Exercise 3 - Bertrand game with asymmetric qualities (a) Consider two firms 1 and 2 which have the same constant marginal cost c. They produce the same type of good, but all N consumers unanimously rank product 1 higher than product 2: the net utility associated with buying one unit of the good (consumers buy at most one unit) is given by: U1=V1-p1 and U2=V2-p2 respectively, with V1>v2. Firms play a simple one-shot game and compete in prices. (Q1) Find the equilibrium solution (or solutions) of the game: which prices are chosen at equilibrium? Which firm sells to consumers? (b) Consider the same setting as (a) above, but assume now that, whereas firm 1 produces a better product (as above, V1>v2), firm 2 is more cost-efficient, since its constant marginal cost is zero, whereas the constant marginal cost of firm 1 is cu>0. (22) Again, find the equilibrium solution(s) of the one-shot game where firms choose prices, and discuss. Exercise 3 - Bertrand game with asymmetric qualities (a) Consider two firms 1 and 2 which have the same constant marginal cost c. They produce the same type of good, but all N consumers unanimously rank product 1 higher than product 2: the net utility associated with buying one unit of the good (consumers buy at most one unit) is given by: U1=V1-p1 and U2=V2-p2 respectively, with V1>v2. Firms play a simple one-shot game and compete in prices. (Q1) Find the equilibrium solution (or solutions) of the game: which prices are chosen at equilibrium? Which firm sells to consumers? (b) Consider the same setting as (a) above, but assume now that, whereas firm 1 produces a better product (as above, V1>v2), firm 2 is more cost-efficient, since its constant marginal cost is zero, whereas the constant marginal cost of firm 1 is cu>0. (22) Again, find the equilibrium solution(s) of the one-shot game where firms choose prices, and discuss