Why can Laspeyres and Paasche bracket the true cost-of-living index?
The base basket ignores substitution and tends high; the current basket tends low.
Follow the cause and effect
Use q0 for Laspeyres and q1 for Paasche.
Price the same basket under both price vectors.
Explain substitution bias and data limitations.
The model you are using
Conditions for this model
Constant product quality, positive prices and quantities; index base is 1 before multiplying by 100.
The exam trap
Do not swap q0 and q1 or call CPI an exact utility measure without conditions.
Connect the reasoning to the graph
What changes
- Compensated budgets show why restoring utility differs from repurchasing the base basket.
What stays fixed
Constant product quality, positive prices and quantities; index base is 1 before multiplying by 100.
Keep these conditions throughout the comparison; change only what the case above specifies.
What to inspect
Explain substitution bias and data limitations.
Compare before and after, and locate the conclusion on the graph.
5 MINUTES · TRANSFER THE IDEA
Can you explain it without the lesson?
Show that if every price is multiplied by 1.5, both L and P equal 1.5.