Questions: Consumer Equilibrium and Utility Maximization

Question 1

A consumer currently has MRS = 3 (willing to give up 3 units of good 2 for 1 unit of good 1) while the price ratio P₁/P₂ = 2. What should this consumer do to increase utility?

• A. Buy more of good 2 and less of good 1, since good 1 is relatively expensive.
• B. Buy more of good 1, since the consumer values it more than the market requires them to pay.
• C. The consumer is already at equilibrium — any reallocation would reduce utility.
• D. Buy less of both goods and save money for future periods.

Answer: (B)

When MRS > P₁/P₂, the consumer values good 1 more (in terms of good 2 sacrificed) than the market charges for it. They are willing to give up 3 units of good 2 but only need to sacrifice 2 to get one unit of good 1 — a beneficial trade. The consumer should reallocate toward good 1 until MRS falls to equal P₁/P₂, exhausting all beneficial trades.

Question 2

At consumer equilibrium, MU₁/P₁ = MU₂/P₂. This condition is best interpreted as:

• A. The consumer has maximized the total utility from each good independently.
• B. The last dollar spent on each good delivers the same marginal utility — no reallocation of spending can improve total utility.
• C. Both goods provide equal total utility to the consumer.
• D. The consumer is spending equal amounts on both goods.

Answer: (B)

MU₁/P₁ = MU₂/P₂ is the 'bang-per-buck' condition: marginal utility per dollar is equalized across goods. If MU₁/P₁ > MU₂/P₂, shifting a dollar from good 2 to good 1 raises total utility — a beneficial reallocation remains. At equilibrium, this arbitrage is exhausted. The condition says nothing about equal spending (D) or equal total utility (C).

Question 3

Consumer equilibrium generally occurs at the tangency between the budget line and an indifference curve.

• T. True
• F. False

Answer: False

Tangency is the condition for interior solutions, but corner solutions are also optimal. If a consumer optimally buys only good 1 (spending all income on it), the MRS at that corner may still exceed P₁/P₂ — but they cannot reduce good 2 below zero. At a corner the tangency condition fails, yet the consumer is at their constrained optimum. Recognizing this exception is essential to a full understanding of consumer theory.

Question 4

If a consumer's MRS exceeds the price ratio P₁/P₂ at their current bundle, they can always increase utility by shifting spending toward good 1 without violating their budget constraint.

• T. True
• F. False

Answer: True

When MRS > P₁/P₂, the consumer values good 1 more than the market charges for it in terms of good 2. Buying a bit more of good 1 and less of good 2 (staying on budget) moves them to a higher indifference curve. This reallocation continues to be beneficial until MRS falls to equal P₁/P₂ (or until a corner is reached). The logic follows directly from the tangency optimality condition.

Question 5

Explain in your own words why MRS > P₁/P₂ means the consumer can improve their utility without spending more money.

Model answer: MRS > P₁/P₂ means the consumer is personally willing to sacrifice more of good 2 to get one more unit of good 1 than the market actually requires. By buying a bit more of good 1 (and less of good 2 to stay on budget), they gain something they value highly at a cost they find acceptable — a profitable internal trade. This reallocation holds total spending constant but reaches a higher indifference curve.

The key insight is that equilibrium is a state of exhausted arbitrage. Any divergence between the consumer's subjective trade-off rate (MRS) and the market's objective trade-off rate (price ratio) creates an opportunity to improve utility at no additional cost. Equilibrium is reached precisely when that opportunity is gone — when the consumer's personal valuation of the trade-off exactly matches market prices.