Question

6. Industry demand is given by:

     QD = 1000 - P

All firms in the industry have identical and constant marginal and average costs of $50 per unit.

1. If the industry is perfectly competitive, what will industry output be? What will be the equilibrium price? What profit will each firm earn?
2. Now suppose that there are five firms in the industry, and that they collude to set price. What price will they set? What will be the output of each firm? What will be the profit of each firm?

Answer 1

QD = 1000 - P

MC = AC = $50

a. In case of perfectly competitive Industry,

P = MC , So , P = $50

QD = 1000 - 50 = 950

So, Quantity demanded = 950

Profit = Total Revenue - Total cost = P*Q - AC*Q = (P - AC)*Q

Since P = AC , Hence

Profit = 0

b. If the five firm collude , then they will charge the monopoly price and produce the monopoly quantity.

      So, they will produce till MR = MC

             Total Revenue TR = P*Q = Q*(1000 - Q)

                MR = dTR/dQ = 1000 - 2Q

              Now. Putting , MR = MC    ,   1000 - 2Q = 50

                    Q = 950/2 = 475

Hence Price set , P = 1000 - Q = 1000 - 475 = 525

Output of each firm q = Q/5 = 475/5 = 95

Profit = Total Revenue - Total cost = P*q - AC*q = (P - AC)*q = (525 - 50)*95 = 475*95

S0, Profit = $45125