Chapter 7 – Revealed Preference
- How we can use information about a consumers demand to discover information about
their preferences, assuming their preferences are stable over the time period that we are
observing their behavior
Assume that there is a unique demanded bundle and the preferences are strictly convex
If (x1, x2) is on the budget line and it is the chosen bundle, then is satisfies the budget
constraint with equality (p1x1 + p2x2 = m)
- But, say that (y1, y2) is underneath the budget line and it is not chosen, then is just
satisfies the budget constraint (p1y1 + p2y2 ≤ m), but it is not the optimal choice
≥
Putting these two together gives you p1x1 + p2x2 p1y1 + p2y2, which tells us that (x1, x2)
is directly revealed preferred to (y1, y2).
- Basically, the consumer chose X when Y also could’ve been chosen.
- If the consumer chooses the best bundle they can afford, then revealed preference implies
preference
Then, if (y1, y2) is revealed preferred to a bundle (z1, z2), then we can see that (x1, x2) is
indirectly implied preferred to (z1, z2) by looking at preference and transitivity
You can use assumptions about consumer preferences to “trap” and find an indifference curve
- If we assume preferences are convex for bundle Y and Z that are revealed preferred to
good X, then we know that all the weighted averages of Y and Z are also preferred to X
- If we assume monotonicity, then all the bundles that have more of both goods than X, Y,
and Z and any of their weighted averages are also preferred to X

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