Consider a monopolist who faces the following demand functio

Consider a monopolist who faces the following demand function: P-10-Q. Which of the following statements is true about the monopolist\'s marginal revenue (MR)? O MR>0 when Q

Solution

(1) Option (2)

P = 10 - Q

Total revenue (TR) = P x Q = 10Q - Q2

MR = dTR/dQ = 10 - 2Q

When MR = 0, we have 10 - 2Q = 0

2Q = 10

Q = 5

(2) Option (2)

P = 10 - Q, therefore Q = 10 - P

Elasticity = (dQ/dP) x (P/Q) = - 1 x (10 - Q) / Q = (Q - 10) / Q = 1 - (10 / Q)

(3) Option (3)

MR = Price x [1 - (1/ (-E))] where E: Elasticity of demand

When Elasticity = - 1,

MR = Price x [1 - (1 / 1)] = Price x (1 - 1) = Price x 0 = 0

Therefore, when Elastiity > - 1, MR > 0 and when Elasticity < - 1, MR < 0.