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 : 627
To solve this utility maximization problem, we need to find the optimal quantities of the two commodities \( X_1 \) and \( X_2 \) that maximize the consumer's utility subject to the budget constraint. ### Step 1: Write the utility function and budget constraint The utility function is: \[ U = X_1^{0.4} \cdot X_2^{0.6} \] The budget constraint is given by: \[ P_1 X_1 + P_2 X_2 = I \] where: - \( P_1 = 3 \) (price of commodity 1), - \( P_2 = 4 \) (price of commodity 2), - \( I = 108 \) (income). This becomes: \[ 3X_1 + 4X_2 __________ _________ _______ __________ _________ ______ ___ ________ ___ ________ __________ _____.
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To solve this utility maximization problem, we need to find the optimal quantities of the two commodities \( X_1 \) and \( X_2 \) that maximize the consumer's utility subject to the budget constraint. ### Step 1: Write the utility function and budget constraint The utility function is: \[ U = X_1^{0.4} \cdot X_2^{0.6} \] The budget constraint is given by: \[ P_1 X_1 + P_2 X_2 = I \] where: - \( P_1 = 3 \) (price of commodity 1), - \( P_2 = 4 \) (price of commodity 2), - \( I = 108 \) (income). This becomes: \[ 3X_1 + 4X_2 __________ _________ _______ __________ _________ ______ ___ ________ ___ ________ __________ _____.
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