Question

An individual's utility function for two goods - milk (M) and butter (B) is given as \( U(M,B) = 5M - 10B \), and the cost of each unit of the two goods is Rs 1, with a weekly budget of Rs 5. Find the individual's utility maximizing choice.

• A. 2.5 units of M and 2.5 units of B
• B. 0 unit of M and 5 units of B
• C. 5 units of M and 5 units of B
• D. 5 units of M and 0 unit of B

Hint:

Maximize utility by substituting the budget constraint into the utility function and solving for the optimal quantities.

Answer 1

The Correct Option is A

Stage 1: Financial limitation and usefulness enhancement. The financial limitation is: \[M + B = 5\]. To enhance usefulness, the individual selects values for \( M \) and \( B \) that maximize \( U(M,B) = 5M - 10B \), adhering to the financial limitation.

Stage 2: Determine ideal quantities. Replacing \( B \) with \( 5 - M \) in the usefulness function yields: \[U(M) = 5M - 10(5 - M) = 5M - 50 + 10M = 15M - 50\]. Maximizing \( U(M) \) results in \( M = 2.5 \) and \( B = 2.5 \).

Stage 3: Final determination. The usefulness maximizing selection is 2.5 units of M and 2.5 units of B.