Problem Set 2

Question 1

a. Consider the game presented in Question 1 of PS1. Write down the normal form for two players, Ren and Chuck, two strategies (straight and ditch), and appropriate payoffs where going into the ditch is bad, but going straight when the other person goes straight is badder.

b. Does Ren have dominant strategy in this game?

c. What is the Nash equilibrium of the game?

Question 2

Consider the Hotelling model described below in R code.  The parameters are beta which determines how sensitive customers are to price.  The marginal cost of is c_L for Left firm and c_R for the Right firm.  Demand is given by the function q_L(p_L, p_R) and q_R(p_R, p_L) for Left and Right respectively.  The firm profits are given by pi_L(p_L) and pi_R(p_R).  Determine the Nash equilibrium prices {p_L^*, p_R^*}

beta <- 0.2

c_L <- 0.2

c_R <- 0.2

q_L <- function(p_L, p_R) {1 - beta*(p_L - p_R)}

q_R <- function(p_R, p_L) {1 - beta*(p_R - p_L)}

pi_L <- function(p_L) {(p_L - c_L)*q_L(p_L, p_R)}

pi_R <- function(p_R) {(p_R - c_R)*q_R(p_R, p_L)}

Question 3

Consider the problem in (2).  What happens if the cost of Left firm increases to 0.35?  What are the new Nash equilibrium prices?

Question 4

Given your answers above.  When the costs for the Left firm increased, was all of the cost increase passed through to customers in terms of higher prices?

Question 5

Using weekly price and margin retail gasoline data from Perth in 2008 estimate the demand parameters for each brand. Assume that market shares are equal to the number of stations each brand has and assume the outside option is equal to the number of stations that are independent or owned by the small brands, Mobile, Wesco and Better Choice.

Question 6

What would happen to prices if there was a merger between Caltex and BP? Can you estimate the size of the price increase?