Question

Suppose there is a market with a big firm and many small price-taking firms (DFCF). Given that the inverse market demand function is ?=100−??p=100−Qd, the inverse supply function for small firms is ?=70+???p=70+Qcf and the marginal cost function of the dominant firm is ??=10+1/4⋅???MC=10+1/4⋅qdf. Calculate the equilibrium output of the dominant firm. Round your answer to the first decimal place.

Answer 1

The inverse market demand function is

p = 100 - Q_d

direct market demand function is

Q_d = 100 - p

The inverse supply function for a small firm is

p = 70 +Q_cf  

direct supply function of a small firm is

Q_cf = p - 70

The demand function for dominant firm is given as

q = Q_d - Q_cf

q_df = 100 - p - (p - 70)

q_df = 100 - p - p + 70

q_df = 170 - 2p

2p = 170 - q_df  

p = 85 -  q_df /2  

The inverse demand function for dominant firm is

p = 85 -  q_df /2  

MR = 85 - q_df

MC = 10 +  q_df /4

MR = MC  

85 - q_df = 10 + q_df /4

85 - 10 =  q_df +  q_df /4

75 = 5q_df /4

300 = 5q_df

q_df = 60

The equilibrium output of dominant firm is q_df = 60