Consumer A's utility function assigns U(pizza) = 100 and U(sushi) = 50. Consumer B's utility function assigns U(pizza) = 6 and U(sushi) = 3. What can we conclude from comparing their utility numbers?
AConsumer A derives twice as much satisfaction from pizza as Consumer B does
BBoth consumers prefer pizza to sushi, but we cannot compare how much each enjoys either food
CConsumer B likes sushi more relative to pizza because her numbers are closer together
DConsumer A likes pizza twice as much as sushi, and Consumer B does too
Utility is ordinal and person-specific — the numbers have no absolute meaning and cannot be compared across individuals. For Consumer A, U(pizza) = 100 > U(sushi) = 50 tells us only that pizza is preferred to sushi. For Consumer B, U(pizza) = 6 > U(sushi) = 3 tells us the same thing. Both consumers prefer pizza, but saying Consumer A 'derives twice as much satisfaction' as Consumer B is meaningless — you cannot compare utility across people. Even saying Consumer A likes pizza 'twice as much' as sushi is misleading: ordinal utility only ranks, it does not measure the magnitude of differences.
Question 2 Multiple Choice
An economist proposes two different utility functions for the same consumer: U₁(x, y) = x + y and U₂(x, y) = 2x + 2y. Do these represent different preferences?
AYes — U₂ assigns higher utility values, so the consumer is better off under U₂
BNo — both functions assign higher values to the same bundles and produce identical rankings
CYes — multiplying by 2 changes the rate at which utility increases, representing different preferences
DIt depends on the consumer's income and which bundles are affordable
Two utility functions represent the same preferences if and only if they rank every bundle identically. U₂ = 2 × U₁, so for any two bundles (x₁, y₁) and (x₂, y₂), U₁(x₁, y₁) > U₁(x₂, y₂) if and only if U₂(x₁, y₁) > U₂(x₂, y₂). The ranking is identical — only the numbers differ. Since only ordinal rankings matter, these two utility functions are completely equivalent representations of the same preferences. Any positive monotonic transformation of a utility function represents the same preferences.
Question 3 True / False
If a consumer's income doubles while their preferences remain unchanged, their utility function changes to reflect that they now get more utility from most bundle.
TTrue
FFalse
Answer: False
Utility functions represent preferences — the consumer's rankings of bundles. A key assumption of the model is that preferences are stable: they do not change when income or prices change. What changes when income doubles is the budget constraint — which bundles are affordable — not the underlying preferences. The consumer can now reach bundles they previously couldn't afford, and they will choose a higher-ranked bundle, resulting in higher utility. But the utility function itself is unchanged: it still assigns the same numbers to the same bundles. Income changes what is achievable, not what is preferred.
Question 4 True / False
Because utility is measured in abstract units ('utils'), a consumer with utility 80 is exactly twice as satisfied as a consumer with utility 40.
TTrue
FFalse
Answer: False
This misapplies cardinal reasoning to ordinal utility. The numbers in a utility function are not meaningful measurements — they are just labels that preserve ranking. Utility 80 is preferred to utility 40, but 'twice as satisfied' has no meaning. The numbers 80 and 40 could be replaced by any increasing sequence (e.g., 3 and 2, or 1,000 and 1) and represent identical preferences. Furthermore, utility is person-specific: comparing utility 80 for one consumer to utility 40 for another is meaningless. Modern consumer theory is built on ordinal utility precisely because cardinal utility (measuring the intensity of satisfaction) is neither observable nor necessary for the theory.
Question 5 Short Answer
Why does modern consumer theory use ordinal utility rather than cardinal utility? What would be needed for cardinal utility, and why is ordinal utility sufficient?
Think about your answer, then reveal below.
Model answer: Ordinal utility requires only that consumers can rank bundles consistently — that they can say A is preferred to B, not that they can measure how much more. This is sufficient to derive indifference curves, the consumer's optimum, and demand curves. Cardinal utility would require measuring the intensity of satisfaction in absolute, interpersonally comparable units — something we have no reliable way to observe. Since the predictions of consumer theory (demand behavior, substitution effects) depend only on rankings, not magnitudes, the weaker ordinal assumption is both more defensible and more than sufficient.
The shift from cardinal to ordinal utility was a major advance in 20th-century economics (associated with Pareto, Hicks, and Allen). Earlier economists spoke of 'utils' as if they were measurable, raising unanswerable questions: is my utility from pizza comparable to your utility? Ordinal utility sidesteps this: it asks only about rankings within a single consumer's preferences. The resulting theory is both more rigorous (fewer unverifiable assumptions) and more powerful (all the same demand predictions follow). The caveat is that welfare comparisons across individuals remain difficult — you cannot simply add up utility across consumers without additional assumptions.