(Cournot Duopoly) Two firms, A and B, are in Cournot (quantity) competition making identical products. Each firm has zero fixed cost and constant marginal cost of $10 per unit of output. The market price is given by P = 130Q, where Q = QA +QB.

a) (4pts) Find Firm A's best response function, i.e. optimal output QA as a function of QB. Hint: write Firm A's profit as a function of QA and QB, then take derivative with respect to QA!

b) (3pts) Use symmetry to find Firm B's best response function. Then combine the two best response functions to find Cournot-Nash equilibrium (QA,QB).

c) (3pts) How much is the price at equilibrium? How much profit each firm makes in equilibrium?

4. (10pts) (Cournot Duopoly) Two firms, A and B, are in Cournot (quantity) competition making identical products. Each firm has zero fixed cost and constant marginal cost of $10 per unit of output. The market price is given by P = 130 -Q, where Q = QA + QB. a) (4pts) Find Firm A's best response function, i.e. optimal output QA as a function of QB. Hint: write Firm A's profit as a function of Q A and QB, then take derivative with respect to QA! b) (3pts) Use symmetry to find Firm B's best response function. Then combine the two best response functions to find Cournot-Nash equilibrium (QA, QB). c) (3pts) How much is the price at equilibrium? How much profit each firm makes in equilibrium