6 Traditional Demand Theory

Transcription

1 Traditiona Deand Theory We have aready discssed soe exapes of coparative statics in pervios ectres and hoework exercises. However, we have spent a big share of or energy discssing how to forate and sove probes of rationa choice in di erent versions. Now, we wi switch the focs soewhat and try to be ore systeatic in or approach to coparative statics. In genera, coparative statics is an exercise where we anayze how the behavior changes when di erent variabes in the environent changes. That is, we try to predict what the behaviora response to di erent (to the conser) exogenos changes shod be. This sort of an exercise is what a arge share of econoics is abot, and we wi do it in any other appications in the rest of the cass. For now, however, we wi stdy what happens as prices and incoe changes for the conser,which is the topic of traditiona deand theory (one of the odest and ost we deveoped branches of econoic theory). x 2 x 2 Z ZZ Ze ZZ Z Z ZZ ZZ e ee Z ZZ Z Z ZZ ZZ x 2 e e e Z ZZ x 2 Z Z ZZ ZZ Z e ZZ ee Z ZZZ Z Z ZZ ZZ Z Z ZZZ ZZ x 1 e e x 1 Z Figre 1: A Change in Price or Incoe Changes the Sotion The rst fact to reaize is trivia, bt iportant: the optia conser choice depends on p 1 ; p 2 and : This shod be obvios fro a graph. In Figre 1 I ve indicated an optia sotion given soe initia prices and incoe (x 1; x 2). In the eft graph we see that when the price increases, then the od optia bnde is no onger a ordabe, so the optia sotion 5

2 with a higher price on good one st be soe di erent bnde (soewhere aong new bdget ine). To the right we see that when incoe increases there are now bndes better than the od optia sotion that are a ordabe, so the sotion st change here as we. write Since we now wi start to vary p 1 ; p 2 and we want notation that akes this cear. We (p 1 ; p 2 ; ) x 2 (p 1 ; p 2 ; ) for the deand fnctions associated with soe particar tiity fnction. What this eans in ters of or optiization probe is that (p 1 ; p 2 ; ) and x 2 (p 1 ; p 2 ; ) together constitte an optia sotion to s.t p 1 + p 2 x 2 ax ;x 2 ( ; x 2 ) Exape 1 CobbDogas. We have actay aready soved for the deand fnctions in cass. (p 1 ; p 2 ; ) and x 2 (p 1 ; p 2 ; ) soves ax x a 1 2 a s.t p 1 + p 2 x 2 and we aready know that (p 1 ; p 2 ; ) = a x 2 (p 1 ; p 2 ; ) = (1 Specia property of CobbDogas: deand for good 1 independent of price of good 2 and vice versa. This is not tre in genera. Aso note that the paraeter fro the tiity fnction a enters the fora for the deand generated by CobbDogas preferences. Sti, we don t think of the deand fnction as a fnction of a: The reason is that a is a deep paraeter re ecting the preferences and coparisons of di erent as wod be to copare di erent decision akers. p 2 p 1 a)

3 .1 Changes in Incoe x 2 Enge Crve Incoe O er Crve e ee 0 e e ee x x 00 1 x x 0 1 x 00 p 1 p 1 p x Figre 2: Graphica Derivation of Enge Crve Now, the deand fnction takes on a qantity for each tripe (p 1 ; p 2 ; )so to graph these things we have to project down into ower diensions. One of the obvios experients to do is then to x prices and see how the sotion changes as incoe changes bt prices are x. This projection of the deand fnction is caed an Enge crve and the graphica derivation of an Enge crve is shown in Figre 2. Observe that whie the natra convention wod be to pot on the vertica axis and on the horizonta, the opposite convention was estabished soe tie in the dark ages and econoists got stck with this. Notice that whether the conser increases or decreases the consption of a particar good when the incoe increases depends on the preferences. That is, in the Cobb Dogas exape we directy see that (p 1 ; p 2 ; ) = a p 1 and x 2 (p 1 ; p 2 ; ) = (1 a) p 2 are both increasing in : In contrast, Figre 3, which is drawn with preferences that satisfy onotonicity and convexity, shows an exape where the consption if is decreasing in over an interva (observe, since consption is zero when = 0 it st be that the consption is initiay increasing in to ake it possibe for the crve to bend backwards). 7

