Question
An individual consumer consumes two commodities X₁ & X₂. The utility function is
The price of commodity one is P₁ = Rs.3.00, the price of commodity two is P₂ = Rs.4.00, the individual's income per period is Rs.108. Determine the utility maximizing level of X₁ & X₂ and derive the demand curves for the two commodities.
Answer :
Word Count : 362
The consumer maximizes utility subject to the budget constraint. The problem is: Utility function: [ U = X_1^{0.4} X_2^{0.6} ] Budget constraint: [ P_1 X_1 + P_2 X_2 = I \quad \Rightarrow \quad 3X_1 + 4X_2 = 108 ] Step 1: Set up the Lagrangian: [ \mathcal{L} = X_1^{0.4} X_2^{0.6} + \lambda (108 - 3X_1 - 4X_2) ] Step 2: _______ ____ _______ _______ ______ ________.
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The consumer maximizes utility subject to the budget constraint. The problem is: Utility function: [ U = X_1^{0.4} X_2^{0.6} ] Budget constraint: [ P_1 X_1 + P_2 X_2 = I \quad \Rightarrow \quad 3X_1 + 4X_2 = 108 ] Step 1: Set up the Lagrangian: [ \mathcal{L} = X_1^{0.4} X_2^{0.6} + \lambda (108 - 3X_1 - 4X_2) ] Step 2: _______ ____ _______ _______ ______ ________.
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