Which of the following describes a correct relation between price elasticity of demand and a monopolist's marginal revenue when inverse demand is linear, P = a-bQ?

Question

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When inverse demand is linear, the monopolist's marginal revenue, MR, can be expressed as follows: MR = a - 2bQ The monopolist's price elasticity of demand is related to MR as follows: If MR > 0, demand is elastic. If MR < 0, demand is inelastic. If MR = 0, demand is unit elastic. Since a and b are both positive (since P and Q are inversely related), we can see that MR is negative for all values of Q. Therefore, demand is always inelastic. However, the degree of inelasticity changes with Q. At lower values of Q (i.e. Q < a/2b), demand is relatively more elastic than at higher values of Q (i.e. Q > a/2b). Thus, the correct choice is D: Demand is elastic when Q < a/2b. When inverse demand is linear, the monopolist's marginal revenue can be represented as MR = a - 2bQ. To determine the elasticity of demand, we need to look at the absolute value of the price elasticity of demand, which is given by |(dQ/dP)*(P/Q)|. Using the linear demand function P = a - bQ, we can solve for Q and P in terms of elasticity: |(dQ/dP)*(P/Q)| = |-1/(b(Q/P))| = |1/(b(P/Q))| Q = (a - P)/b P = a - bQ |-1/(b(P/Q))| = |-(Q/P)|/(a - Qb) Therefore, elasticity depends on the value of Q, and will be elastic when Q is less than a/2b (i.e. Q < Qe), inelastic when Q is greater than a/2b (i.e. Q > Qe), and unit elastic when Q equals a/2b (i.e. Q = Qe). So, the correct answer is D, which states that demand is elastic when Q < a/2b.

Which of the Following Describes a Correct Relation Between Price Q>a/2bQ > a / 2 bQ>a/2b

Which of the Following Describes a Correct Relation Between Price $Q > a / 2 b$