Consider a Cournot duopoly with two firms

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 = 18 − Q where Q = q1 + q2. The unit cost of firm 1 is c1 = 5 and the unit cost of firm 2 is c2 = 12. (a) [4 points] Drawing the best response functions in a diagram, identify Nash Equilibrium (NE) quantities of firms 1,2 and find their numerical values. (b) [4 points] Suppose firm 2 is constrained by capacity K2 = 1, while firm 1 has no capacity constraint. Draw the best response functions and find NE quantities of this capacity constrained duopoly. (c) [4 points] Suppose firm 1 is constrained by capacity K1 = 3, while firm 2 has no capacity constraint. Draw the best response functions and find NE quantities of this capacity constrained duopoly. (d) [4 points] Suppose both firms 1,2 are capacity constrained. Firm 1 is constrained by capacity K1 = 3 and firm 2 is constrained by capacity K2 = 1. 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. https://www.studyhelpus.com/Questions & Answers/consider-a-cournot-duopoly-with-two-firms/