Penn ECON 402 Assignment 2 – Based on lecture 3&4

Penn ECON 402 Assignment 2 – Based on lecture 3&4

Subject: Economics    / General Economics
Question
Econ 402, Spring 2017
Assignment 2 – Based on lecture 3&4
Question 1
There is a collection of n NGOs operating in the health sector of a country, where n?3. Each NGO
can choose either to invest in a large-scale and collaborative project with other NGOs, or invest in
an independent, small-scale, project where the NGO does not have to collaborate with other
NGOs.
A small-scale project is always successful and gives the NGO a payoff of S. For the large-scale
project to succeed, at least m NGOs have to invest in it (where 2?m<n). If the large-scale project is
successful, the value that it generates is L, which is evenly divided between the collaborating NGOs.
Assume that L/n > S > 0. If the large-scale project fails, each collaborating NGO gets 0.
a) Describe the normal form of this game
b) Find the BR function for an NGO.
c) Find all NE (in pure strategies).
Question 2 – Complementary Monopoly
A firm sells vacation packages consisting of a plane trip and a hotel stay. Demand for complete
vacations is given by q(pv) = 100 – pv, where pv is the total price of the vacation. That is, pv = ph +
pa, where ph and pa are the prices of the hotel stay and plane trip, respectively. Let ch be the cost of
each hotel stay and ca be the cost of each plane trip.
a) Suppose the firm chooses pv in order to maximize total profit. How much should it charge
for each vacation? How many vacations are sold? What is its profit? (Note that profits ? =
p*q-c)
b) Suppose that the hotel division and airline division are run by separate managers, each of
whom cares only about the profit earned by his own division. Given that the hotel division
charges ph, what price would the airline division charge (i.e., what price maximizes profit
earned by the airline division)? Note: your answer will give pa as a function of ph.
c) Derive the Nash equilibrium prices in the game played between the managers of the two
divisions. What are the corresponding quantities and profits? Question 3 – Revisiting Hotelling’s Model
Two political parties, Left wing and Right wing compete in electoral elections. There is a continuum
of voters uniformly distributed on the interval [0, 1] where 0 represents the leftmost view (extreme
left) and 1 the rightmost. Each party can declare that their view is x where 1 ? ? and each
voter votes to the party that declare that their views are closest to his views. For example, if a voter’s
view is represented by 0.3, the left party chose 1/4 and the right party chose 1/2, this voter votes for
the left party as 1/4 is closer to 0.3. If both parties choose the same spots they will split the votes
between them.
Each party’s objective is to have the highest percentage of voters voting for it. To clarify: they care
about the number of votes they get, not just about getting a majority.
i) Describe the normal form of the game (players, strategies, payoffs). ii) Solve the game using (pure strategy) Nash equilibrium.