Question

Market demand is given by P=14-(q_i+q_e), where is the output of the incumbent frim and is the output of a potential entrant into the market. The incumbent firm’s total cost function is TC=2q_i where as the cost function for the entrant is TC=9+2q_e a)Derive the best response function for each firm b)Calculate the Cournot equilibrium output for each firm c)Estimate the industry output and then find the market clearing price d)Calculate the profit for each firm

Answer 1

P=14-(qi+qe)

TC1= 2qi

TC2=9+2qe

Reaction curve for firm 1

= MR1=MC1

(14qi-qi2-qiqe)/qi=2qi/qi

14-2qi-qe=2

= qi=12-2=6+(qe/2)

Reaction curve for firm 2

(14qe-qiqe-qe2)/qq=(9+2qe)/qe

=14-qi-2qe=2

= 2qe=12+qi

= qe= 6+(qi/2)

b) output for each firm can be derived by putting one value in other

= qi=6+(qe/2) so by replacing the value of qe

= qi= 6+1/2[6+1/2qi]

=qi=12, qe=12

P=14-(12+12)=10

Q= 24

c) TR-TC

=10*24-24= 116 profit for firm 1

240-[9+(2*12)=207 profit for firm 2