Question

3. There are two firms that compete according to Cournot competition. Fim 1 has a cost func tion Cia1) 318. Firm 2 has a cost function C2()3. These firms cannot discriminate, so there is just one price that is determined by the aggregate demand. The inverse demand equation is P Q) 300-0 Where total supply 0-2 (a) Setup the profit maximization problem for firm 1 with all necessary equations plugged in. (2 point) (b) Solve firm I's profit maximization peoblem for their best response equation qi2 (2 points) (c) Setup the profit maximization problem for firm 2 with all necessary equations plugged in. (2 point (d) Solve firm 2's profit maximization peoblem for their best respoase equation q2(g (2 points) (e) Graph the best response equations on the graph below. Clearly label your lines. Identify the equilibeium quantities. (4 points) 42 900 800 700 600 500 400 300 200 100 ฐา 100 200 300 400 500 600 700 800 900 12 (t) Use your best response equations to mathematically solve for the equilibrium quantities g.4, Q', equilibrium price p., and profit for each firm π, π (7 points) (g) Now assume the two firms are colluding. Setup the joint profit maximization for the colluding firms (also known as the joint monopoly or cartel problem). (2 points) (h) Solve the collusion profit maximization problem for equilibrium quantities q,4,Q', Remember the firms split their equilibrium. price p., and profit for each firm πǐ, joint profits equally so = π-形. (8 points)

Answer 1

Profit = Total Revenue - Total Cost

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