Question

The inverse market demand function for pizza is: P = 100 − Q

There are 115 fringe firms in the market and the total cost function for each is: Cf = 50qf

The total cost function for the dominant firm is: Cd = 10qd + 0.5qd^2

Calculate the market price, total market output and dominant firm's output respectively.

Answer 1

Given the cost function of each fringe firm is Cf = 50qf

=> MCf = 50; Then, supply curve of a firm is given by P = MCf = 50

Total supply curve is the horizontal summation of each individual firm

Since supply curve of a firm is P = 50 which is horizontal, horizontal summation of all 115 firm's supply curve is P = 50

Thus market supply S : P - 50 = 0

Demand curve for dominant firm qd = D - S

D : Q = 100 - P

qd = 100 - P - P + 50= 150 - 2P ; => 2P = 150 - qd; =>P = 75 - qd /2

=> MR = 75 - 2qd/2= 75 - qd

Since Cd = 10qd + 0.5qd2; =>MCd = 10 + qd

Given the optimal condition, set MR = MCd

=> 75 - qd = 10 + qd; =>75 - 10 = qd + qd; =>qd = 32.5

P = 75 - 32.5/2 = 75 - 16.25 = 58.75

Total market output Q = 100 - 58.75 = 41.25