Bertrand model - Identical products
EXERCISE 1: -
Suppose total demand is P = 100?2Q
the costs of company 1 are C1(Q1) = 10Q1
Firm 2's costs are C2(Q2) = 10Q2
a) Does (P?1, P?2) = (55, 55) is a set of Nash equilibrium prices in Bertrand?(assume they would split the demand if they had the same price)
b) Compute the set of Nash equilibrium prices. Briefly explain why this is an equilibrium by Nash.
EXERCISE 2: - Bertrand model: Identical products Since the total demand is P = 10 ? Q the costs of companies 1 and 2 are respectively:
C1(Q1) = Q1
C2(Q2) = 2Q2
Compute the set of Nash equilibrium prices.
Also, calculate the resulting output and profit