Chapter 8. Slutsky Equation

Transcription

1 Chapter 8 Slutsky Equation

2 Effects of a Price Change When a commodity s price decreases: Substitution Effect: Consumers substitute this cheaper good for now relatively more expensive other commodities. You give up less of one good to get more of this good.

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

4 Effects of a Price Change y Consumer s budget is $y. Original choice p 2

5 Effects of a Price Change y p 2 Consumer s budget is $y. Substitution Effect: Lower price for commodity 1 pivots the constraint outwards.

6 Effects of a Price Change y p 2 y' p 2 Consumer s budget is $y. Income Effect: Now only $y are needed to buy the original bundle at the new prices, as if the consumer s income has increased by $y - $y.

7 Effects of a Price Change Income Effect: Changes to quantities demanded due to this seemingly extra income.

8 Effects of a Price Change Slutsky: Discovered that changes to demand from a price change are always the sum of a pure substitution effect and an income effect.

9 Real Income Changes Slutsky assertion: 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

10 Real Income Changes Original budget constraint and choice

11 Real Income Changes Original budget constraint and choice New budget constraint

12 Real Income Changes Original budget constraint and choice New budget constraint: Rise in real income (budget line shifts outwards)

13 Real Income Changes Original budget constraint and choice

14 Real Income Changes Original budget constraint and choice New budget constraint

15 Real Income Changes Original budget constraint and choice New budget constraint: Rise in real income (budget line shifts inwards)

16 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?

17 Income & Substitution Effects Shift to new budget line happens in two parts: subs effect (bundle X to Y); then Income effect (Y to Z). 17

18 Budget Change If prices change from p to p, the budget line changes as follows: This is analogous to the pivoted budget line. 18

19 Budget Example Suppose you can purchase 20 candy bars per week at price p = $.50. The price increases by.10 (p = p+.10). How much does your candy budget have to change to buy the same amount of candy? m = x1 p m = (20)(.10) = $

20 Pure Substitution Effect Only

21 Pure Substitution Effect Only

22 Pure Substitution Effect Only

23 Pure Substitution Effect Only

24 Pure Substitution Effect Only

25 Pure Substitution Effect Only Lower p 1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1.

26 Pure Substitution Effect Only Lower p 1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1. (, ) (, ) is the pure substitution effect.

27 Calculating the Substitution Effect Consumer demand function for milk: Income (m) = $120; Price of milk (p1) = $3 Original Demand for Milk: Suppose p1 = $2. The total change in demand: 27

28 Calculating the Substitution Effect (1) Calculate the budget change for original quantity x1: Income (m ) = $120 + (-14) = $106; Original Demand for Milk: (2) Recalculate demand with the new budget (m ): (3) Subtract x1(2,106) x1(3,120) = =

29 And Now The Income Effect (, )

30 And Now The Income Effect The income effect is (, ) (, ). (, )

31 Calculating the Income Effect The income effect in the change of quantity demanded: (demand with new price, old budget) (demand with new price, new budget 31

32 The Overall Change in Demand The change to demand due to lower p 1 is the sum of the income and substitution effects: (, ) (, ). (, ) Since your budget is not exhausted, you can purchase more of each good.

33 Slutsky s Effects for Normal Goods Most goods are normal (i.e. demand increases with income). The substitution and income effects reinforce each other when a normal good s own price changes.

34 Slutsky s Effects for Normal Goods Good 1 is normal because higher income increases demand (, )

35 Slutsky s Effects for Normal Goods Good 1 is normal because higher income increases demand, so the income and substitution effects reinforce each other. (, )

36 Slutsky s Effects for Normal Goods Since both the substitution and income effects increase demand when own-price falls, a normal good s ordinary demand curve slopes down. The Law of Downward-Sloping Demand therefore always applies to normal goods.

37 Slutsky s Effects: Income-Inferior Goods Some goods are income-inferior (i.e. demand is reduced by higher income). The substitution and income effects oppose each other when an incomeinferior good s own price changes.

38 Slutsky s Effects for Income-Inferior Goods

39 Slutsky s Effects for Income-Inferior Goods

40 Slutsky s Effects for Income-Inferior Goods

41 Slutsky s Effects for Income-Inferior Goods

42 Slutsky s Effects for Income-Inferior Goods The pure substitution effect is as for a normal good. But,.

43 Slutsky s Effects for Income-Inferior Goods But the income effect is in the opposite direction. (, )

44 Slutsky s Effects for Income-Inferior Goods Good 1 is income-inferior because an increase to income causes demand to fall. (, )

45 Slutsky s Effects for Income-Inferior Goods The overall changes to demand are the sums of the substitution and income effects. (, )

46 Giffen Goods Giffen Goods: In rare cases of extreme incomeinferiority, the income effect may be larger in size than the substitution effect, causing quantity demanded to fall as own-price rises.

47 Slutsky s Effects for Giffen Goods A decrease in p 1 causes quantity demanded of good 1 to fall.

48 Slutsky s Effects for Giffen Goods A decrease in p 1 causes quantity demanded of good 1 to fall.

49 Slutsky s Effects for Giffen Goods A decrease in p 1 causes quantity demanded of good 1 to fall. Substitution effect Income effect

50 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 incomeinferior goods.