Question

Firm A and Firm B are the only producers of Coffee in the market. The total cost functions for each firm are given as follow: TCF = QF^2 TCA = 120QA + 0.5QA^2 The market demand function of Coffee is given as follow: Q = 600 − P

i. Calculate the profit for each firm under Cournot equilibrium. (8 marks)

ii. After Christmas the demand for Coffee decreased sharply that the market demand function becomes: Q* = 450 − 1.5P In order to survive the two firms merged into a single firm and becomes monopoly in the market. What is the profit maximizing output level and price for Coffee now?

Answer 1

i) TCF=QF^2,TCA= 120QA+0.5QA^2 this gives TCB=(QA+QB)^2-120QA-0.5QA^2

Q=600-P, P=600-QA-QB

Profit(A)=(600-QA-QB)*QA-120QA-0.5QA^2,

For maximizing taking differential wrt QA and assuming QB constant

600-2QA-QB-120-QA=0 This gives QA=(480-QB)/3----(i)

Similarly Profit(B) =(600-QA-QB)*QB-(QA+QB)^2+120QA+0.5QA^2

Differentiating wrt QB with QA as constant gives,600-3QA-4QB=0 This gives QB=(600-3QA)/4

Putting value of QB in (i) we get QA=(480-(600-3QA)/4)/3 gives QA=88 and correspondingly QB= 84, P=600-84-88=428

Profit A=428*88-120*88-0.5*88^2=$23232

Profit B=428*84-172^2+120*88+0.5*88^2=$20800

ii)Q=450-1.5P Gives P=(450-Q)/1.5 TCF=Q^2

For Profit maximization , (450-Q)/1.5*Q-Q^2 differentiation wrt Q

(450-2Q)/1.5 -2Q=0 gives Q=90, Price =(450-90)/1.5=$240