Intermediate Microeconomics · free preview
Revealed Preference and WARP
Choice data alone can rank bundles without utility, if the chosen bundle was affordable while another was cheaper, it is revealed preferred, and the Weak Axiom forbids the same pair from revealing itself both ways around.
1. Preference read off receipts
Preference read off receipts
2. The Weak Axiom
The Weak Axiom
3. What WARP does and does not pin down
What WARP does and does not pin down
4. From axioms to index numbers
From axioms to index numbers
5. The definition
Bundle x is chosen at prices p. When exactly is x revealed preferred to y?
6. Testing the candidate pair
Observation one chooses x equals (40, 60) at p (1, 1), m 100. Observation two chooses y equals (60, 40) at p prime (1, 2), m 160. What does the arithmetic show?
7. Why WARP is only a sieve
Data passes WARP. What has been established?
8. Index number logic
Why do Laspeyres and Paasche price indices bracket the true cost-of-living change?
9. The cross cost
In the violation example, compute p prime times x, the cost of bundle x at prices (1, 2), and write the number.
10. The other cross cost
Compute p times y, the cost of bundle y at prices (1, 1), and write the number.
11. The borderline counts
In observation two, x of (40, 60) costs exactly 160, the full budget. Does the knife-edge equality still count as affordable for WARP?
12. One receipt, one revelation
At observation one, x of (40, 60) is chosen at prices 1 and 1 with income 100. What is revealed?
13. The counterfactual rescue
Had the second income been 150 instead of 160, with the same prices and choice y of (60, 40), what changes?
14. What the indices assume
Why does the Laspeyres index use old quantities while Paasche uses new?
15. The chosen bundle's cost at new prices
At prices 1 and 2, compute the cost of bundle y of (60, 40), and write the number.
16. The first receipt's total
At prices 1 and 1, compute the cost of bundle x of (40, 60), and write the number.
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