Ch08Slutsky Equation(中级微观经济学-清华大学,钟笑寒)

Chapter EightSlutsky Equation

What We Do Here? Until

now, consumer theory seemed to have no particular content: – Demand could go up or down when income increased – Demand could go up or down when a price increased. If a theory doesn t restrict observed behavior in some fashion it isn t much of a theory. A model that is consistent with all behavior has no real content.

What We Do Here? We

want a way to decompose the effect of a price change into “simpler” pieces. – That s what analysis is all about – Break up into simple pieces to determine behavior of whole

What We Do Here? We

will break up price change into a pivot and a shift –two hypothetical changes – Changes in demand due to pivot is the substitution effect. – Changes in demand due to shift is the income effect.

Effects of a Price Change What

happens when a commodity s price decreases? – Substitution effect: the commodity is relatively cheaper, so consumers substitute it for now relatively more expensive other commodities.

Effects of a Price Change– Income effect: the consumer s budget of $y can purchase more than before, as if the consumer s income rose, with consequent income effects on quantities demanded.

08.01

Pure Substitution Effect Slutsky

isolated the change in demand due only to the change in relative prices by asking “What is the change in demand when the consumer s income is adjusted so that, at the new prices, she can only just buy the original bundle?”

Pure Substitution Effect Onlyx2

x2

x 1

x1

Pure Substitution Effect Onlyx2

x2

x 1

x1

Pure Substitution Effect Onlyx2

x2

x 1

x1

Pure Substitution Effect Onlyx2

x2 x2

x 1

x1

x1

Pure Substitution Effect Onlyx2

x2 x2

x 1

x1

x1

Pure Substitution Effect Onlyx2Lower p1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1.

x2 x2

x 1

x1

x1

Pure Substitution Effect Onlyx2Lower p1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1. (x1 ,x2 ) (x1 ,x2 ) is the pure substitution effect.

x2 x2

x 1

x1

x1

Substitution Effect How

much we have to adjust money income in order to keep the old bundle just affordable? – Let y be the amount of money income that will just make the original consumption bundle (x1,x2) affordable. – Since (x1,x2) is just affordable at both (p1,p2,y) and (p1 ,p2,y ), we have