IGNOU BECC 115 2024 2025 - Consider the following Cobb-Douglas utility functionU(X1, X2)= X12

Question

Consider the following Cobb-Douglas utility function

U(X1, X2)= X12X22

P₁= 10, P2= 5

Where x₁ and x₂ are the two goods and P₁ and P₂ are their respective prices.

(i) Determine the optimal choice of consumption of x1 and x2

(ii) Find the expression for Indirect Utility Function

03 Mar 2026

Answer :

Word Count : 395

To determine the optimal consumption bundle for the Cobb-Douglas utility function ( U(X_1, X_2) = X_1^2 X_2^2 ) with prices ( P_1 = 10 ) and ( P_2 = 5 ), we begin by setting up the consumer’s budget constraint. Let the consumer have income ( I ). The budget constraint is: [ P_1 X_1 + P_2 X_2 = I \implies 10 X_1 + 5 X_2 = I ] The Cobb-Douglas utility function can be expressed as ( U(X_1, X_2) = X_1^2 X_2^2 ). In general, for a Cobb-Douglas utility function of the form ( U(X_1, X_2) = X_1^a X_2^b ), the optimal consumption is given by allocating expenditure proportionally according

___ ____ _________ _____ _______ _____ ___ _________ ______.
_____ ___ __________ ___ _____ ________ ______ ______ _______ ________.
__________ ________ ________ ____ ______ _______ _______ ______ _________ __________ ________.
_________ ____ ______ ____ __________ _________ _________.
________ ____ ________ ________ ___.
______ ____ ______ __________ _________ ____ ________.
___ ______ ________ ___ ___ __________ ________ ____ ___ ____.
______ _____ _____ _________ _______ ___ _________ _______ _________ ________.
___ ______ _________ _______ ___ _________ ______ ___.
____ __________ ______ _________ ______ __________ ___.
____ ______ _____ _________ ________ ________ ________ _______ _______ ___ _______ ___.
________ ___ _________ ___ _____ _________ ________ _________.
______ ______ _______ __________ _____ _______ _____ ________.
_____ ___ _____ ________ _________ __________.
______ _______ __________ ______ _____ ________ _______ _____.
_________ _______ _____ ___ __________ ________ ____ ___ _____.
__________ __________ ______ ___ ________ _____ __________ ______ _______ ____ ________.
_____ _____ ____ __________ ____ ____.
___ __________ _________ ___ ________ ________ _________.
___ _______ ____ ______ _________ ______ _________ ________ ________ ________.
____ ______ ____ _____ ___ _________.
______ __________ _______ ________ _________ _______ _________ ______ _________.
___ ________ ______ _______ _________ __________ _______.
_________ ___ ______ __________ __________.
_________ ______ __________ __________ _______ ___ ______ ________ __________.
__________ ________ ____ ______ _______ ____ ______.
_____ ____ ________ _________ _______ ___ _______ _______ __________ ___.
________ ____ __________ ______ _________ ___ __________.
_________ _____ ________ ________ _________ ____ _________ ___.
_______ _______ _______ __________ _____ ________ ________ ___ __________.
_________ ____ __________ ___ ________ ___ __________ _____ ______ _____.
_______ ________ ___ ____ ___.
_____ _______ ________ _________ _____ ________ ____ __________ ___ _____ _________ ________.
_________ _____ _________ _______ _______.
_________ _______ ________ __________ ________ _______.

IGNOU ACADEMY

Your IGNOU journey, made easier.

Solved Assignments
Study Notes
Guess Papers
Question Papers

Call Us WhatsApp

STUDY • PREPARE • SUCCEED

Skip in 10