Question

g Consider three firms that face market demand P = 101 - Q. The cost functions are c_1(q_1)=5q_1^2 for firm 1, c_2(q_2)=3q_2^2 for firm 2, and c_3(q_3)=3q_3^2 for firm 3. Firm 1 is the Stackelberg leader and firms 2 and 3 are the followers. What is firm 1's equilibrium output q_1^*?

Answer 1

The firms equilibrium output is given as:

q_1 = 0.2c_1

Step-by-step explanation:

Given the cost function for firm 1 is

c_1(q_1) = 5q_1^2

The firms equilibrium output is given as follows:

c_1 = 5q_1

q_1 = (1/5)c_1

= 0.2c_1