Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › IIT JAM › IIT JAM 2022 › Q40
2 marksMicroeconomics › Monopoly and price discrimination › Lerner index and monopoly powerHardabout 3 min

IIT JAM 2022 Question 40: Monopoly and price discrimination

A monopolist faces demand Q=PeQ = P^{e}Q=Pe, where eee is the price elasticity of demand (e<−1e < -1e<−1), and Marginal Cost = Average Cost = α\alphaα. Let PCP_CPC​ and PMP_MPM​ be the prices under perfect competition and monopoly, and CSMCS_MCSM​, CSCCS_CCSC​ the consumer surplus under monopoly and perfect competition. Which is/are NOT correct?

Select all that apply.

Answer and worked solution

Answer: (A) and (C)

Under perfect competition price equals marginal cost, so PC=αP_C = \alphaPC​=α, not α(e1+e)\alpha\left(\dfrac{e}{1+e}\right)α(1+ee​); statement (A) is NOT correct. The monopoly markup rule MR=MCMR = MCMR=MC with constant elasticity gives PM=α1+1/e=α(e1+e)P_M = \dfrac{\alpha}{1 + 1/e} = \alpha\left(\dfrac{e}{1+e}\right)PM​=1+1/eα​=α(1+ee​), so (B) is correct.

With Q=PeQ = P^{e}Q=Pe, consumer surplus is P e+1−(e+1)\dfrac{P^{\,e+1}}{-(e+1)}−(e+1)Pe+1​, so CSMCSC=(PMPC)e+1=(e1+e)e+1\dfrac{CS_M}{CS_C} = \left(\dfrac{P_M}{P_C}\right)^{e+1} = \left(\dfrac{e}{1+e}\right)^{e+1}CSC​CSM​​=(PC​PM​​)e+1=(1+ee​)e+1. At e=−2e=-2e=−2 this equals 12≠1\tfrac12 \neq 121​=1, so CSM≠CSCCS_M \neq CS_CCSM​=CSC​ and (C) is NOT correct. As e→−1e \to -1e→−1 the ratio rises towards 1 (for example 0.410.410.41 at e=−5e=-5e=−5, 0.500.500.50 at e=−2e=-2e=−2, 0.790.790.79 at e=−1.1e=-1.1e=−1.1), so (D) is correct. The NOT-correct statements are (A) and (C).

The trap: (B) PM=α(e1+e)P_M = \alpha\left(\dfrac{e}{1+e}\right)PM​=α(1+ee​)

The markup formula α(e1+e)\alpha\left(\dfrac{e}{1+e}\right)α(1+ee​) genuinely gives the monopoly price, so it is correct for (B); the error in (A) is applying that markup to the competitive price, which should just equal marginal cost.

Plain-text version

A monopolist faces demand Q = P^e, where e is the price elasticity of demand (e < -1), and Marginal Cost = Average Cost = α. Let P_C and P_M be the prices under perfect competition and monopoly, and CS_M, CS_C the consumer surplus under monopoly and perfect competition. Which is/are NOT correct? (A) P_C = α(e/(1+e)) (B) P_M = α(e/(1+e)) (C) For e = -2, CS_M = CS_C. (D) For e closer to -1, the ratio CS_M/CS_C increases.

Also written as: A monopolist faces demand Q = P^e, where e is the price elasticity of demand (e < -1), and Marginal Cost = Average Cost = alpha. Let P_C and P_M be the prices under perfect competition and monopoly, and CS_M, CS_C the consumer surplus under monopoly and perfect competition. Which is/are NOT correct?

Monopoly and price discrimination has come up 128 times in 7 exams since 2004.

What this question tests

This question is on Lerner index and monopoly power, part of Monopoly and price discrimination in Microeconomics.

The mark-up of price over marginal cost and its link to the elasticity of demand.

TestStop has 12 past-paper questions on this subtopic.

Take this paper as a timed mockMore on Lerner index and monopoly power

Question from the IIT JAM 2022 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.