Two competing hospitals in small city can choose whether to offer only basic health care, allpurpose...

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Two competing hospitals in small city can choose whether to offer only basic health care, allpurpose care, or specialized care. The following payoff table denotes profits for eachhospital:
	
Document Preview: Managerial Economics – Fall 2012 
 
Problem Set 4 
 
DUE: Wednesday December 5th at beginning of lecture 
 
Short, precise answers will be better rewarded than long, vague ones.  All of the questions in can be 
answered with 5 sentences or less.  Include graphs only when requested 
 
No late assignments will be accepted. 
 
You can work in groups, but each student has to submit his/her OWN work.   
 
You are required to answer all problems. 
 
Problem XXXXXXXXXXpoints) 
 
Two competing hospitals in small city can choose whether to offer only basic health care, all-
purpose care, or specialized care.  The following payoff table denotes profits for each 
hospital: 
 
  Hospital B’s Services 
  Basic All-Purpose Specialty 
Basic 5, 7 5, 4 12, 6 
Hospital A’s 
All-Purpose 4, 5 8, 7 7, 4 
Services 
Specialty 6, 10 3, 12 3, 3 
 
a) Does either hospital have a dominant strategy (or any dominated strategy)?  Assuming 
that they determine their strategies independently of one another, what are the 
hospitals’ respective Nash equilibrium strategies?  Explain why. 
b) Suppose instead that the hospitals coordinate.  What actions should they each take? 
c) What general economic reasons might there be for a hospital merger to generate an 
increase in profit?

1Problem XXXXXXXXXXpoints) 
 
Since dry cleaning produces air pollution, a small town with two dry cleaning companies has 
decided to regulate the dry cleaning industry.  The two dry cleaning companies, Company A 
and Company B, currently produce 350 units of air pollution, which the town wants to reduce 
to 200 units.  The accompanying table shows the current pollution level produced by each 
company and each company’s marginal cost of reducing its pollution.  The firms’ production 
marginal cost is constant. 
 
Companies Initial pollution level Marginal cost of reduction pollution 
(kgs per year) ($ per kg) 
A 230 $5 
B 120 $2 
 
a) Suppose that the town were to pass an environmental standards law that limits each...

David · Accepted Answer

Answer to 1:
a) 
A strategy of a player is called dominant strategy if the payoffs associated with that strategy 
strictly exceeds the payoffs associated with his any other strategy. 
Using following logic, Hospital A has no dominant strategy but Hospital B has one dominant 
strategy, which is to provide ‘Basic Services’.  This is because the payoffs associated with 
strategy ‘Basic’ strictly exceeds payoffs associated with his strategy ‘Specialty’. So ‘Basic’ is 
dominant strategy for Hospital B and ‘Specialty’ is dominated strategy for Hospital B. 
There are two Nash equilibriums; (Specialty, Basic) and (All-purpose, All-purpose). 
These two are Nash equilibrium because no player has incentive to deviate from this point. For 
example; suppose Hospital A is providing Specialty Service, then Hospital B can do no better but 
to provide ‘Basic’ services. Similarly if Hospital B is providing ‘Basic Services’, Hospital A can 
do no better but to provide ‘Specialty’ services. So (Specialty, Basic) is the point from which no 
player would like to deviate and hence it is one of Nash equilibrium. 
(All-purpose, All-purpose): Now suppose Hospital A is providing ‘All-purpose’ Services, then 
Hospital B can do no better but to provide ‘All-purpose’ services. Similarly if Hospital B is 
providing ‘All-purpose Services’, Hospital A can do no better but to provide ‘All-purpose’ 
services. So (All-purpose, All-purpose) is the point from which no player would like to deviate 
and hence it is another Nash equilibrium. 
b) 
In coordination,

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