4 x 2 Incoe O er Crve Enge Crve 00 0 x 00 1 x p 1 p 1 Figre 3: An Inferior Good The concsion is ths that we cannot a priori say anything abot whether the consption is increasing or decreasing in incoe. For ftre reference we wi sipy create soe terinoogy that assigns naes to the di erent cases: De nition 2 Good 1(2) is said to be a nora good if (p 1 ; p 2 ; ) (x 2 (p 1 ; p 2 ; )) is increasing in De nition 3 Good 1(2) is said to be an inferior good if (p 1 ; p 2 ; ) (x 2 (p 1 ; p 2 ; )) is decreasing in In concrete exapes one can either jst ook at the deand fnction to see if it is increasing in or not. If the deand fnction is ore copicated, t is soeties sef to observe that one can check this by ooking at the partia derivative (p 1 ; p 2 ; ) : In the CobbDogas case (p 1 ;p 2 ;) = a p 1 > 0: In genera, noraity corresponds to a positive partia derivative with respect to incoe, and inferiority corresponds with a negative partia derivative. 8

5 Typicay noraity is taken to ean that the qantity deanded is increasing in for a (p 1 ; p 2 ) ; bt conventions di er and I wi not be picky on things ike that. Observe however that it is ipossibe for a good to be aways inferior. If one wants to be caref, one aso has to ake ones ind p whether (p 1 ;p 2 ;) 0 or (p 1 ;p 2 ;) for noraity, bt yo need not worry too ch abot that detai. > 0 is the criterion.2 Changes in Prices The next obvios experient is to see how a deand fnction behaves as and the price of the other good(s) are hed constant. This projection of the deand fnction is caed the deand crve. Figre 4 shows how this crve can in principe be derived fro the sa indi erence crve graph. Notice the convention (which has stck for historica reasons) that (the independent variabe ) price is on the vertica axis. Maybe ore srprisingy (ness yo ve seen it in an earier cass) the e ect on consption fro a change in the price is aso abigos. If we again ook at the CobbDogas exape we see that (p 1 ; p 2 ; ) p 1 = x 2 (p 1 ; p 2 ; ) p 2 = a p 2 1 < 0 (1 a) p 2 2 < 0; so in this case the e ect fro a price increase is what one wod intitivey expecta decrease. However, it is possibe that consption of a good decreases when the price decreases, which graphicay corresponds to an pwards soping deand crve. Notice (we wi coe back to this) that the indi erence crves in the graphica constrction of an pward soping deand in Figre 5 ook rearkaby siiar to those of an inferior good. The conventiona terinoogy (which isn t sed as ch as the nora/inferior distinction for reasons that wi becoe apparent) is: De nition 4 Good 1(2) is said to be a ordinary good if (p 1 ; p 2 ; ) (x 2 (p 1 ; p 2 ; )) is increasing in p 1 (p 2 ) 9

6 x 2 SB BS B S B S BB S SS B BB S B BB S SS S S S B BB p1 p 0 1 S p 00 1 p p 0 1 p 00 1 p Deand Crve Figre 4: Graphica Derivation of (Inverse) Deand CrveOrdninary Good De nition 5 Good 1(2) is said to be a Gi en good if (p 1 ; p 2 ; ) (x 2 (p 1 ; p 2 ; )) is decreasing in p 1 (p 2 ) Again, soeties the easiest way to check is by taking the partia derivative with respect to (own) price. 70

7 x 2 S B BS B S B S BB S SS B BB S B BB S SS p1 p 0 1 B BB p 0 1 Deand Crve S S S S p 00 1 p p 00 1 p Figre 5: A Gi en Good.3 Exapes.3.1 Cobb Dogas Preferences We have that (p 1 ; p 2 ; ) = a p 1 71

