that there are N hospitals in a market, each with s; percent of the market share, where E Si = 1. Recall that the index is defined as follows: H=E 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 has increased with the entry of the new firm into the market? Calculate the value that competition 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?
that there are N hospitals in a market, each with s; percent of the market share, where E Si = 1. Recall that the index is defined as follows: H=E 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 has increased with the entry of the new firm into the market? Calculate the value that competition 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?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:THE HOSPITAL INDUSTRY
121
that there are N hospitals in a market, each with s; percent of the market share, where
S; =1. Recall that the index is defined as follows:
i3D1
H=s;
os A aletigeod
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
%3D
10
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?
aggon 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.
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
e
orle
market?
aw aleiigeor
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