Reference no: EM133084015

Consider a Cournot duopoly with two firms 1,2. Let q1, q2 be the quantities produced by firms 1,2. The price p is given by the inverse demand p = 24 - Q where Q = q1 + q2. The unit cost of firm 1 is c1 = 2 and the unit cost of firm 2 is c2 = 14.

(a) Drawing the best response functions in a diagram, identify Nash Equilibrium (NE) quantities of firms 1,2 and find their numerical values.

(b) Suppose firm 1 is constrained by capacity K = 8, while firm 2 has no capacity constraint. Draw the best response functions and find NE quantities of this capacity-constrained duopoly.

(c) Suppose firm 2 is constrained by capacity K = 3, while firm 1 has no capacity constraint. Draw the best response functions and find NE quantities of this capacity-constrained duopoly.

(d) Suppose both firms 1,2 are capacity constrained. Firm 1 is constrained by capacity K1 = 8 and firm 2 is constrained by capacity K2 = 3. Draw the best response functions and find NE quantities of this capacity-constrained duopoly.

You can use the following result without proving it

For a Cournot duopoly with inverse demand p = a - Q, where firm 1 has unit cost c1 and firm 2 has unit cost c2, the best response functions are given as follows.

Best response of firm 1 (BR1) to q2 is: choose q1 = (a - c1 - q2)/2 if q2 < a - c1 and choose q1 = 0 if q2 ≥ a - c1.

Best response of firm 2 (BR2) to q1 is: choose q2 = (a - c2 - q1)/2 if q1 < a - c2 and choose q2 = 0 if q1 ≥ a - c2.