Utility Maximization

The individual has a budget of Rs 5, and the cost of each good is Rs 1. Therefore, the total expenditure is given by: M + B = 5 This represents the budget constraint. The utility function is given as: U(M, B) = 5M - 10B We need to maximize the utility subject to the budget constraint. To find the utility-maximizing combination of goods, we can set up the Lagrange multiplier method. However, in this case, we can simply test the different combinations of M and B to check which one gives the maximum utility.

- (A) 2.5 units of M and 2.5 units of B: Substitute M = 2.5 and B = 2.5 into the budget constraint: M + B = 2.5 + 2.5 = 5 (which satisfies the budget constraint) Now calculate the utility: U(2.5, 2.5) = 5(2.5) - 10(2.5) = 12.5 - 25 = -12.5 This gives a utility of -12.5.
- (B) 0 unit of M and 5 units of B: Substitute M = 0 and B = 5 into the budget constraint: M + B = 0 + 5 = 5 (which satisfies the budget constraint) Now calculate the utility: U(0, 5) = 5(0) - 10(5) = 0 - 50 = -50 This gives a utility of -50, which is less than the utility in option (A).
- (C) 5 units of M and 5 units of B: Substitute M = 5 and B = 5 into the budget constraint: M + B = 5 + 5 = 10 (which exceeds the budget constraint) Thus, this option is not feasible.
- (D) 5 units of M and 0 unit of B: Substitute M = 5 and B = 0 into the budget constraint: M + B = 5 + 0 = 5 (which satisfies the budget constraint) Now calculate the utility: U(5, 0) = 5(5) - 10(0) = 25 - 0 = 25 This gives a utility of 25. The utility-maximizing choice is (A) 2.5 units of M and 2.5 units of B, as it satisfies the budget constraint and gives the maximum utility.

Final Answer: (A) 2.5 units of M and 2.5 units of B.