Although one would expect electric cars and gasoline cars to be substitutes, business analysts argue that electric cars and gasoline cars can be complements, with the former being used for short distance trips and the latter for long distance trips. Consider the following model for the markets for these two types of cars. There are two firms, one selling gasoline cars and the other selling electric cars. Demand functions for the two firms are,

where and are the outputs of firm selling gasoline car and electric car respectively. The parameter measures the degree that the two goods are related in demand. If > 0 the goods are substitutes. If < 0 the goods are complements. Each firm has a constant marginal cost that is normalized to zero.

1. For the case where = 1,

(a) Find the Bertrand equilibrium prices and profits of each firm.

(b) Find the Cournot equilibrium prices, quantities and profits.

2. Re-do question 1 with = -1.

3. For the each of the two cases, = 1 and = -1, are the firms better of when they are competing in prices, or when they are competing in quantities?