ECON 301: Microeconomics Winter 2015 1 CONTINUE Problem Set 4 Due at the start of class on March 11. You may work with your teammates, but you must turn in your own version. All solutions should be neatly and clearly written. Be sure to label any graphs and clearly indicate your reasoning. Each part of each question is worth five (5) points; the total possible points is 115. 1. Tax Incentive Arms Race. Tax incentives are frequently used by cities and states in the U.S. in an attempt to make their jurisdictions more desirable places for businesses to invest than other jurisdictions. However, to the extent that other jurisdictions also offer tax incentives, any benefits in terms of attracting new investment are nullified, and all jurisdictions end up suffering as a result of lower tax revenues. Suppose two states, Pennsylvania and New Jersey, are each deciding whether to offer tax incentives to attract new businesses. The payoffs for each state are as follows: (a) Explain in words what a Nash equilibrium is. (b) Assume that each state is rational, that rationality is common knowledge, and that the game is common knowledge. If the tax incentive arms race game will be played one time, what is the Nash equilibrium of the game? (c) Could the Nash equilibrium outcome be different if this game were to be played each year for the next 10 years? Explain why or why not. (d) The phenomenon you described in this problem is often referred to as a “race to the bottom.” Explain why that is an appropriate name for this phenomenon. 2. Princess Bride Game. Our hero Westley (in the guise of Dread Pirate Roberts) challenges the evil Vizzini to a “battle of wits.” Two cups of wine are placed on a table, one in front of Westley and one in front of Vizzini. Westley has poisoned one of the two cups of wine with deadly iocane powder (which is colorless, odorless, and tasteless); which cup is poisoned is unknown to Vizzini. The challenge to Vizzini is to select one of the two cups to drink; Westley must drink the other. The payoffs of the game are as follows: Pennsylvania No Tax Incentives No Tax Incentives Offer Tax Incentives Offer Tax Incentives New Jersey 15 5 10 10 0 0 15 5 ECON 301: Microeconomics Winter 2015 2 CONTINUE (a) What are the Nash equilibrium of this game? Show how you came to your answer. (b) Suppose that, unbeknownst to Vizzini, Westley is immune to iocane powder, and in fact poisoned both cups. If Westley gets a payoff of 5 from drinking a cup of wine poisoned with iocane powder when Vizzini also drinks a cup of wine poisoned with iocane powder (and Vizzini’s payoff is still -10 from drinking a cup poisoned with iocane powder), draw the new game board. What payoffs must each of the two players now get?1 3. Governor Race Game. An incumbent governor from a conservative party faces a ...

1. ECON 301: Microeconomics
Winter 2015
1 CONTINUE
Problem Set 4
Due at the start of class on March 11. You may work with your
teammates, but you must turn in
your own version. All solutions should be neatly and clearly
written. Be sure to label any graphs
and clearly indicate your reasoning. Each part of each question
is worth five (5) points; the total
possible points is 115.
1. Tax Incentive Arms Race. Tax incentives are frequently used
by cities and states in the U.S.
in an attempt to make their jurisdictions more desirable places
for businesses to invest than
other jurisdictions. However, to the extent that other
jurisdictions also offer tax incentives,
any benefits in terms of attracting new investment are nullified,
and all jurisdictions end up
suffering as a result of lower tax revenues.
Suppose two states, Pennsylvania and New Jersey, are each
deciding whether to offer tax
incentives to attract new businesses. The payoffs for each state
are as follows:

