a monopolist restricts itself to o§ering a menu with at most a Önite number n of varieties. We prove that (i) the marginal beneÖt of adding one more variety is diminishing in n; (ii) the loss due to the restriction on the number of varieties is of order no more than 1=n2 ; (iii) the marginal beneÖt of adding one more variety is of order no more than 1=n3 ; and (iv) o§ering only two varieties can make more than two-third of the potential proÖt that can be made by the second best o§ering. Roughly speaking, our analysis predicts that the monopolist should very plausibly o§er only a small number of varieties in the menu