1 markMicroeconomicsDemand theory and elasticityIncome elasticity, normal and inferior goods and Engel curvesModerateabout 2 min

IIT JAM 2021 Question 49: Demand theory and elasticity

A consumer's utility is $u(x_1, x_2) = x_1 + 2\sqrt{x_2}$ . At current prices and income the optimal bundle is $(x_1 = 10, x_2 = 10)$ . If income rises by 50% with prices unchanged, the optimal choice of $x_2$ is _______ (in integer).

Answer and worked solution

Answer: 10

With quasilinear utility, the optimality condition $\dfrac{1}{\sqrt{x_2}} = \dfrac{p_2}{p_1}$ fixes $x_2 = \left(\dfrac{p_1}{p_2}\right)^2$ , which does not depend on income.

The original optimum gives $x_2 = 10$ , and since prices are unchanged and $x_1$ stays positive, the extra income all goes to $x_1$ . So $x_2$ remains $10$ . The answer is $10$ .

Plain-text version

A consumer's utility is u(x₁, x₂) = x₁ + 2√(x₂). At current prices and income the optimal bundle is (x₁ = 10, x₂ = 10). If income rises by 50% with prices unchanged, the optimal choice of x₂ is _ (in integer).

Also written as: A consumer's utility is u(x_1, x_2) = x_1 + 2sqrt(x_2). At current prices and income the optimal bundle is (x_1 = 10, x_2 = 10). If income rises by 50% with prices unchanged, the optimal choice of x_2 is _ (in integer).

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.

IIT JAM 2022 · Q21An 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…

Take this paper as a timed mock More on Income elasticity, normal and inferior goods and Engel curves

Question from the IIT JAM 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.