Intermediate microeconomics. Lecture 2: Consumer Theory II: demand. Varian, chapters 6, 8, 9

Transcription

1 Interediate icroeconoics Lecture 2: Consuer Theory II: deand. Varian, chapters 6, 8, 9

2 Agenda 1. Noral and inferior goods 2. Incoe offer curves and Engel curves 3. Ordinary goods and Giffen goods 4. Price offer curves and deand curves 5. Substitutes and copleents 6. The Slutsky equation 7. The Law of Deand 8. The Slutsky equation with enowents Ada Jacobsson, Departent of Econoics 2

3 1. Noral and inferior goods Definition 1 (noral good). A good is noral if the deanded quantity increases if non-labour incoe increases: dx # d > 0. Definition 2 (inferior good). A good is inferior if the deanded quantity decreases if non-labour incoe increases: dx # d < Ada Jacobsson, Departent of Econoics 3

4 Exaple: Noral good: increases: < Good 2 x 1 x 1 Good Ada Jacobsson, Departent of Econoics 4

5 Exaple: Inferior good: increases: < Good 2 x 1 x 1 Good Ada Jacobsson, Departent of Econoics 5

6 Good 2 Incoe offer curve Incoe offer and Engel curves - > x 1 x 1 Good 1 Engel curve x 1 x 1 Good Ada Jacobsson, Departent of Econoics 6

7 3. Ordinary and Giffen goods Definition 3 (Ordinary good). A good is ordinary if the deanded quantity decreases when the price of the good increases: dx # < 0. dp i Definition 4 (Giffen good). A good is a Giffen good if the deanded quantity increases when the price of the good increases: dx # dp i > Ada Jacobsson, Departent of Econoics 7

8 Exaple: Ordinary good: increases: < p - 1 Good 2 x 1 x 1 Good 1 p Ada Jacobsson, Departent of Econoics 8

9 Exaple: Giffen good: increases: < p - 1 Good 2 x 1 x 1 Good 1 p Ada Jacobsson, Departent of Econoics 9

10 Good 2 Price offer curve Price offer and Deand curves < p - 1 x 1 x 1 Good 1 p 1 p - 1 Deand curve x 1 x 1 Good Ada Jacobsson, Departent of Econoics 10

11 5. Substitutes and Copleents Definition 5. Good 1 is a substitute for good 2 if dx 1 d > 0. Definition 6. Good 1 is a copleent for good 2 if dx 1 d < Ada Jacobsson, Departent of Econoics 11

12 6. The Slutsky equation A change in the price of a good has two effects: 1. The relative price of the good is affected: Substitution effect 2. The purchasing power is affected: Incoe effect Ada Jacobsson, Departent of Econoics 12

13 Deriving the Slutsky equation, ethod 1: ( decreases: > p 1 ) Good 2 x 1A (,, ) x 1B (p 1,, ) x 1C (p 1,, ) SE = x 1B (p 1,, ) - x 1A (,, ) C IE = x 1C (p 1,, ) - x 1B (p 1,, ) A B SE IE x 1A x 1B x 1C Good 1 p 1 p Ada Jacobsson, Departent of Econoics 13

14 The total change in deanded quantity is SE+IE! Δx 1 = x 1B (p 1,, ) x 1A (,, ) Ex s 1 + x 1C (p 1,, ) x 1B (p 1,, ) Ex n 1 We define Δx 1=-Δx n 1. We then get: Δx 1 = Δx s 1 - Δx 1 (1) Divide both sides by Δ to get the rates of change : Ex 1 E = Exs 1 E Ex 1 E (2) Ada Jacobsson, Departent of Econoics 14

15 For and we have: = x 1 + x 2 = p - 1x 1 + x 2 I (3) Where the budget lines intersect (point A) we have: Δ = - = x 1 p - 1 = x 1 Δ (4) or Δ = EN O 1 (5) Equations (5) and (2) give us the Slutsky equation Ada Jacobsson, Departent of Econoics 15

