Comparative Statics Slutsky Equation

Transkripsi

1 Comparative Statics Slutsky Equation 1

2 Perbandingan Statis Perbandingan 2 kondisi ekuilibrium yang terbentuk dari perbedaan nilai parameter dan variabel eksogen Contoh: Perbandingan 2 keputusan konsumen (consumer s behaviour) dengan perubahan harga 2

3 Secara umum, harga dan jumlah permintaan berbanding terbalik. Artinya, jika harga naik maka permintaan akan turun. Tetapi ternyata ada permintaannya yang jumlahnya menurun dengan menurunnya harga barang tersebut, yang dikenal dengan GIFFEN GOOD 3

4 Slutsky s Identity Let xi(p i,m) be consumer s demand for good i when price of good i is p i and income is m holding other prices constant Similarly for If the price of good i changes from to Total change in demand denoted by x i = x x (p,m) i i (p,m)- i i x i (p,m) i p i p i 4

5 Slutsky s Identity m Now let be the new level of income such that the consumer is just able to buy the original bundle of goods Total change in demand x i = xi (p i,m)- xi (p i,m) can be rewritten as x i = [xi (p i,m)- x i(p,m)] i + [x (p,m)- x (p,m) i i i i ] or denote x i = x is + x n i where x is = substitution effect and x n i = income effect 5

6 Slutsky s Identity m -m Note that is the amount of the change in money income such that the consumer is just able to buy the original bundle of goods (i.e. purchasing power is constant) Denote m = and p i = m = p i m -m p i -pi x i (p,m) i This is the amount of money that should be given to the consumer to hold purchasing power constant 6

7 Slutsky s Identity In terms of the rates of change, we can write Slutsky s Identity as xx x s x m i x i x i x i (p i, m) p i p i m where x i n = x i m 7

8 Dampak Perubahan Harga Apa yang terjadi jika harga satu barang turun? Efek Substitusi: barang tersebut menjadi relatif murah. Konsumen akan meningkatkan konsumsinya terhadap barang yang menjadi relatif murah. Efek Pendapatan (Income effect): Dengan budget yang tetap, konsumen dapat mengkonsumsi lebih banyak barang, seolah-olah pendapatnya meningkat. Dan sebaliknya (Vice versa) untuk kenaikan harga 8

9 Effects of a Price Change m p 2 Consumer s budget is $m. Original choice 9

10 Effects of a Price Change m p 2 Harga turun untuk komoditi 1 Menyebabkan pergeseran batasan (pivot) New Constraint: Daya beli (purchasing power) naik pada rasio harga yang baru 10

11 Effects of a Price Change m p 2 m' p p 2 Sekarang budget yang dibutuhkan hanya sebesar $m' agar konsumen dapat mempertahankan tingkat konsumsinya Imagined Constraint: Income is adjusted to keep purchasing power constant 11

12 Effects of a Price Change Perubahan jumlah permintaan akibat perubahan extra income ($m - $m') merupakan income effect akibat perubahan harga. Slutsky menemukan bahwa perubahan jumlah permintaan selalu merupakan penjumlahan dari pure substitution effect dan income effect. 12

13 Real Income Changes Menurut Slutsky pada harga yang baru, 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 13

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

15 Real Income Changes Less income is needed to buy original bundle. Hence,.. 15

16 Real Income Changes Original budget constraint and choice New budget constraint 16

17 Real Income Changes More income is needed to buy original bundle. Hence, 17

18 Real Income Changes Absence of Money illusion If money income and prices increase (or decrease) by the same proportion, e.g. double budget constraint and consumer s choice remain unchanged 18

19 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? 19

20 Budget Constraints and Choices Original budget constraint and choice Original Indifference Curve x1 20

21 Budget Constraints and Choices New budget constraint when relative price of is lower 21

22 Budget Constraints and Choices Imagined budget constraint 22

23 Budget Constraints and Choices x 2 Imagined Budget Constraint, Indifference Curve, and Choice x x

24 Efek Substitusi (bundle yang sama) x 2 Lower p 1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1. (, ) (, ) is the pure substitution effect x 1 24

25 The Income Effect (bundle beda) x 2 The income effect is (, ) (, ) x ( x, ) 1 x 1 25

26 Total Effect x 2 The change in demand due to lower p 1 is the sum of the income and substitution effects, (, ) (, ) ( x, x ) 1 x 1 26

27 Slutsky s Effects for Normal Goods Umumnya barang bersifat normal (i.e. demand naik dengan pertambahan income). The substitution and income effects reinforce each other when a normal good s own price changes. 27

28 Slutsky s Effects for Normal Goods x 2 Good 1 is normal because.. x ( x, ) 1 x 1 28

29 Slutsky s Effects for Normal Goods x 2 so the income and substitution effects each other x ( x, ) 1 Total Effect x1 x 1 29

