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Questions › GATE › GATE 2025 › Q38
1 markMicroeconomics › Consumer preferences and utility › Homothetic and quasilinear preferencesHardabout 3 min

GATE 2025 Question 38: Consumer preferences and utility

A Constant Elasticity of Substitution (CES) utility function is given as:

UCES(z1,z2)=1δ(z1δ+z2δ)U_{CES}(z_1,z_2) = \frac{1}{\delta}\left(z_1^\delta + z_2^\delta\right)UCES​(z1​,z2​)=δ1​(z1δ​+z2δ​)

where z1z_1z1​ and z2z_2z2​ are two goods, and δ≤1,δ≠0\delta \le 1, \delta \ne 0δ≤1,δ=0.

A Quasi-linear (QL) utility function is given as:

UQL(z1,z2)=2z1+log⁡z2U_{QL}(z_1,z_2) = 2z_1 + \log z_2UQL​(z1​,z2​)=2z1​+logz2​

where z1z_1z1​ and z2z_2z2​ are two goods.

Which of the following statements is/are NOT CORRECT?

Select all that apply.

Answer and worked solution

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Plain-text version

A Constant Elasticity of Substitution (CES) utility function is given as: U_(CES)(z₁,z₂) = 1/δ(z₁^δ + z₂^δ) where z₁ and z₂ are two goods, and δ ≤ 1, δ ≠ 0. A Quasi-linear (QL) utility function is given as: U_(QL)(z₁,z₂) = 2z₁ + log z₂ where z₁ and z₂ are two goods. Which of the following statements is/are NOT CORRECT? (A) The CES utility function is homothetic but the QL utility function is non-homothetic. (B) For δ = 1, the CES utility function is not strictly convex. (C) The Marginal Rate of Substitution (MRS_(z₁z₂)) for the CES utility function and the QL utility function are dependent on both z₁ and z₂. (D) If z₁ = z₂, the Marginal Rate of Substitution (MRS_(z₁z₂)) is 2 for both the CES and the QL utility functions.

Also written as: A Constant Elasticity of Substitution (CES) utility function is given as: U_(CES)(z_1,z_2) = 1/delta(z_1^(delta) + z_2^(delta)) where z_1 and z_2 are two goods, and delta <= 1, delta != 0. A Quasi-linear (QL) utility function is given as: U_(QL)(z_1,z_2) = 2z_1 + log z_2 where z_1 and z_2 are two goods. Which of the following statements is/are NOT CORRECT?

Consumer preferences and utility has come up 93 times in 7 exams since 2007.

What this question tests

This question is on Homothetic and quasilinear preferences, part of Consumer preferences and utility in Microeconomics.

Preferences whose expansion paths are straight lines (homothetic), or whose demand for one good ignores income (quasilinear).

TestStop has 5 past-paper questions on this subtopic.

Take this paper as a timed mockMore on Homothetic and quasilinear preferences

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