8 and to draw an Enge crve we ony need to set a; p 1 to soe speci c vaes and pot the reation between and : Say for concreteness that a = 1=2 and p 1 = 4 ) (4; p 2 ; ) = = 8 ) = 8 ; so the Enge crve is a straight ine starting at the origin with sope 8 x1 Figre : The Enge Crve for ( ; x 2 ) = ven any p 2 and p 1 = 4 In genera we see that = a x 2 = p 1 (1 a) p 2 Since the reationship between and is inear we see fro this that the Enge crves are straight (pwards soping) ines starting at the origin. Hence, good 1 is a nora good and everything is syetric for good 2 so we concde that both goods are nora for a conser with Cobb Dogas preferences To sketch the deand crve for good 1 we x a and and vary p 1 : If we again set the preference paraeter a = 1=2 and set = 10 we get = p 1, p 1 = 5 ; so = 1 ) p 1 = 5; = 2 ) p 1 = 2:5; = 5 ) p 1 = 1::: 72

9 p 1 5 s 2:5 s 1 s x1 Figre 7: The Deand Crve for ( ; x 2 ) = ven any p 2 and = 10 Again we see that in genera, the (inverse) deand crves are given by p 1 = a p 2 = (1 a) x 2 ; where yo shod think of as a constant when yo pot these crves. Obviosy this eans that deand crves are downward soping, so we concde that both goods are ordinary.3.2 Perfect Sbstittes ( ; x 2 ) = 5 + x 2 : Reca fro one of yor hoework exercises that this tiity fnction generates interior sotions ony in knifeedge cases. Indi erence crves are straight ines, so the typica case is a corner sotion (draw pictre if yo don t see this!). The ony tricky part is to deterine when (that is for which prices & incoe) which corner is optia and the easy way to this is to check what happens if the conser spends everything on ; that is ( ; x 2 ) = p 1 ; 0 : The corresponding vae of the tiity fnction is 5 p 1 : 73

10 If on the other hand the conser spends everything on x 2 ; then the tiity is p 2 : Ceary, spending everything on (x 2 ) is better if 5 p 1 > p 2, p 1 p 2 whie the conser is indi erent if p 1 p 2 = 5: Ths the deand crve is 8 p >< 1 if p 1 p 2 < 5 i (p 1 ; p 2 ; ) = h0; p1 if p 1 p 2 = 5 : >: 0 if p 1 p 2 > 5 As an exape, consider p 1 = p 2 = 1 )sope of bdget ine: 1 )Enge crve for good 1: = )Enge crve for good 2: x 2 = 0 for a (foows vertica axis) < 5 ( 5 p 1 < p 2, p 1 p 2 > 5), Given that we ony reqire the deand to be weaky increasing in incoe, this is consistent with noraity. Deand crve: Set = 10; p 2 = 1 p x1 Figre 8: Deand Crve for ( ; x 2 ) = 5 + x 2 given = 10 and p 2 = 2 = 0 for p 1 > 5 [0; 2] for p 1 = 5 decreasing over p 1 in [0; 5] If we aow ordinary goods to have ranges where the deand is constant, this is an ordinary good. 74

