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.
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.
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Maximize utility by substituting the budget constraint into the utility function and solving for the optimal quantities.
Updated On: Sep 24, 2025
- 2.5 units of M and 2.5 units of B
- 0 unit of M and 5 units of B
- 5 units of M and 5 units of B
- 5 units of M and 0 unit of B
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The Correct Option is A
Solution and Explanation
Step 1: Budget constraint and utility maximization.
The budget constraint is:
\[
M + B = 5
\]
To maximize utility, the individual will choose values of \( M \) and \( B \) that maximize \( U(M,B) = 5M - 10B \), subject to the budget constraint.
Step 2: Solve for optimal quantities.
Substitute \( B = 5 - M \) into the utility function:
\[
U(M) = 5M - 10(5 - M) = 5M - 50 + 10M = 15M - 50
\]
Maximizing \( U(M) \) gives \( M = 2.5 \) and \( B = 2.5 \).
Step 3: Conclusion.
The utility maximizing choice is 2.5 units of M and 2.5 units of B.
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