Question

A firm with market power has an inverse demand curve of P = 450 - 5Q and marginal cost of MC = 400, where Q is measured in thousands. What is the deadweight loss from market power at the firm's profit-maximizing output level? $15,000 $280,000 $22.500 $9.400

Answer 1

40Q. With the Given that the inverse demand curve is P 450-5Q and the marginal cost is given inverse demand curve, the total revenue curve is derived by multiplying the price with the quantity. Therefore, the total revenue function will become TR PxQ (450-5Q)xQ 450Q-50 Marginal Revenue (MR) quantity. Therefore, MR will be MR = 450-10Q can be derived by differentiating the TR curve with respect to A monopolist produces at the point where the MR is equal to the MC. Thus MR MC 450-10Q 40Q 450 50Q Q =9 At this quantity, price will be P 450-50 =450-5(9) -450-45 P 405 The deadweight is loss below as the green shaded area:

Price MC 405 360 AR 10 Quantity MR In the above diagram, to calculate the deadweight loss, curve intersects the MC curve. Since AR and price we need the quantity where the AR curve are same, AR MC 450-50 40Q 450 450 Q 10 Also to the value of MR at 9 units of output, therefore, need a price which is equal we MR 450-10Q =450-10(9) =450-90 360 follows Using the above information, deadweight loss is calculated as

Deadweight loss Area of shaded triangle -x(405-360)x(10-9) =-x45x1 =22.5 Since the values are in thousands, the deadweight loss is equal to option C) $22,500.