Josephine is buying candy and gum. If she is maximizing her utility for the combination of candy and gum she buys, which of the following must hold?

Question

BlackTom AI · Accepted Answer

Equalizing marginal utility per dollar spent across goods is the condition for utility maximization under a budget constraint, so MU_c/P_c = MU_g/P_g.

1) Relevant knowledge points and concepts
- Utility maximization: a consumer chooses quantities of goods (candy C and gum G) to maximize utility U(C,G) subject to a budget constraint.
- Marginal utility (MU): additional utility from one more unit of a good.
- First-order conditions (Lagrange multiplier method) yield the interior optimality condition that marginal utility per dollar spent must be equal across goods.
- Assumes an interior solution (positive amounts of both goods) and diminishing marginal utility.

2) Complete reasoning process (step by step)
Set budget: P_c C + P_g G = M (income). Form Lagrangian:
L = U(C,G) + λ(M − P_c C − P_g G).
First-order conditions:
∂L/∂C = MU_C − λ P_c = 0  => MU_C = λ P_c. 
∂L/∂G = MU_G − λ P_g = 0  => MU_G = λ P_g.
∂L/∂λ = M − P_c C − P_g G = 0 (budget holds).

3) Intermediate algebraic steps
From MU_C = λ P_c and MU_G = λ P_g, divide the two equations:
(MU_C) / (P_c) = λ = (MU_G) / (P_g),
hence MU_C / P_c = MU_G / P_g.

4) Why the correct answer is correct
This condition equates the extra utility per dollar from spending on candy to the extra utility per dollar from spending on gum. If they differed, the consumer could reallocate spending toward the higher MU per dollar good and increase total utility until equality holds.

5) Why other options are incorrect
- Total utility × price equalization: irrelevant — total utility is not the marginal decision metric and multiplying by price has no economic meaning for marginal tradeoffs.
- Marginal utility × price equalization: MU_c·P_c = MU_g·P_g is algebraically different and not derived from the FOCs.
- Total utility/price equality: uses total rather than marginal values; optimization depends on marginal changes.
- MU/Total utility equality: MU/Total is not the correct criterion; decisions are based on MU per dollar, not MU relative to total utility.

6) Conclusion
Therefore the required condition is MU_c/price_c = MU_g/price_g, which matches the provided correct answer.

Josephine is buying candy and gum. If she is maximizing her utility for the combination of candy and gum she buys, which of the following must hold?Single choice

Similar Questions

A consumer maximizes total utility when:

(APPX) Refer to the figure below. Given the existing budget line, the consumer maximizes utility:

The utility function for Maurice is U = MIN(4M, C), where M = pints of milk and C = boxes of cereal. Maurice has $90 in income and the price of cereal is PC = $2 and the price of a pint of milk is PM = $1. What is Maurice's utility-maximizing consumption bundle?

Suppose that MUX = Y and MUY = X. The prices of Good X and Good Y are PX = $5 and PY = $4. How many units of Good X does the consumer buy if she has an income of $410?

Suppose that MUY = 14, MUX = 11, PY = 2 and PX = $2. Which of the following statements is correct?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler