Consider a Cournot duopoly market with two identical firms, i: 1,2.Market Demand is P = 10 - Q where Q = q₁+ q₂.

Both firms have a constant marginal cost of MC_i= 2.

a. Derive the best response function for each firm.

b. Derive the Cournot-Nash equilibrium output, i.e. q₁and q₂.

c. Derive the equilibrium price.

d. What are the Cournot equilibrium price and aggregate output if there are three identical firms in this market (rather than 2 as assumed under a-c).

e. What would be the market price and the aggregate equilibrium output if there are an infinite number of identical firms in this market?

f. What would be the equilibrium prices P₁, P2 and the aggregate output Q if there are only two firms in the market, but the firms compete inprices?