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M14.L05 ā€” Revealed Preference and the Weak Axiom

Module: Module 14 ā€” Consumer Choice and Demand Lesson: L05 of 05 Duration: ~30 minutes Level: Intermediate Provenance: Principles of Microeconomics (Curtis and Irvine) | Khan Academy Microeconomics

Learning Objective

Test consumer consistency using revealed preference theory.

Revealed Preference Concepts

Directly Revealed Preferred (DRP): Bundle A is DRP to B if A chosen when B was affordable

Weak Axiom of Revealed Preference (WARP): If A DRP to B, then B cannot be DRP to A under different prices/budget

Australian application: Test whether household energy choices (2019 vs 2023) satisfy WARP despite price shocks.

Worked Example

Adelaide Grocery Choices

Observation 1 (Jan): pā‚=\(4 (milk), pā‚‚=\)5 (juice), chosen bundle A=(2,3) Observation 2 (Jul): pā‚'=\(5, pā‚‚'=\)4, chosen bundle B=(3,2)

Check WARP: 1. Cost of A at Jan prices: 4Ɨ2 + 5Ɨ3 = $23 Cost of B at Jan prices: 4Ɨ3 + 5Ɨ2 = $22 ā†’ A was feasible when B chosen 2. Cost of B at Jul prices: 5Ɨ3 + 4Ɨ2 = $23 Cost of A at Jul prices: 5Ɨ2 + 4Ɨ3 = $22 ā†’ B was feasible when A chosen 3. Violation: Both A DRP to B and B DRP to A

Common Misconception

"WARP violations mean irrationality"

Australian consumers may rationally violate WARP due to: - Changing preferences (seasonal produce) - Quality adjustments (smaller "shrinkflation" packages) - New information (health studies)

Key Takeaways

  • Choices reveal preferences without utility functions
  • WARP tests consistency across budget scenarios
  • Index numbers (Laspeyres/Paasche) measure welfare changes
  • Australian CPI uses revealed preference logic
  • Policy applications: NBN adoption, Medicare utilization

Practice

  1. Check WARP for bundles A=(1,4) at prices (\(10,\)5) and B=(4,1) at (\(5,\)10)
  2. Calculate Laspeyres index for above if base is Observation 1
  3. Explain why fuel choice data might show WARP violations

Further Resources

Provenance: Principles of Microeconomics (Curtis and Irvine) | Khan Academy Microeconomics