30 Slutsky s Effects for Normal Goods When p i decreases, p i is negative ( ) p i x i = x is + x n i ( ) ( ) ( ) ( ) both substitution and income effects increase demand when own-price falls. Alternatively, x i x s i x m i x i (p i, m) p = i p i m ( ) ( ) ( ) x ( ) 30

31 Slutsky s Effects for Normal Goods When p i decreases, p i is positive (+) p i x i = x is + x n i (+) ( ) ( ) ( ) both substitution and income effects decrease demand when own-price rises. Alternatively, x i x s i x m i x i (p i, m) p = i p i m ( ) ( ) ( ) x ( ) 31

32 Slutsky s Effects for Normal Goods In both cases, a change is own price results in an opposite change in demand x i is always p i a normal good s ordinary demand curve slopes down. The Law of Downward-Sloping Demand therefore always applies to normal goods. 32

33 Slutsky s Effects for Income-Inferior Goods Tetapi ada barang yang bersifat incomeinferior (i.e. Permintaan berkurang dengan bertambahnya higher income). Efek substitusi sama dengan barang normal tetapi efek income berlawanan arah. Dengan demikian, efek substitusi dan efek income berlawanan arah jika harga barang inferior berubah. 33

34 Slutsky s Effects for Income-Inferior Goods 34

35 Slutsky s Effects for Income-Inferior Goods x ( x, ) 2 2 x 2 Good 1 is incomeinferior because x 1 35

36 Slutsky s Effects for Income-Inferior Goods x ( x, ) 2 2 x 2 Substitution and Income effects.. each other Total Effect x1 x 1 36

37 Slutsky s Effects for Income-Inferior Goods When p i decreases, p i is negative ( ) p i x i = x is + x n i ( ) ( ) ( ) ( ) substitution effect increases demand while income effect reduces demand Alternatively, x i x s i x m i x i (p i, m) p = i p i m ( ) ( ) ( ) x ( ) 37

38 Slutsky s Effects for Income-Inferior Goods When p i decreases, p i is positive (+) p i x i = x is + x n i (+) ( ) ( ) ( ) both substitution and income effects decrease demand when own-price rises. Alternatively, x i x s i x m i x i (p i, m) p = i p i m ( ) ( ) ( ) x ( ) 38

39 Slutsky s Effects for Income-Inferior Goods In general, substitution effect is greater than income effect. Hence, xx i is usually positive when p i decreases. and x i is usually negative when p i increases. x i That is is.. p i and Demand Curve slopes downward 39

40 Giffen Goods In rare cases of extreme income-inferiority, the income effect may be larger in size than the substitution effect, causing quantity demanded to fall as own-price rises. Such goods are called Giffen goods. 40

41 Slutsky s Effects for Giffen Goods x 2 Income effect Substitution effect. x 2 x 1 Substitution effect Income effect 41

42 Slutsky s Effects for Giffen Goods x 2 A decrease in p 1 causes quantity demanded of good 1 to fall. Total Effect x 1 x1 42

43 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 Giffen goods. 43

44 Hick s Income and Substitution Effects Previously, we learn Slutsky s Substitution Effect: the change in demand when purchasing power is kept constant. Hick proposed another type of Substitution Effect where consumer is given just enough money to be on the same indifference curve. Hick s Substitution Effect: the change in demand when utility is kept constant. 44

45 Hick s Income and Substitution Effects Total change in demand when price changes x i = can be rewritten as x i = x + (p,m)- i i x i i (p,m) i [x (p i,e(p i,u))- x i (p,m) i ] [x (p,m) - x (p, e(p i i i i i,u)) ] Where e( p i,u) is minimum income needed to achieve the original utility u at price i [x (p i,e(p i,u))- x i(p,m)] i [x (p,m) - x (p i i i i,e(p i,u))] p = substitution effect = income effect i 45

46 Hick s Income and Substitution Effects New budget constraint when p1 falls Original choice New choice Original budget constraint 46

47 Hick s Income and Substitution Effects x 2 x 2 Substitution Effect is optimal choice found on the original indifference curve using the new relative prices x 1 x 1 Income Effect 47

48 Hick s Income and Substitution Effects x 2 x 2 As before, Substitution and Income effects.. each other x 1 x 1 48

49 Demand Curves Marshallian (Ordinary) Demand shows the quantity actually demanded when own price changes holding.. constant Slutsky Demand shows Slutsky substitution effect when own price changes holding constant Hicksian (Compensated) Demand shows Hick substitution effect when own price changes holding.. constant 49

50 Comparison: Hick and Slutsky Substitution Effects when own price falls.. budget constraint x budget constraint x 2 1 H S 1 x Substitution. Substitution 50

51 Demand Curves for Normal Good when p 1 Own Price Falls p 1 Demand. Demand p 1.. Demand x1 x H S x1 1 51