Two utility functions U(x,y) = x + y and V(x,y) = 3(x + y) represent the same consumer preferences. Which statement about them is correct?
AThey represent different preferences because V gives higher numbers.
BThey represent the same preferences because any monotonic transformation of a utility function preserves the ranking of bundles.
CV is a better utility function because it gives more precise measurements of well-being.
DThey represent the same preferences only if x and y are perfect substitutes.
Utility is ordinal: only the ranking of bundles matters, not the utility numbers themselves. Multiplying by 3 is a monotonic transformation — it preserves the ordering (if U(A) > U(B) then V(A) > V(B)). The two functions describe identical preferences. Saying V is 'more precise' reflects the cardinal misconception — utility numbers have no absolute meaning.
Question 2 True / False
A consumer who donates to charity is acting irrationally according to the standard microeconomic model of consumer preferences.
TTrue
FFalse
Answer: False
Rationality in microeconomics means preferences are complete, transitive, and consistent — it says nothing about what those preferences contain. A consumer whose utility function includes others' welfare (altruism) is perfectly rational in the economic sense. The model does not assume selfishness, only consistency in choice.
Question 3 Short Answer
Why is utility described as 'ordinal' rather than 'cardinal,' and why does this distinction matter for analyzing consumer choices?
Think about your answer, then reveal below.
Model answer: Ordinal means utility only encodes rankings — bundle A is preferred to bundle B — not the size of the preference difference. It matters because we cannot say a consumer is 'twice as happy' with one bundle as another, and we cannot add utilities across consumers to compare social welfare.
A cardinal scale (like temperature) supports statements about differences and ratios. An ordinal scale (like a race finishing position) only supports statements about order. Utility functions are ordinal because the theory only requires the consumer to be able to rank options; there is no behavioral test for the magnitude of preference differences. This limits what economists can claim about interpersonal welfare comparisons.