Consider a Bertrand duopoly with two firms 1,2 who sell the same good that has

demand curve Q = 8 p if p < 8 and Q = 0 if p 8. Firm 1 has unit cost c1 = 2 and firm 2 has

unit cost c2 = 6. Firms 1,2 set prices p1, p2. If they set different prices, the firm which sets the

minimum price receives the demand at that price while its rival receives zero demand. If both

firms set the same price, they equally split the demand at that price.

(a) [4 points] Fix p2 = 7. Draw the profit of firm 1 as function of p1 and find all best responses of

firm 1 to p2 = 7.

(b) [4 points] Fix p1 = 5. Draw the profit of firm 2 as function of p2 and find all best responses of

firm 2 to p1 = 5.

(c) [2 points] Determine if (p1 = 5, p2 = 7) is a Nash Equilibrium of this Bertrand duopoly.