16 The Slutsky equation Δ = Δ x 1 Use (5) in (2) to rewrite the incoe effect: First let us rewrite the incoe effect: Ex 1 Ex = x 1 E 1 E (2) Then becoes: Ex 1 P E QRSTU VWWVXS = Exs 1 YE Z[\]S VWW. x 1 Ex 1 E ^_XRNV VWW. (6) Ada Jacobsson, Departent of Econoics 16

17 Exaple: noral good and increases Ex s 1 E <0 a negative substitution effect & x 1 Ex 1 E >0 a positive incoe effect yields: Δx 1 Y Δ QRSTU VWWVXS = Δxs 1 Y Δ Z[\]S VWW. Δx 1 x 1 <0 Δ ^_XRNV VWW. Let us work through an exaple! Ada Jacobsson, Departent of Econoics 17

18 Deriving the Slutsky equation, ethod 2: ( decreases: > p 1 ) Now we keep the utility constant instead of purchasing power. Good 2 The Hicksian substitution effect E(p - 1,, ub) A B C is virtually the sae as the Slutsky subst effect for sall changes in. u c SE IE E(p - 1,, ub) p 1 Good Ada Jacobsson, Departent of Econoics 18 ub p 1

19 7. The law of deand If deand for a good increases when non-labour incoe increases, then deand for the sae good will decrease if the price of the good increases. That is: If a good is noral, then it ust be ordinary. Proof: Ex 1 E P QRSTU VWWVXS = Exs 1 YE (d) Ex x 1 1 <0 E (e) (d) The opposite need not be true! Ada Jacobsson, Departent of Econoics 19

20 8. The Slutsky equation with endowents Now assue that individuals incoe () is coposed of endowents of the two goods: = ω 1 + ω 2 Where ω 1 is the endowent of good 1 and ω 2 is the endowent of good 2. (ω 1 could be the aount of apples and ω 2 the aount of oranges that a farer produces each year) A change in, for exaple, will have the following effects: a substitution effect (as before), an ordinary incoe effect (as before), and an endowent incoe effect Ada Jacobsson, Departent of Econoics 20

21 Assue increases to p 1 which eans the value of the endowent (incoe) is now: This eans that: = p 1 ω 1 + ω 2 Δ = (p - 1ω 1 + ω 2 ) ( ω 1 + ω 2 ) = -- = Δ ω 1 Proceeding as we did with the first Slutsky equation: x (p 1 1,, ) x ( 1,, ) = Δ x 1 (p- 1,, -) x ( 1,, ) (Marshallian substitution effect) Eg 1 x 1 (p- 1,, -) x 1 (p- 1,, ) (ordinary incoe effect) Eg 1 + x 1 (p- 1,, --) x 1 (p- 1,, ) (endowent incoe effect) Eg 1 Can be re-written as: Δ = Nvv dn w 1

22 By definition of the ordinary incoe effect, see equation (5): Δ = - x 1 and by definition of the endowent incoe effect: Δ = Nvv dn w 1, we can rewrite the new Slutsky equation: x 1 (p 1,, ) x 1 (,, ) Δ = x 1 (p 1,, ) x 1 (,, ) Δ x 1 (p 1,, ) x 1 (p 1,, ) - x 1 + x 1 (p 1,, ) x 1 (p 1,, ) -- ω Ada Jacobsson, Departent of Econoics 22

23 Re-writing using s: Δx 1 Y Δ QRSTU VWWVXS = Δxs 1 Y Δ Z[\]S VWW. x 1 Δx 1 Δ { }. #_XRNV VWW. + ω 1 Δx ω 1 Δ ~_}. #_XRNV VWW. For sall changes i price: EON 1 EN EOw 1 EN Δx 1 Y Δ QRSTU VWWVXS = Δxs 1 Y Δ Z[\]S VWW. + (ω 1 x 1 ) Δx 1 Δ QRSTU #_XRNV VWW Ada Jacobsson, Departent of Econoics 23