Optimal Price of Entry Into a Competition

Abstract

A continuum of contestants are choosing whether to enter a competition. Each contestant has a type, and of those who enter, the ones with highest types receive prizes. A profit-maximizing firm controls entry, and charges a price for it. I show that an increase in the value of each prize leads the firm to raise the price while keeping the intensity of entry fixed. Conversely, when the mass of prizes increases, the firm initially keeps the price constant while allowing entry to increase; and later-raises the price. (JEL C72, D82, D83) * I thank my editor Stefano Barbieri, two anonymous referees, as well as Philipp Denter for valuable comments that helped improve the paper. Support from Comunidad de Madrid (grant S2015/HUM-3444) is gratefully acknowledged.