Two indifference curves for the same consumer intersect at bundle X. What must be true?
ABundle X lies on the budget constraint
BThe consumer is indifferent between all bundles on both curves
CBundle X gives the consumer maximum utility
DA logical contradiction exists — the consumer would simultaneously prefer and be indifferent to the same bundles
If curves cross at X, transitivity of preferences implies a contradiction. A bundle on the higher curve is preferred to X, but X is also on the lower curve, making it indifferent to other points on that curve that should be ranked as worse. Crossing curves violate the consistency required by well-behaved preferences.
Question 2 True / False
Indifference curves are convex to the origin primarily because of diminishing marginal utility — consuming more of a good typically produces less additional satisfaction.
TTrue
FFalse
Answer: False
Convexity reflects a diminishing marginal rate of substitution (MRS), which captures a preference for variety: as you give up more of one good, each remaining unit becomes more valuable relative to the good you are gaining. While related to diminishing marginal utility, these are distinct concepts — MRS can be diminishing even when cardinal utility behaves differently, and convexity is defined by the preference structure, not by a cardinal measure of satisfaction.
Question 3 Short Answer
What does the slope of an indifference curve at a point represent, and why does its absolute value decrease as you move down and to the right along the curve?
Think about your answer, then reveal below.
Model answer: The slope (in absolute value) equals the marginal rate of substitution (MRS) — the quantity of good Y a consumer is willing to give up to receive one more unit of good X. As you move right, you have more X and less Y, so Y becomes relatively scarcer and more valuable. This means the consumer is willing to give up less and less Y for each additional unit of X, causing the MRS and the curve's slope to diminish.
The MRS equals the ratio of marginal utilities MU_x / MU_y. Moving right increases X (reducing MU_x via diminishing returns) and decreases Y (raising MU_y), so the ratio falls. This is the algebraic expression of the intuition that variety has value: the more lopsided the bundle, the less willing you are to trade away the scarce good.