11 .4 Sbstittes and Copeents Fina qestionhow is the deand of a ected by a change in p 2 : Know that for perfect copeents the deand is decreasing since a (p 1 ; p 2 ; ) = bx 2 (p 1 ; p 2 ; ) The deand can then by fond by soving a p 1 (p 1 ; p 2 ; ) + p 2 b (p 1 ; p 2 ; ) = ) (p 1 ; p 2 ; ) = a p 1 + p 2 b so & when p 2 % : On the other hand, for perfect sbstittes, either nothing happens or an increase in p 2 ) % : Given these exapes the foowing de nitions see natra:.4.1 (Gross) Sbstittes If (p 1 ; p 2 ; ) is increasing in p (Gross) Copeents If (p 1 ; p 2 ; ) is deceasing in p 2 Yo can check that goods are neither sbstittes or copeents for CobbDogas, sbstittes for perfect sbstittes and copeents for perfect copeents..5 Incoe & Sbstittion E ects This is covered in Varian Chapter 8 ( and 8.7). We fond fro straightforward indi erence crve anaysis that (in the case of a Gi en good) it is indeed possibe that the deand is increasing in price. Whie we think that this is priariy a criosity (that is, the conventiona wisdo is that ost goods are not ike this) it is instrctive to think abot why this can happen. Brie y pt, the answer is that two things happen when the price of a good goes down. First of a the reative price changes aking the good cheaper in ters of other good. 75

12 Moreover, the prchasing power of the conser increasesa fa in one price akes the conser richer since consption of a goods can now be increased. We wi now try to separate ot these e ects into incoe and sbstittion e ects. Yo shod be warned that there are two di erent ways to do this. Exacty as in Varian I wi spend ost tie expaining the diagraaticay ost straightforward decoposition (caed the Stsky decoposition), bt check Varian 8.8 for another possibe decoposition. x 2 A AA A AA s sx x 0 A A sx 00 A Sbst E ect A A A A A A Inco e E ect A A p 1 p 0 1 x1+p2x2 p 0 1 p 0 1 Figre 9: Sbstittion and Incoe E ects The idea is that we can contro for the fact that the conser gets richer when the price fas by adjsting the incoe so that the od optia bnde is on the bdget ine with the new reative prices. The optia bnde for this ctitios bdget set is what the conser wod optiay choose nder the new prices if incoe was taken away so as to ake the od optia bnde barey a ordabe. Hence the di erence between this and the od consption can be thoght of as the change in consption that is attribted to the change in reative prices and this change is what is caed the SUBSTITUTION EFFECT. The INCOME EFFECT is then the change fro this (hypothetica) bnde with new reative prices and adjsted incoe to the optia bnde with the new prices and the (nchanged) incoe that the conser actay has. 7

13 This is istrated in Figre 9 where x = ( ; x 2 ) is the deand given (p 1 ; p 2 ; )and x 0 is the deand given (p 0 1; p 2 ; )(the ony change is the price of good 1 that has decreased fro p 1 to p 0 1). Diagraaticay, the sbstittion e ect is fond by pivoting the bdget ine so that a new bdget ine with sope p 0 1 p 2 that goes thogh the od optia bnde is constrcted. The sbstittion e ect is then the di erence between the deand given this new bdget ine and the origina deand. The incoe e ect is the di erence between the deand given the price change (the rea thing with nchanged incoe) and the (hypothetica) deand jst constrcted (x 00 in the pictre) To expain this soewhat ore carefy it is sef to se the notation for deand fnctions we ve introdced 1. The incoe that keeps ( (p 1 ; p 2 ; ); x 2 (p 1 ; p 2 ; )) exacty on the bdget ine when the price of good 1 changes fro p 1 to p 0 1 is 0 = p 0 1 (p 1 ; p 2 ; ) + p 2 x 2 (p 1 ; p 2 ; ) 2. The TOTAL EFFECT on the deand of good 1 the price of good 1 changes fro p 1 to p 0 1 is = (p 0 1; p 2 ; ) (p 1 ; p 2 ; ) 3. The SUBSTITUTION EFFECT is x S 1 = (p 0 1; p 2 ; 0 ) (p 1 ; p 2 ; ) 4. The INCOME EFFECT is x N 1 = (p 0 1; p 2 ; ) (p 0 1; p 2 ; 0 ) In words: 1. Tota e ect: e ect on deand fro a price change fro p 1 to p

