Refer to the following information. Q=q1+q2 P=120-3Q Marginal Cost=12 NO FIXED C

Question

Refer to the following information.

Q=q1+q2

P=120-3Q

Marginal Cost=12

NO FIXED COSTS

MRa=120-6q1-3q2

MRb=120-3q1-6q2

Output: q1 & q2 = 12

Market Price = 48

Answer the following.

Suppose that Firm a chooses its output first. Firm b observes this choice and then Firm b chooses its output. If a firms total revenue is given be aq-bq^2 where q is the firm's quantity of output, then its Marginal Revenue = a-2bq

A. How mcuh output will each firm produce in Stackelberg equilibrium?

B. What will be the market price of the good?

C. What is the deadweight loss that results from this duopoly?

D. How much profit does each firm make?

Explanation / Answer

here A act as leader and b act as follower , hence b follow his own reaction function ;

reaction function of b is derived by proit maximizing equation of firm B , 120 - 3q1 - 6q2 = 12;

18 - 0.5q1 = q2 ;

substitute the q2 in profit equation of firm A .

profit (a) = (120 - 3q1 - 3q2 )(q1) - 12(q1) ;

= (120 -3q1 -54 +1.5q1)(q1) - 12(q1);

for profit max. differentiate above w.r.t. q1 ; and equate it to zero

66-3q1 -12 = 0 ;

54= 3q1 ;

q1 = 18 ;

hence q2 = 18 - 9 = 9 .

price = 120-3(9+18) = 120 - 81 = 39 ;

profit of firm A = 39*18 - 12*(18) = 486 ; ,

profit for firm B = 39*9 -12*9 = 243;

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