A monopolist faces inverse demand P = a - bQ. The monopolist's marginal revenue function is:

Question

Quizplus · Accepted Answer

The marginal revenue (MR) of a monopolist is given by the derivative of its total revenue (TR) with respect to quantity (Q). 
TR = P × Q = (a - bQ)Q = aQ - bQ² 
Taking the derivative of TR with respect to Q gives: 
MR = dTR/dQ = a - 2bQ, which is option C. The monopolist's marginal revenue function can be found by taking the derivative of the inverse demand function: 
P = a - bQ 
MR = dP/dQ = -b 
Therefore, MR = a - 2bQ is the correct answer. Option A is actually the inverse demand function, not the marginal revenue function. Option B is incorrect because it assumes a constant marginal cost, which is not specified in the question. Option D is incorrect because it is not a valid function of MR.

A Monopolist Faces Inverse Demand P = a - BQ MR=a−bQM R = a - b QMR=a−bQ

A Monopolist Faces Inverse Demand P = a - BQ $M R = a - b Q$