Intermediate Microeconomics
ECON 340
Problem Set 6
Due on Thursday April 28th at the beginning of class
You must show how you arrived at every single answer on the problem set. You will
receive ZERO credit for any answer where you don’t show your work.
1. (10 pts) Suppose Sony and Apple are the first companies to introduce to the
market 'smart' Blu-ray players to both play discs and stream movies from cloudbased apps like Netflix. Studies by the firms suggest that consumers who
purchase consumer electronics are very brand-loyal. To capture future loyalties,
each firm will attempt to maximize its initial market share, for one time only, by
setting prices simultaneously. An economist has estimated the profits (in millions)
of each firm under different pricing scenarios. Her results are captured in the
following payoff matrix.
Apple
Price
Low
Medium
High
Low
750 250
800 200
1000 0
Medium
700 300
750 350
800 200
Sony
High
600 400
700 300
750 250
a. (5 pts) Identify the best responses of each firm. Are there any Dominant
Strategies? Are there any Dominated Strategies?
b. (5 pts) Identify the Nash Equilibrium strategies and outcomes of the game? Is
there a Dominant Strategy Equilibrium? Explain. 2. (20 pts) The NCAA prohibits schools that are caught paying athletes from
participating in bowl games, and sometimes the punishment is more severe. To
understand why schools don’t break away from the NCAA and form a league in
which athletes can legitimately be paid, let’s analyze the following normal-form
game:
Assume there are only two schools (A and B). If both schools pay athletes, then
athletes extract virtually all of the profits, and each school is left with only $1
million in profits. If both schools don’t pay athletes, each school earns $7 millions
in profits, since less money goes to the athletes. If one school pays athletes and
the other school does not, the school that pays athletes earns profits of $15 million
and the school that does not pay athletes loses $15 million.
a. (5 pts) Write the normal form representation of this game
b. (5 pts) Find the Nash equilibrium for a one-shot version of this game. Find the
Nash equilibrium if this game is repeated 5000 times.
c. (5 pts) Now suppose the game is infinitely repeated. Describe the Grim trigger
strategies that the schools can use to sustain the outcome with the highest
aggregate payoff (the collusive outcome).
d. (5 pts) For what values of the interest rate can collusion be sustained? ECON 340 Spring 2016 1 3. (10 pts) Consider the following two-player, sequential-move game. There are only
two gas stations near the Purdue campus, Smart Shop and Speedway. Smart
Shop is thinking of implementing a third degree price discrimination scheme by
giving Purdue students a special discount. Speedway must decide whether to offer
student discounts as well. If both firms decide to offer student discounts, each
expects profits to be $75k per week. If both firms decide not to offer student
discounts, each expects profits to be $50k per week. However, if one firm offers
students discounts and the other does not, the firm that offers the discounts will
earn $100k per week and the other firm profits will be $40k per week
a. (3pts) Show the extensive form of this game assuming Smart Shop moves
first.
b. (3pts) Identify, graphically, the Nash Equilibrium outcomes
c. (2pts) Find the Sub game Perfect Nash Equilibrium outcomes
d. (2pts) What would be the Sub game Perfect Nash Equilibrium outcomes if
Speedway moves first? Explain 4. (10 pts) You are considering entering a market serviced by a monopolist. You
currently earn $0 economic profits, while the monopolist earns $15. If you enter
the market and the monopolist engages in a price war, you will lose $10 and the
monopolist will earn $8. If the monopolist doesn’t engage in a price war, you will
each earn profits of $10.
a. (5pts) Write out the extensive form of the above game.
b. (3pts) There are two Nash equilibria for the game. What are they?
c. (2pts) Is there a subgame perfect equilibrium? Explain. 5. (15 pts). You are a temporary worker considering two job opportunities. Job Offer
1 pays a salary of $63 that day for sure. Job Offer 2 pays a base salary of $25, but
offers the possibility of a $56 bonus on top of your base salary. You believe that
there is a 0.70 probability that you will earn the bonus. You have a utility function
given by U = X1/2
a. (4 pts) What is the expected salary under each offer? What is the variance of
the salary under each offer?
b. (4 pts) Compute the expected utility of each offer. Which job offer would you
accept?
c. (2 pts) Based on your answer to (a) and (b), are you risk averse, risk loving, or
risk neutral? Explain.
d. (5 pts) What salary in Job Offer 1 would make you indifferent between the
two Job offers? Explain. Interpret the difference between your answer and the
current salary in job offer 1. ECON 340 Spring 2016 2 6. (10 pts) Identify if an individual with the following utility functions is risk averse,
risk loving, or risk neutral. Clearly explain why.
a. (2 pts) U(x)= 2x +5
b. (2 pts) U(x)= X3
c. (2 pts) U(x)= -0.5e-2x
d. (2 pts) U(x)= -x-2 where x>0
e. (2 pts) U(x) = 2x + 10x1/2 7. (25 pts) Suppose that the market is comprised of 4 groups of people of differing
risk categories. Individuals know their own risk, but insurers cannot tell which
group a person belongs to. Each individuals has a current income equal to
$40,000 and faces a risk of requiring medical treatment costing $7,600.
Each individual has an utility function given by U = X1/2
Each group’s probability of requiring medical treatment is as follows:
Group
# of People
Probability of
Medical Treatment 1
1,000
0.20 2
1,000
0.40 3
1,000
0.60 4
1,000
0.80 a. (5 pts) What is the most money each group will be willing to pay for an
insurance policy that fully insures them in the event they require medical
treatment (risk premium)?
b. (4 pts) What is the expected loss for each group? How does it compare to their
maximum willingness to pay for insurance? Why are these different?
c. (4 pts) What is the average riskiness of a person seeking insurance?
If an insurance company were to charge all its clients the same premium to
fully insure them, what would the fair premium be?
Which group(s) would buy insurance at this price? Why?
d. (4 pts) What is the average riskiness of the persons now seeking insurance?
(the group(s) identified in the last part of question (c) above).
What would be the new fair premium that the insurance company would
charge all its clients?
Which group(s) would buy insurance at this price? Why?
e. (4 pts) What is the average riskiness of the persons now seeking insurance?
(the group(s) identified in the last part of question (d) above).
What would be the new fair premium that the insurance company would
charge all its clients?
Which group(s) would buy insurance at this price? Why?
f. ECON 340 (4 pts) Is this an efficient outcome? Explain.
Describe the different options the firm has to address this problem. Spring 2016 3
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Posted 06 Sep 2017 07:09 AM
My Price 10.00
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