14 2. Sbstittion e ect: e ect on deand fro a price change fro p 1 to p 0 1 and a sitaneos incoe change fro to 0 where 0 is cacated as to ake the od deand exacty a ordabe at new prices 3. Incoe e ect: e ect on deand fro a change in incoe fro 0 to : (given new prices). Observe nay that the decoposition is OK since x S 1 + x N 1 = (p 0 1; p 2 ; 0 ) (p 1 ; p 2 ; ) + (p 0 1; p 2 ; ) (p 0 1; p 2 ; 0 ) = (p 0 1; p 2 ; ) (p 1 ; p 2 ; ) =. Exape: Copting Sbstittion and Incoe E ects for CobbDogas Preferences Reca that if ( ; x 2 ) = x a 1 2 a ; the deand fnctions are (p 1 ; p 2 ; ) = a x 2 (p 1 ; p 2 ; ) = p 1 (1 a) p 2 : For concreteness, set a = 1 2 and et (p 1; p 2 ; ) = (2; 2; 40) : Consider a change in the price of good 1 fro p 1 = 2 to p 0 1 = 1 ) )The tota e ect is given by (2; 2; 40) = = 10 x 2 (2; 2; 40) = = 10 (1; 2; 40) = = 20 = (1; 2; 40) (2; 2; 40) = = 10 78

15 To copte the sbstittion e ect we sove for 0 = 1 (2; 2; 40) + 2x 2 (2; 2; 40) = = = 30; so the sbstittion e ect is x S 1 = (1; 2; 30) (2; 2; 40) = = = 5: The incoe e ect is x N 1 = (1; 2; 40) (1; 2; 30) = = 5; bt reay we aready knew this since in genera x N 1 = x S 1 and we had aready copted = 10 and x S 1 = 5:.7 Sign of the Sbstittion E ect Ceary, the incoe e ect ay be negative or positive depending on whether the good is nora or not, bt the sbstittion e ect can be signed, which is why the decoposition is of soe se in econoics. Cai The sbstittion e ect is aways negative. What this eans is that when p 1 goes p (and incoe is adjsted), the deand goes down, whie if p 1 goes down, then the deand goes down after the adjstent in incoe. To see this ook at Figre 10, where x 0 = (x 0 1; x 0 2) is the optia bnde given soe prices and incoe (corresponding with the steeper bdget ine). Now, if the sbstittion e ect tends to decrease the consption when the price on good one goes down, the new optia bnde st be to the eft of x 0 on the pivoted bdget ine. Ca this bnde x 00 : Now, the crcia thing to reaize is that this bnde is a ordabe given the od prices and incoe, so 79

16 x 2 \ \\ x 00 2 x 0 2 b \ bbb s \\ x 00 b x \ bbb s 0 \ \\ b bbb \ \ \\ b bbb x 00 1 x 0 1 b b Figre 10: Why Sbstittion E ect can t be Positive the conser cod have boght x 00 before. Moreover, if preferences are onotonic, then everything to the northeast of x 00 is stricty better than x 00 which st be at east as good as x 0 was a ordabe given the od prices and incoe. Hence, x 0 cod not have been optia in the rst pace. The concsion of this is that the optia bnde after the pivot st be soewhere to the right of x 0 on the pivoted bdget ine, so the deand increases when the price goes down. The exact sae argent works for a price increase as we. Reark: The argent ses the principe of reveaed preference. We wi not spend too ch tie on this in this cass, bt yo shod know that this principe akes it possibe to observe preferences. Indeed, since we cod get data that vioates reveaed preference, this akes or ode of rationa choice reftabe, eaning that this is actay soething that qai es as a scienti c theory. See chapter 7 in Varian r detais on how reveaed preference can be sed to draw inference abot preferences. WE CAN THEN CONCLUDE: 1. p 0 1 < p 1 ) (p 0 1; p 2 ; 0 ) (p 1 ; p 2 ; ) 2. p 0 1 > p 1 ) (p 0 1; p 2 ; 0 ) (p 1 ; p 2 ; ) ; 80

