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Questions › IIT JAM › IIT JAM 2022 › Q21
2 marks, −0.667Microeconomics › Demand theory and elasticity › Income elasticity, normal and inferior goods and Engel curvesModerateabout 2 min

IIT JAM 2022 Question 21: Demand theory and elasticity

An analyst estimated the demand function QE=0.75−1.5PE+2.5PF−0.5PB+3.2IQ_E = 0.75 - 1.5P_E + 2.5P_F - 0.5P_B + 3.2IQE​=0.75−1.5PE​+2.5PF​−0.5PB​+3.2I, where QEQ_EQE​ is electric vehicles (thousand per year), PEP_EPE​, PFP_FPF​, PBP_BPB​ are unit prices (Rs. lakh) of the EV, a fossil-fuel vehicle and the battery, and III is personal disposable income (Rs. lakh). At PE=6.5P_E=6.5PE​=6.5, PF=4.5P_F=4.5PF​=4.5, PB=0.5P_B=0.5PB​=0.5, I=10I=10I=10, the income elasticity eQEIe_{Q_E I}eQE​I​ and the cross price elasticity eQEPFe_{Q_E P_F}eQE​PF​​ satisfy

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Answer and worked solution

Answer: (D)

At the given values QE=0.75−1.5(6.5)+2.5(4.5)−0.5(0.5)+3.2(10)=34Q_E = 0.75 - 1.5(6.5) + 2.5(4.5) - 0.5(0.5) + 3.2(10) = 34QE​=0.75−1.5(6.5)+2.5(4.5)−0.5(0.5)+3.2(10)=34 (thousand per year).

Income elasticity eQEI=∂QE∂I⋅IQE=3.2⋅1034=0.941e_{Q_E I} = \dfrac{\partial Q_E}{\partial I}\cdot\dfrac{I}{Q_E} = 3.2\cdot\dfrac{10}{34} = 0.941eQE​I​=∂I∂QE​​⋅QE​I​=3.2⋅3410​=0.941. Cross price elasticity eQEPF=∂QE∂PF⋅PFQE=2.5⋅4.534=0.331e_{Q_E P_F} = \dfrac{\partial Q_E}{\partial P_F}\cdot\dfrac{P_F}{Q_E} = 2.5\cdot\dfrac{4.5}{34} = 0.331eQE​PF​​=∂PF​∂QE​​⋅QE​PF​​=2.5⋅344.5​=0.331. Both land in the ranges of option (D).

The trap: (C) 0.98≤eQEI≤0.990.98 \le e_{Q_E I} \le 0.990.98≤eQE​I​≤0.99 and 0.45≤eQEPF≤0.460.45 \le e_{Q_E P_F} \le 0.460.45≤eQE​PF​​≤0.46

Using the wrong base quantity (for example forgetting to compute QE=34Q_E=34QE​=34 first) shifts both elasticities; the cross-price value in particular must use PFP_FPF​ and QEQ_EQE​, not PEP_EPE​.

Plain-text version

An analyst estimated the demand function Q_E = 0.75 - 1.5P_E + 2.5P_F - 0.5P_B + 3.2I, where Q_E is electric vehicles (thousand per year), P_E, P_F, P_B are unit prices (Rs. lakh) of the EV, a fossil-fuel vehicle and the battery, and I is personal disposable income (Rs. lakh). At P_E=6.5, P_F=4.5, P_B=0.5, I=10, the income elasticity e_(Q_E I) and the cross price elasticity e_(Q_E P_F) satisfy (A) 0.98 ≤ e_(Q_E I) ≤ 0.99 and 0.33 ≤ e_(Q_E P_F) ≤ 0.34 (B) 0.94 ≤ e_(Q_E I) ≤ 0.95 and 0.45 ≤ e_(Q_E P_F) ≤ 0.46 (C) 0.98 ≤ e_(Q_E I) ≤ 0.99 and 0.45 ≤ e_(Q_E P_F) ≤ 0.46 (D) 0.94 ≤ e_(Q_E I) ≤ 0.95 and 0.33 ≤ e_(Q_E P_F) ≤ 0.34

Demand theory and elasticity has come up 161 times in 7 exams since 2004.

What this question tests

This question is on Income elasticity, normal and inferior goods and Engel curves, part of Demand theory and elasticity in Microeconomics.

How demand responds to income, how goods are classified by that response, and Engel's law.

TestStop has 33 past-paper questions on this subtopic; the nearest in year are below.

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