Question

If a monopolist is facing a linear demand equation, then the marginal revenue equation for a monopolist:

a. Has the same slope and twice the intercept.

b. Has the same intercept, and the same slope.

c. Is the derivative of the demand equation.

d. Has the same intercept and twice the slope.

Answer 1

Linear Demand of a monopolist is given by :

P = c - dQ where P = price, Q = quantity demand, c and d are constants and also c > 0 and d > 0 because Monopolist faces downward sloping demand curve.

Slope of demand curve = dP/dQ = -d

Intercept of demand curve will be the value of P when Q = 0

=> P = c - d*0 = c => P = c and hence intercept of demand curve = c

Marginal revenue(MR) = d(TR)/dQ = d(P*Q)/dQ = c - 2dQ, where TR = Total revenue = P*Q

Intercept of MR curve will be the value of MR when Q = 0

=> MR = c - 2d*0 = c => MR = c and hence intercept of MR curve = c

Hence Intercept of both demand curve and Marginal revenue curve is same

Slope of MR curve = d(MR)/dQ = -2d = 2*Slope of demand curve

Hence, Slope of MR curve is twice of Demand curve.

Hence, the correct answer is (d) Has the same intercept and twice the slope.