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L07

L07. Slutsky Equation. Previous Class. Demand function How the demand is affected by p 1 change, holding p 2 and m constant m change, holding p 2 and m constant p 2 change, holding p 1 and m constant Geometric and analytical answer! Classification of goods. Price Change. p 1 ’ =1,.

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L07

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  1. L07 Slutsky Equation

  2. Previous Class Demand function How the demand is affected by • p1 change, holding p2 and m constant • m change, holding p2 and m constant • p2 change, holding p1 and m constant Geometric and analytical answer! Classification of goods

  3. Price Change p1’=1, Change p1=2, Fix p2=1 and m=10. x2 What happens to 1) a relative price? 2) a purchasing power (real income)? Can we separate the two effects? x1

  4. Today 2 questions • How to measure Real Income (PP) • Decomposition of the change in demand • The effect resulting from the change of a relative price (substitution effect) • The effect resulting from the change of real income (income effect)

  5. Change of Real Income p1’=1, p1=2, p2=1 and m=10 and What m’ makes just affordable at x2 x1

  6. Real Income Change • If, at the new prices, • less income is needed to buy the original bundle then “real income” is increased • more income is needed to buy the original bundle then “real income” is decreased

  7. Real Income Changes Suppose p1, p2changes to p1’, p2’ x2 Original budget constraint and choice New budget constraint • Q: Real income • Increases • Decreases • Stays the same x1

  8. Real Income Changes Suppose p1, p2, changes to p1’, p2’ x2 Original budget constraint and choice New budget constraint x1

  9. Substitution and Income Effect • If P1 changes, both relative price and real income are affected • Slutsky isolates the change in demand due only to the change in relative prices KEY IDEA: “What is the change in demand when the consumer’s income is adjusted (to m’) so that, at the new prices, her real income is the same?”

  10. Total Change x2 T.CH x1

  11. Income Effect Substitution effect x2 IE SE x1

  12. Substitution and Income Effect • What happens to the demand • Instead of going directly, 2 steps: Total Change SE IE

  13. Cobb-Douglass example Data , change

  14. Cobb-Douglass example Data , change

  15. Perfect Complements , change

  16. Perfect Complements , change

  17. Normal, Inferior and Giffent goods • Normal Goods • Inferior goods • Effects: Reinforce or cancel out?

  18. Normal Goods x2 x1

  19. Slutsky’s Effects for normal Goods • Normal good: demand increases in income. Substitution and income effects always have the same sign

  20. Slutsky’s Effects for Inferior Goods • Some goods are inferior (i.e. demand is reduced by higher income). Q: substitution and income effects • Always have the same sign • Always have opposite signs • Depends of assumed parameters

  21. Inferior Goods x2 x1

  22. Giffen Goods x2 x1

  23. Slutsky’s Effects for Giffen Goods • Slutsky’s decomposition of the effect of a price change into a pure substitution effect and an income effect thus explains why the Law of Downward-Sloping Demand is violated for extremely income-inferior goods.

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