Chapter 8 SLUTSKY EQUATION

Substitution Effect and Income Effect

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

Inferior goods

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.

8.7 Examples of Income and Substitution Effects Perfect substitutes  the entire change in demand is due to the substitution effect.

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’

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.