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Questions › IIT JAM › IIT JAM 2022 › Q36
2 marksMicroeconomics › Perfect competition › Market equilibrium and comparative staticsHardabout 3 min

IIT JAM 2022 Question 36: Perfect competition

Demand QxD=f(Px,I)Q_x^D = f(P_x, I)QxD​=f(Px​,I) and supply QxS=g(Px,A)Q_x^S = g(P_x, A)QxS​=g(Px​,A), where III (income) and AAA (advertisement) are exogenous. Given ∂f∂Px<0\dfrac{\partial f}{\partial P_x} < 0∂Px​∂f​<0, ∂g∂Px>0\dfrac{\partial g}{\partial P_x} > 0∂Px​∂g​>0, while ∂f∂I\dfrac{\partial f}{\partial I}∂I∂f​ and ∂g∂A\dfrac{\partial g}{\partial A}∂A∂g​ may take any sign, and an equilibrium QxD=QxS=QQ_x^D = Q_x^S = QQxD​=QxS​=Q exists, which is/are CORRECT?

Select all that apply.

Answer and worked solution

Answer: (A) and (B)

Differentiate the equilibrium f(Px,I)=g(Px,A)f(P_x,I) = g(P_x,A)f(Px​,I)=g(Px​,A) with respect to AAA holding III fixed: ∂f∂PxdPxdA=∂g∂PxdPxdA+∂g∂A\dfrac{\partial f}{\partial P_x}\dfrac{dP_x}{dA} = \dfrac{\partial g}{\partial P_x}\dfrac{dP_x}{dA} + \dfrac{\partial g}{\partial A}∂Px​∂f​dAdPx​​=∂Px​∂g​dAdPx​​+∂A∂g​, giving dPxdA=∂g/∂A∂f/∂Px−∂g/∂Px\dfrac{dP_x}{dA} = \dfrac{\partial g/\partial A}{\partial f/\partial P_x - \partial g/\partial P_x}dAdPx​​=∂f/∂Px​−∂g/∂Px​∂g/∂A​, which is statement (B).

Multiplying by APx\dfrac{A}{P_x}Px​A​ and inserting PxQ\dfrac{P_x}{Q}QPx​​ into numerator and denominator turns this into the elasticity in statement (A), which is therefore also correct. Statement (C) uses ∂g∂I\dfrac{\partial g}{\partial I}∂I∂g​, but ggg does not depend on III, so it is meaningless. Statement (D) is false because ∂g∂A\dfrac{\partial g}{\partial A}∂A∂g​ is the numerator of dPxdA\dfrac{dP_x}{dA}dAdPx​​ and clearly determines its sign. The correct statements are (A) and (B).

The trap: (C) ePxI=(∂g∂IIQ)/(∂f∂PxPxQ−∂g∂PxPxQ)e_{P_x I} = \left(\dfrac{\partial g}{\partial I}\dfrac{I}{Q}\right) \Big/ \left(\dfrac{\partial f}{\partial P_x}\dfrac{P_x}{Q} - \dfrac{\partial g}{\partial P_x}\dfrac{P_x}{Q}\right)ePx​I​=(∂I∂g​QI​)/(∂Px​∂f​QPx​​−∂Px​∂g​QPx​​)

Statement (C) borrows the advertisement result but wrongly attaches ∂g∂I\dfrac{\partial g}{\partial I}∂I∂g​; income shifts demand (fff), not supply (ggg), so the income comparative static must use ∂f∂I\dfrac{\partial f}{\partial I}∂I∂f​.

Plain-text version

Demand Qₓ^D = f(Pₓ, I) and supply Qₓ^S = g(Pₓ, A), where I (income) and A (advertisement) are exogenous. Given (∂ f)/(∂ Pₓ) < 0, (∂ g)/(∂ Pₓ) > 0, while (∂ f)/(∂ I) and (∂ g)/(∂ A) may take any sign, and an equilibrium Qₓ^D = Qₓ^S = Q exists, which is/are CORRECT? (A) e_(Pₓ A) = ((∂ g)/(∂ A)A/Q) / ((∂ f)/(∂ Pₓ)Pₓ/Q - (∂ g)/(∂ Pₓ)Pₓ/Q) (B) dPₓ/dA = ((∂ g)/(∂ A)) / ((∂ f)/(∂ Pₓ) - (∂ g)/(∂ Pₓ)) (C) e_(Pₓ I) = ((∂ g)/(∂ I)I/Q) / ((∂ f)/(∂ Pₓ)Pₓ/Q - (∂ g)/(∂ Pₓ)Pₓ/Q) (D) The sign of dPₓ/dA does not depend on (∂ g)/(∂ A).

Also written as: Demand Q_x^D = f(P_x, I) and supply Q_x^S = g(P_x, A), where I (income) and A (advertisement) are exogenous. Given (d f)/(d P_x) < 0, (d g)/(d P_x) > 0, while (d f)/(d I) and (d g)/(d A) may take any sign, and an equilibrium Q_x^D = Q_x^S = Q exists, which is/are CORRECT?

Perfect competition has come up 115 times in 7 exams since 2006.

What this question tests

This question is on Market equilibrium and comparative statics, part of Perfect competition in Microeconomics.

Finding equilibrium from demand and supply and tracing how it moves when either curve shifts.

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