2. (a) Explain in words what a Nash equilibrium is.
(b) Assume that each state is rational, that rationality is
common knowledge, and that the
game is common knowledge. If the tax incentive arms race game
will be played one time,
what is the Nash equilibrium of the game?
(c) Could the Nash equilibrium outcome be different if this
game were to be played each
year for the next 10 years? Explain why or why not.
(d) The phenomenon you described in this problem is often
referred to as a “race to the
bottom.” Explain why that is an appropriate name for this
phenomenon.
2. Princess Bride Game. Our hero Westley (in the guise of
Dread Pirate Roberts) challenges
the evil Vizzini to a “battle of wits.” Two cups of wine are
placed on a table, one in front of
Westley and one in front of Vizzini. Westley has poisoned one
of the two cups of wine with
deadly iocane powder (which is colorless, odorless, and
tasteless); which cup is poisoned is
unknown to Vizzini. The challenge to Vizzini is to select one of

3. the two cups to drink;
Westley must drink the other. The payoffs of the game are as
follows:
Pennsylvania
No Tax
Incentives
No Tax
Incentives
Offer Tax
Incentives
Offer Tax
Incentives
New Jersey
15 5
10
10
0
0
15
5
ECON 301: Microeconomics

4. Winter 2015
2 CONTINUE
(a) What are the Nash equilibrium of this game? Show how you
came to your answer.
(b) Suppose that, unbeknownst to Vizzini, Westley is immune to
iocane powder, and in fact
poisoned both cups. If Westley gets a payoff of 5 from drinking
a cup of wine poisoned
with iocane powder when Vizzini also drinks a cup of wine
poisoned with iocane powder
(and Vizzini’s payoff is still -10 from drinking a cup poisoned
with iocane powder), draw
the new game board. What payoffs must each of the two players
now get?1
3. Governor Race Game. An incumbent governor from a
conservative party faces a challenger
from a liberal party. They are choosing political platforms. The
incumbent chooses first. If
both choose the same platform, the incumbent wins; otherwise,
the challenger wins.
Let the value of winning be 20 and the value of compromising

5. one’s political views be -10;
the payoff is the sum of these values. Therefore, there are four
possible outcomes:
liberal, in which case the
incumbent wins (payoff = 20 – 10 = 10) and the challenger loses
(payoff = 0).
conservative, in which case
the incumbent loses (payoff = 0 – 10 = -10) and the challenger
wins (payoff = 20-10
= 10).
chooses liberal, in which case
the incumbent loses (payoff = 0) and the challenger wins
(payoff = 20).
chooses conservative, in
which case the incumbent wins (payoff = 20) and the challenger
loses (payoff = 0 –
10 = -10).
(a) Draw the game tree corresponding to this sequential game.
Note that the incumbent
chooses first whether to pursue a liberal or conservative
platform, then the challenger
chooses his/her platform after observing what the incumbent
chose.
(b) Using backward induction, determine the outcome of the

6. game. Explain how you arrived
at your answer.
(c) What if the incumbent becomes convinced that the
challenger so strongly stands by
his/her principles that the value of compromising his/her views
is -30 (but it is still -10
for the incumbent). Would that change the outcome of the
game? Draw a new game tree
with the new payoffs and explain why the outcome would or
would not change.
1 If you have not seen the movie, I encourage you to watch this
scene. In it, Vizzini makes an attempt at backward induction to
figure out from which cup he should drink:
https://www.youtube.com/watch?v=U_eZmEiyTo0
Westley
Poison W’s
Cup
Drink W’s
Cup
Poison V’s
Cup
Drink V’s
Cup
Vizzini
10 -10

7. 10
-10
-10
10
-10
10
ECON 301: Microeconomics
Winter 2015
3 CONTINUE
4. Two airlines, Drexel Air and Dragon Jet, operate flights from
Philadelphia to Miami. Weekly
demand for seats on flights from Philadelphia to Miami is given
by Q = 1300 – 2P, where Q
is the number of seats and P is the price in dollars. Suppose that
both airlines have a marginal
cost of $50 per seat. Suppose that Drexel Air and Dragon Jet
simultaneously choose the
quantity of seats to offer on the route (i.e., suppose they are
Cournot competitors).
(a) Given that Drexel Air and Dragon Jet choose their quantities
simultaneously, solve for
the optimal quantities for each to offer. What is the price of a
seat in this market? What
are the economic profits for Drexel Air and Dragon Jet?
(b) Suppose that executives at both companies realize that their
competition on the

