Question

A market with the inverse demand function p= 5-0.05xQd is supplied by a dominant firm (DF) and a competitiVe fringe (CF). The inverse supply function by the CF is p= 4+Qcf. Calculate the output level at which the residual demand function of DF has a kink

Answer 1

p = 5 - 0.05Qd  

0.05Qd = 5 - p

Qd = 100 - 20p

The supply function by the CF is

p = 4 + Q_CF

Q_CF = p - 4  

Residual demand function of DF

Q_DF = Qd - Q_CF

= 100 - 20p - (p - 4)

= 100 - 20p - P + 4

= 104 - 21p

Residual demand function of DF is Q_DF = 104 - 21p

Residual demand function of DF will have kink when p = 4

Q_DF = 104 - 21p

= 104 - 21(4)

= 104 - 84

= 20

so the output level at which residual demand function of DF has a kink is Q_DF = 20