A monopoly's marginal revenue curve is always:

A. is always above the demand curve.

B. identical to that of a perfectly competitive firm.

C. twice as steep as the demand curve.

D. None of the above.

C. twice as steep as the demand curve.

• A linear market demand function that a monopolist faces is given as P=a−bQP=a−bQ where P is the good's price and Q is the quantity demanded.

Total revenue equals price times quantity:

• TR=P×QTR=(a−bQ)×QTR=aQ−bQ2TR=P×QTR=(a−bQ)×QTR=aQ−bQ2

Marginal revenue, MR, equals the derivative of total revenue taken with respect to quantity

• MR=dTRdQMR=a−2bQMR=dTRdQMR=a−2bQ

We can compare the marginal revenue equation with demand equation. They have the same intercept (a) but the slope of the marginal revenue (-2b) is twice as steep as the demand curve (-b).

Hence a monopoly's marginal revenue curve is always twice as steep as the demand curve.