8. Philadelphia-Miami route may be costing them profits. In a
closed-door meeting, they
decide to collude. What’s the greatest economic profit they
could each make by colluding
(assuming they split production and profits equally under
collusion)?
(c) Show mathematically and explain in words why the
collusive arrangement you solved for
in part (c) is not sustainable if this “game” is played once. In
what sense is this situation
similar to a prisoner’s dilemma game?
(d) Suppose the two firms are not colluding, but Drexel Air
figures out a way to cram more
seats onto a plane such that its marginal cost is $44 per seat
instead of $50. Assuming
Dragon Jet’s marginal cost is still $50 per seat, solve for the
new optimal quantities,
price, and economic profits.
5. Suppose that, unlike in the previous question, Drexel Air and
Dragon Jet move sequentially
instead of simultaneously (i.e., suppose that they are
Stackelberg competitors). Weekly
demand for seats on flights from Philadelphia to Miami is still
given by Q = 1300 – 2P,
where Q is the number of seats and P is the price in dollars.
Assume again that both airlines
have a marginal cost of $50 per seat.
(a) Assuming that Drexel Air chooses its quantity of seats first
and Dragon Jet chooses its
quantity second, solve for the optimal quantity of seats for each

9. airline to offer. What is
the price of a seat in this market? What are the economic profits
for Drexel Air and
Dragon Jet in this case?
(b) Compare your answer in (a) of this question to your answer
from part (a) of question 4.
Does Drexel Air gain an advantage by moving first? Explain in
words why or why not.
(c) Suppose now that the two firms proposed to merge to
become a monopolist on this route.
Concerned about the decrease in quantity of seats supplied and
increase in prices that
might result from the merger, the Department of Justice moves
to block the merger. In
response, the two airlines claim that because of cost efficiencies
that will arise as a result
of the merger, their marginal cost will fall from $50 per seat to
$25 per seat. If this is true,
will the monopoly price for tickets in fact be lower than the
Stackelberg price that you
solved for in part (a)?
(d) Suppose that the Department of Justice allows the merger to
occur. Calculate the
deadweight loss under Stackelberg competition and under
monopoly (assuming that, as
the airlines claimed, the marginal cost falls to $25 after they
merge). Did the deadweight
loss surplus increase, decrease, or stay the same?
ECON 301: Microeconomics
Winter 2015

10. 4 END
6. Suppose that Drexel is auctioning off a VIP food truck pass
that gives the owner free food at
any food truck on campus for a year. Your valuation of the pass
is $250.
(a) Suppose that Drexel is using a first-price, sealed-bid
auction. If there is only one other
bidder in the auction and you believe his valuation has equal
odds of being anywhere
from $100 to $300, what is your optimal bid? What is your
expected surplus?
(b) If there were more bidders in the first-price, sealed-bid
auction (and you believe that all
have valuations with equal odds of being anywhere from $100
to $300), would that
increase, decrease, or not change your optimal bid relative to
what you solved for in part
(a)? Explain in words.
(c) Explain in words why a Dutch auction is equivalent to a
first-price, sealed bid auction in
terms of bidding strategies.
(d) Now suppose that Drexel is using a second-price, sealed-bid
auction. If there is only one
other bidder in the auction and you believe his valuation has
equal odds of being
anywhere from $100 to $300, what is your optimal bid? What is
your expected surplus?

11. (e) If there were more bidders in the second-price, sealed-bid
auction (and you believe that
all have valuations with equal odds of being anywhere from
$100 to $300), would that
increase, decrease, or not change your optimal bid relative to
what you solved for in part
(d)? Explain in words.
(f) Explain in words why an English auction is equivalent to a
second-price, sealed-bid
auction in terms of bidding strategies.