15 Herfindahl-Hirschman indexing. The Herfindahl-Hirschman Index, H, gives economists a way of measuring how much competition there is in a market. Suppose that there are N hospitals in a market, each with s; percent of the market share, where 1. Recall that the index is defined as follows: N N H= - i=1 a Suppose that there are N= 10 firms in a market, and each of them has an equal share of the market, so that s == for each firm. What is the value of the Herfindahl-Hirschman Index in this market? b Suppose instead that one firm in this market dominates such that it has 90% of the market share, while the remaining nine firms each have an equal share of the remainder. What is the value of the Herfindahl-Hirschman Index in this case? Do increases in H represent an increase or a decrease in competition? c What is the largest value H can take? When is H equal to this number? d Now suppose a new firm enters the market and pulls away market share from each of the incumbent firms such that s = Would you say that competition has increased with the entry of the new firm into the market? Calculate the value of H after the firm has entered. e Under perfect competition, there are an infinity of firms in the market, each with an infinitesimal market share. What is the value of H in a perfectly competitive market?