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_i percent of the market share, where Ni

Recall that the index is defined as follows:

a. Suppose that there are N = 10 firms in a market, and each of them has an equal share of the market, so that

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_i = 1/11. 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?

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N Σ1s=1.