17 where 0 = p 0 1 (p 1 ; p 2 ; ) + p 2 x 2 (p 1 ; p 2 ; ).8 Sign of the Incoe E ect x 2 x 2 s s Nora Good s s Inferior Good x1 Figre 11: Incoe E ect for Nora vs Inferior Good The incoe e ect ceary depends on whether the good is nora or inferior and the ony thing to watch ot for is the direction of the shifts. First of a note that if x = ( ; x 2 ) is the deanded bnde given (p 1 ; p 2 ; ) ; then 0 = p p 2 x 2 (de nition of pivot) = p 1 + p 2 x 2 (since x is optia ) on bdget ine) Cobining these we have = 0 = (p 0 1 p 1 ) = p 1 ; so p 1 > 0, > 0: SAME SIGN, so Increased price )Increased Incoe Decreased price)decreased Incoe, so we say that The incoe e ect is negative for nora goods (since p 1 %) % and the e ect is shift fro hypothetica to acta incoe) 81

18 The incoe e ect is positive for inferior goods..9 A Gi en Good is Very Inferior The easy way to think abot these things is to iagine an increase in price. However, interpreting as opposite of the sign of the change in the price and + as the sae sign as the change in the price the expressions beow are tre no atter which way the price changes. CASE 1: If good 1 is a nora good, everything is cear since negative = x S 1 negative (aways) + x N 1 negative (def of nora good) )Nora goods have downward soping deand crves. CASE 2: If good 1 is inferior, then? = x S 1 negative (aways) + x N 1 Positive (def of inferior good) Hence, if the incoe e ect is strong enogh it ay doinate the sbstittion e ect) ay be positive (eaning that it oves in the sae direction as the change in the price), in which case good 1 is a Gi en good. The concsion of this is that any Gi en good st be an inferior good (whie the opposite ipication doesn t hod), so it is no coincidence that exapes for inferior and Gi en good often coincide. I a not an epirica econoist, bt, according to coeages, there is no convincing epirica stdy that has been abe to nd a reaword Gi en good. I don t think that is too srprising. The incoe e ects need to be arge for the incoe e ects to doinate the sbstittion e ects, and for that to be the case the good in qestion st be a fairy iportant good in the sense that a qite arge share of the incoe is spent on it. Typica textbook exapes of Gi en goods are potatoes on Ireand or rice in China (this is aso the kind of goods epricists have ooked at in vain), bt it sees dobtf that the consption of the basic sorce of carbohydrates wod decine as incoe rises. Rather, one wod expect 82

19 peope to eat as ch potatoes (or ore) as before and top it p with soe eat, vegetabes, and aybe a Giness or two 7 Labor Sppy Varian pages (bt ignore his terinoogy abot endowent incoe e ects. Before starting with eqiibri theory I wi discss one na appication/interpretation of the standard conser choice ode that I have postponed becase I wanted to tak abot incoe and sbstittion e ects before discssing it. We now think abot an agent who ikes consption, disikes work (who doesn t rather spend tie watching Who wants to... ) and is seing his/her tie on the arket. Let C be consption p be the price of the consption good L be the aont of abor sppied L be the endowent of tie (i.e., 24 hors) w be the wage (doars per nit of tie) M be nonabor incoe The sceptic ay nd it strange that athogh sppy of abor has an obvios tie diension, consption has not. This is a fair copaint, bt as sa we are abstracting away fro ots of reais in order to ake the ode as sipe as possibe. Sti, this basic ode has proven to be very sef and is sti sed in abor econoics extensivey. 7.1 The Bdget Constraint The obvios way to write down the bdget constraint is to observe that Expenditres=tota incoe, that is pc = M + wl: 83

20 This for is ne for setting p the reevant axiization probe, bt not very sef for drawing indi erence crve graphs. Instead, we observe that pc = M + wl:, pc wl = M, add wl on both sides :pc + w L L = M + wl Finay et C be the consption the conser wod have if not working, that is C = M p and we can write the bdget constraint as pc + w L L {z } eisre = pc + wl {z } vae of endowent This for of the bdget constraint shod ake cear that we can think of the abor sppy probe in the sae way as the standard ode, where the conser is prchasing consption goods and eisre. C Sope r w p C L L L Figre 12: The Bdget Set for the Labor Sppy Probe The way to think abot it is that if the conser doesn t trade then he/she conses the endowent, which is C nits of the consption good and L nits of eisre. However, 84

