Consider a monopolist with linear (inverse) demand p = a – bQ and cons

Consider a monopolist with linear (inverse) demand p = a – bQ and constant average and marginal cost, c. Derive the monopolist’s profit and the deadweight loss generated.

Show that in such cases of linear demand and constant average and marginal cost, the deadweight loss is 50% of the monopolist’s profits.

ANSWER

Profit = (a – bQ)Q – cQ
dProfit/dQ = a – 2bQ – c = 0
Q = (a – c)/2b
p = (a + c)/2
Profit = (a – c)2/4b
DWL = (a – c)2/8b