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
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, ___ ___ ____ _____ ____ __________ ____ ___.
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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, ___ ___ ____ _____ ____ __________ ____ ___.
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