At the consumer optimum, the marginal rate of substitution (MRS) equals the price ratio P_x/P_y. What does this condition mean intuitively?
AThe consumer spends equal dollar amounts on both goods
BThe consumer's personal willingness to trade X for Y matches the rate the market requires
CThe marginal utility of X equals the marginal utility of Y
DThe budget line is as far from the origin as the indifference curve allows
MRS is the consumer's subjective exchange rate — how much Y they willingly give up for one more X while remaining equally satisfied. P_x/P_y is the market's objective exchange rate — how much Y they must sacrifice to buy one more X at prevailing prices. At the optimum, these rates are equal. If MRS > P_x/P_y, the consumer values X more than the market charges for it and should buy more X; they stop when the marginal valuations equalize.
Question 2 True / False
If an indifference curve is tangent to the budget line at an interior point, this guarantees that the consumer is at a utility maximum rather than a minimum.
TTrue
FFalse
Answer: False
Tangency is necessary but not sufficient for a maximum. If preferences are not globally concave — for instance, if indifference curves are bowed away from the origin rather than toward it — an interior tangency can be a utility minimum. The second-order condition requires that the indifference curve be more curved than the budget line at the tangency (diminishing MRS). Standard convex preferences satisfy this, but the tangency condition alone does not guarantee a maximum.
Question 3 Short Answer
State the equimarginal principle and explain why a consumer who violates it can improve their allocation.
Think about your answer, then reveal below.
Model answer: The equimarginal principle states MU_x/P_x = MU_y/P_y at the optimum: the last dollar spent on each good yields the same marginal utility. If MU_x/P_x > MU_y/P_y, the consumer gets more utility per dollar from X than from Y. Shifting one dollar of spending from Y to X gains more utility than it loses, so the original allocation was not optimal.
The principle normalizes marginal utilities into a common unit — utility per dollar — making different goods directly comparable. Optimality requires these ratios to be equalized across all goods purchased; any inequality signals a profitable reallocation. This is mathematically equivalent to the MRS = price ratio tangency condition.