Consider a Stackelberg duopoly with firms 1.2 where firm 1 is the leader and firm 2...

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Consider a Stackelberg duopoly with firms 1.2 where firm 1 is the leader and firm 2 the follower. Firm 1 moves first and chooses its quantity g₁. Firm 2 observes 91 and then chooses its quantity 92. The price p is given by the inverse demand p = 20 - Q where Q = 91 +92. Both firms have the same unit cost 4. (a) [4 points] Solving the problem of firm 2 (follower), determine best response of firm 2 to g₁. (b) [4 points] Taking the solution of the problem of firm 2 into account, solve the problem of firm 1 (leader) and find Stackelberg equilibrium quantities. Question 2 [12 points] Consider a Bertrand duopoly with two firms 1.2 who sell the same good that has demand curve Q = 16-p if p < 16 and Q = 0 if p≥ 16. Both firms have same constant unit cost 4. Firms 1,2 set prices pi. 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 = 3. Draw the profit of firm 2 as function of p2 and find all best responses of firm 2 to p1 = 3. (c) [4 points] Determine if (p1 = 3. p2 = 7) is a Nash Equilibrium (NE) of this Bertrand duopoly. Question 3 [16 points] Consider a Cournot duopoly with two firms 1.2. Let 9₁. 92 be the quantities produced by firms 1,2. The price p is given by the inverse demand p = 18 - Q where Q = 91 +92. The unit cost of firm 1 is c₁ = 12 and the unit cost of firm 2 is c₂ = 5. Consider a Stackelberg duopoly with firms 1.2 where firm 1 is the leader and firm 2 the follower. Firm 1 moves first and chooses its quantity g₁. Firm 2 observes 91 and then chooses its quantity 92. The price p is given by the inverse demand p = 20 - Q where Q = 91 +92. Both firms have the same unit cost 4. (a) [4 points] Solving the problem of firm 2 (follower), determine best response of firm 2 to g₁. (b) [4 points] Taking the solution of the problem of firm 2 into account, solve the problem of firm 1 (leader) and find Stackelberg equilibrium quantities. Question 2 [12 points] Consider a Bertrand duopoly with two firms 1.2 who sell the same good that has demand curve Q = 16-p if p < 16 and Q = 0 if p≥ 16. Both firms have same constant unit cost 4. Firms 1,2 set prices pi. 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 = 3. Draw the profit of firm 2 as function of p2 and find all best responses of firm 2 to p1 = 3. (c) [4 points] Determine if (p1 = 3. p2 = 7) is a Nash Equilibrium (NE) of this Bertrand duopoly. Question 3 [16 points] Consider a Cournot duopoly with two firms 1.2. Let 9₁. 92 be the quantities produced by firms 1,2. The price p is given by the inverse demand p = 18 - Q where Q = 91 +92. The unit cost of firm 1 is c₁ = 12 and the unit cost of firm 2 is c₂ = 5.

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