Chapter 8 SLUTSKY EQUATION

Substitution Effect and Income Effect x1x1 x2x2 m/p 2 m’/p 2 X Y Z Substitution Effect Income Effect Shift Pivot

8.1 The Substitution Effect Substitution effect: change in demand when the purchasing power remains constant.

8.2 The Income Effect Income effect: Change in demand resulting from the change in the purchasing power.

8.3 Sign of the Substitution Effect The income effect can be positive or negative:  Normal good: negative;  Inferior good: positive. The substitution effect is negative:  The consumer will choose a point on the pivoted budget line;  The point must lie above the original budget line;  Demand for good 1 increased.

8.4 The Total Change in Demand The Slutsky equation

8.4 The Total Change in Demand Normal good  Substitution and income effects are both negative Inferior, but non-Giffen good  Substitution effect dominates Giffen good  Income effect dominates

Non-Giffen inferior good x1x1 x2x2 m/p 2 m’/p 2 X Y Z

Giffen good x1x1 x2x2 m/p 2 m’/p 2 X Y Z

8.5 Rates of Change

8.6 The Law of Demand If the demand for a good increases when income increases, then the demand for that good must decrease when its price increases.

8.7 Examples of Income and Substitution Effects Perfect complements  the entire change in demand is due to the income effect. x1x1 x2x2 shift pivot

8.7 Examples of Income and Substitution Effects Perfect substitutes  the entire change in demand is due to the substitution effect. Original budget line final budget line final choice original choice x1x1 x2x2

8.7 Examples of Income and Substitution Effects Quasilinear preferences: the entire change in demand is due to the substitution effect.

EXAMPLE: Rebating a Tax The original budget constraint: px+y=m The budget constraint in the presence of the tax-rebate plan: (p+t)x’+y’=m+tx’ x y m m+tx’ (x,y)(x,y) (x’,y’) Indifference curves Budget line after tax and rebate Budget line before tax

8.8 Another Substitution Effect x1x1 x2x2 m/p 2 m’/p 2 X Y Z Substitution Effect Income Effect

8.8 Another Substitution Effect Recalling revealed preference: p 1 x 1 +p 2 x 2 ≤p 1 y 1 +p 2 y 2 q 1 y 1 +q 2 y 2 ≤q 1 x 1 +q 2 x 2 it follows that (q 1 -p 1 )(y 1 -x 1 )+(q 2 -p 2 )(y 2 -x 2 )≤0 q 2 =p 2 since we are changing the price of good 1 only: (q 1 -p 1 )(y 1 -x 1 )≤0 The Hicksian substitution effect must be negative.