21 the conser can trade eisre for consption by sppying abor in the arket. Note here that: 1. w is the price, or opportnity cost, of eisre. The point of this is that if yo think that it is free to watch The Bacheor (or The Bacheorette) yo shod seriosy rethink! What yo pay for doing it is the incoe yo wod earn if yo went ot working the tie spent on the coch (or, in a richer ode where yo can invest in ftre earnings opportnities by getting a good grade in Econ 301, yor present vae of the expected extra earning yo wod get by spending that extra tie on yor hoework probe for Friday). 2. The sope of the bdget ine, w=p is say referred to as the rea wage. 7.2 Optia Labor Sppy Decisions We now asse that the conser has soe preferences over consption and eisre given by U C; L L Sbstitting in the bdget constraint gives the probe in the sa for ax U C + wp L; L L 0LL and the rst order condition wi give a tangency condition of exacty the sae for as before with the interpretation that the argina rate of sbstittion between consption and eisre has to be eqaized with the sope of the bdget constraint. The optia abor sppy decision is depicted in Figre 13. Yo shod a try to nd the reevant rst order conditions and think abot the, I wi restrict ysef to graphica anaysis. Qestion: Sppose the wage goes p, what happens with abor sppy? Sees to be a reevant qestion. Often arged that redcing taxation on incoe wi ead to ore incentives to sppy abor) ore goods prodced... 85

22 C r Sope w p C Leisre r Labor L L L Figre 13: Optia Labor Sppy For sipicity et M = 0 (no nonabor incoe). To graph the bdget set we then note that the intercept at the eisre axis in L; whie if the conser has no eisre the (doar) incoe is wl; so that the intercept with the consption axis is that wl : Figre 14 shows p the e ect of increasing the wage fro w to w 0 and we note that: An increase in the wage is exacty as a decrease in price of the consption good. Hence, how consption of eisre (sppy of abor) is a ected depends on whether eisre and the consption good are sbstittes or copeents. Yo are encoraged to work ot detais! e ects: An aternative way to ook at it is to decopose the change in incoe and sbstittion Sbstittion E ect w=p %)eisre ore expensive)work ore/ess eisre. Incoe E ect w=p %)conser richer and can increase consption of both goods. If eisre is a NORMAL good) conser bys ore eisre. 8

23 C w 0 L p wl p H H H H H H H H H H H H H L L L Figre 14: E ect on Bdget Set Fro Higher Wage THUS: INCOME AND SUBSTITUTION EFFECTS TEND TO GO IN OPPOSITE DIRECTIONS FOR NORMAL GOODS RATHER THAN FOR INFERIOR GOODS (AS IN STANDARD TWO GOODS MODEL). Since there see to be no a priori reason why eisre shod be inferior we expect sa responses in ters of abor sppy and even backwards bending at high incoes. Eventay this eans that the response to changes in the rea wage is an epirica qestion and whie the evidence is ixed sa responses is the nor and backwards bending has been fond in ots of stdies. 7.3 Exape: CobbDogas Preferences I asse no nonabor incoe. The probe is then to sove sbj to pc = wl ax n C + (1 ) n L L C;L or w ax n 0LL p L + (1 ) n L L 87

24 J J J J T C TT J J J T J TT J r J Tr J T J r TT J J T J w T Sope J p TT J J C r J L L L Figre 15: Sbstittion and Incoe E ects (Incoe E ect Doinating) FOC w (1 ) w L + p p L L ( 1) = 0, Labor sppy constant fnction of rea wage. L L = (1 ) L w L = L p Incoe and sbstittion e ect cance each other ot copetey. 88