Acura and Volvo offer warranties on their automobiles, where wA is the number of years of an Acura warranty and wV is the number of years of a Volvo warranty. The revenue for Firm i, i = A for Acura and V for Volvo, is Ri = 27,000w/(wA + wV). Its cost of providing the warranty is Ci = 2,000wi. Acura and Volvo participate in a warranty setting game in which they simultaneously set warranties.
a. What is the profit function for each firm?
b. Suppose Acura and Volvo can set warranties in year lengths only, with a maximum of five years. Fill in a 5 × 5 payoff matrix with Acura's and Volvo's profits.
c. Determine the Nash equilibrium warranties.
d. Compare the Nash equilibrium warranties. If the two manufacturers offer the same warranty, explain why. If they offer different warranties, explain why.
e. Suppose Acura and Volvo collude in setting warranties. What warranties do they set?
f. Suppose Acura's cost of offering warranties decreases to CV = 1,000wV. What is the new Nash equilibrium? Explain the effect of the decrease in Volvo's cost function on the equilibrium warranties.