A monopolist can produce at constant average and marginal costs of AC = MC =
9. The firm faces a demand curve given by:
q = 75 – p
a. Calculate the profit‐maximizing price quantity combination for the
monopolist. Also calculate the monopolist’s profits.
b. What output would be produced by this industry under perfect competition?
Show that PM > PC and QC = 2QM.
AC = MC = 9, q = 75 – p
a. The profit‐maximizing quantity can be found in the point where MR = MC, and the price we can find from the demand curve: MR = TR' = (p*q)' = (75q - q^2)' = 75 - 2q MR = MC = 75 - 2q = 9 2q = 66 q = 33 units p = 75 - 33 = $42 Monopolist’s profit = (p - AC)*q = (42 - 9)*33 = $1089
b. Under perfect competition monopolist will produce output in the point, where demand equals marginal cost: p = MC = $9 q = 75 - 9 = 66 units So, PM > PC and QC = 66 = 2QM.