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1 Comparative Statics Slutsky Equation. Perbandingan Statis Perbandingan 2 kondisi ekuilibrium yang terbentuk dari perbedaan nilai parameter dan variabel.

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Presentasi berjudul: "1 Comparative Statics Slutsky Equation. Perbandingan Statis Perbandingan 2 kondisi ekuilibrium yang terbentuk dari perbedaan nilai parameter dan variabel."— Transcript presentasi:

1 1 Comparative Statics Slutsky Equation

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 4 Slutsky’s Identity Let 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 = Let 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 =

5 5 Slutsky’s Identity 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 = can be rewritten as ∆x i = + or denote ∆x i = ∆x i s + ∆x i n where ∆x i s = substitution effect and ∆x i n = income effect

6 6 Slutsky’s Identity 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 This is the amount of money that should be given to the consumer to hold purchasing power constant

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

8 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

9 9 Effects of a Price Change x2x2 x1x1 Original choice Consumer’s budget is $m.

10 10 Effects of a Price Change x1x1 Harga turun untuk komoditi 1 Menyebabkan pergeseran batasan (pivot) x2x2 New Constraint: Daya beli (purchasing power) naik pada rasio harga yang baru

11 11 Effects of a Price Change Sekarang budget yang dibutuhkan hanya sebesar $m' agar konsumen dapat mempertahankan tingkat konsumsinya x1x1 x2x2 Imagined Constraint: Income is adjusted to keep purchasing power constant

12 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.

13 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

14 14 Real Income Changes x1x1 x2x2 Original budget constraint and choice New budget constraint

15 15 Real Income Changes x1x1 x2x2 Less income is needed to buy original bundle. Hence, ……………………..

16 16 Real Income Changes x1x1 x2x2 Original budget constraint and choice New budget constraint

17 17 Real Income Changes x1x1 x2x2 More income is needed to buy original bundle. Hence, ………………………

18 18 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 Real Income Changes

19 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?”

20 20 Budget Constraints and Choices x2x2 x1x1 Original budget constraint and choice Original Indifference Curve

21 21 x2x2 x1x1 New budget constraint when relative price of x 1 is lower Budget Constraints and Choices

22 22 x2x2 x1x1 Imagined budget constraint Budget Constraints and Choices

23 23 x2x2 x1x1 Imagined Budget Constraint, Indifference Curve, and Choice Budget Constraints and Choices

24 24 Efek Substitusi ( bundle yang sama) x2x2 x1x1 Lower p 1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1. (, )  (, ) is the pure substitution effect

25 25 The Income Effect ( bundle beda ) x2x2 x1x1 (, ) The income effect is  (, )

26 26 Total Effect The change in demand due to lower p 1 is the sum of the income and substitution effects,  x2x2 x1x1 (, )

27 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.

28 28 Slutsky’s Effects for Normal Goods Good 1 is normal because.…… ……………………………………. x2x2 x1x1 (, )

29 29 Slutsky’s Effects for Normal Goods x2x2 x1x1 (, ) so the income and substitution effects ………… each other Total Effect

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

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

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

33 33 Slutsky’s Effects for Income-Inferior Goods Tetapi ada barang yang bersifat income- inferior (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.

34 34 x2x2 x1x1 Slutsky’s Effects for Income-Inferior Goods

35 35 Slutsky’s Effects for Income-Inferior Goods x2x2 x1x1 (, ) Good 1 is income- inferior because ……………………… ……………………… ………………………

36 36 Slutsky’s Effects for Income-Inferior Goods Substitution and Income effects ……….. each other x2x2 x1x1 (, ) Total Effect

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

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

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

40 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.

41 41 Slutsky’s Effects for Giffen Goods x2x2 x1x1 Income effect ………… Substitution effect. Substitution effect Income effect

42 42 Slutsky’s Effects for Giffen Goods x2x2 x1x1 A decrease in p 1 causes quantity demanded of good 1 to fall. Total Effect

43 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.

44 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.

45 45 Total change in demand when price changes ∆x i = can be rewritten as ∆x i = + Where is minimum income needed to achieve the original utility u at price = substitution effect = income effect Hick’s Income and Substitution Effects

46 46 x2x2 x1x1 New budget constraint when p 1 falls Original budget constraint Original choice Hick’s Income and Substitution Effects New choice

47 47 x2x2 x1x1 Hick’s Income and Substitution Effects Substitution Effect is optimal choice found on the original indifference curve using the new relative prices Income Effect

48 48 x2x2 x1x1 Hick’s Income and Substitution Effects As before, Substitution and Income effects ……….. each other

49 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

50 50 x2x2 x1x1 Comparison: Hick and Slutsky Substitution Effects when own price falls ……… budget constraint ……….. budget constraint …… Substitution ………. Substitution

51 51 Demand Curves for Normal Good when Own Price Falls x1x1 p1p1 …………… Demand ………. Demand ……….. Demand


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