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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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 53E
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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
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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