The dead-weight loss (allocative inefficiency)

Consider an (inverse) demand curve P = 30 - Q. And a total cost curve of C(Q) = 12Q.
(a) Assume a monopolist is operating in this market.
(i) Calculate the quantity (qM) chosen by a profit-maximizing monopolist.
(ii) At the profit-maximizing quantity, what is the monopolistic market price (pM) of the
product.
(iii) Calculate the dead-weight loss (allocative inefficiency) associated with this monopoly
market.

Sample Solution