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 ____ ________ _____ ________ __________ ___ ____ _______.
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