Demand. Demand and Comparative Statics. Graphically. Marshallian Demand. ECON 370: Microeconomic Theory Summer 2004 Rice University Stanley Gilbert

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1 Demnd Demnd nd Comrtve Sttcs ECON 370: Mcroeconomc Theory Summer 004 Rce Unversty Stnley Glbert Usng the tools we hve develoed u to ths ont, we cn now determne demnd for n ndvdul consumer We seek demnd functons x * = x (,, m) nd x * = x (,, m) From our revous exmle references of the form: u = x α y α And budget constrnt: x x + y y m Result n demnds: x * = αm / x y * = ( α)m / y Econ Ordnl Utlty Mrshlln Demnd Grhclly In generl, we re nterested n trcng out Mrshlln Demnd Curves. A Mrshlln Demnd Curve descrbes how demnd for good chnges: As ts own rce chnges, nd Holdng ll other rces nd ncome constnt Functonlly, tht mens grhng x * = x (,, m) Versus And holdng nd m constnt Demnd for Good references x 3 3 x Q Econ Ordnl Utlty 3 Econ Ordnl Utlty 4

2 Aggregtng Demnd Ultmtely, we wnt to look t mrket demnd Tht s, we wnt to see how the demnds for mny eole dd together to mke u mrket demnd If we hve n eole And let = n Two goods, x, nd x Aggregtng Demnd (cont) Consumer s ordnry demnd functon for good j s x j (,, m ) (notce tht we mke llownce for dfferent consumers hvng dfferent ncome) Then ggregte demnd for good x j s: X j (,, m,, m n ) = Σ =n x j (,, m ) If ll consumers re dentcl, then X j (,, M) = n x j (,, m) Where M = n m Econ Ordnl Utlty 5 Econ Ordnl Utlty 6 Aggregtng Demnd Grhclly Grhclly, we dd demnd curves holdng rce constnt Tht s, horzontlly Aggregtng Demnd Grhclly Grhclly, we dd demnd curves holdng rce constnt Tht s, horzontlly Consumer Consumer Mrket Consumer Consumer Mrket Q Q Q m Q Q Q m Econ Ordnl Utlty 7 Econ Ordnl Utlty 8

3 The Lw of Demnd Wht, n Economcs s clled the Lw of Demnd sys Demnd curves lwys sloe downwrd Tht s, Demnd for good lwys decreses s the rce for tht good ncreses (holdng everythng else constnt) Ths sttement s dfferent from wht s n your book whch I wll dscuss n due tme but t s the more usul sttement of the lw of demnd The Lw of Demnd (cont) The Lw of Demnd s not lw n the sense tht t s requred by Economc theory A good tht does not obey the lw of demnd s theoretclly ossble nd s clled Gffen Good (A good tht obeys the lw of demnd s clled n Ordnry Good) However, so fr, no one hs ever dentfed Gffen good So the Lw of demnd s good descrton of emrcl relty Econ Ordnl Utlty 9 Econ Ordnl Utlty 0 Elstcty of Demnd One queston we re nterested n s how resonsve demnd s to chnges s rce We use somethng clled Elstcty to mesure t In generl, Elstcty s the rto of the ercent chnge of (here) demnd to ercent chnge n rce Tht s: % x ε = % Clcultng Elstcty There re two tyes of Elstcty: ont Elstcty: Arc Elstcty: ε = ε = dx d x dx = x d x + = x x + We wll lmost lwys use ont Elstcty x x x Econ Ordnl Utlty Econ Ordnl Utlty 3

4 Elstcty n Generl There re mny dfferent Elstctes Own-rce Elstcty mesures how demnd chnges s ts own rce chnges Income Elstcty mesures how demnd chnges s ncome chnges Cross-rce Elstctes mesure how demnd chnges s the rces of other goods chnge Observtons on Demnd Elstcty Own-rce Elstcty my be dfferent t dfferent onts on the demnd curve Snce demnd generlly decreses s rce ncreses, we hve ε < 0 But usully for convenence we work wth ε. We cll demnd Elstc f ε > We cll demnd Inelstc f ε < In generl, when demnd s elstc, t resonds strongly to chnges n rce when demnd s nelstc, t resonds wekly to chnges n rce Econ Ordnl Utlty 3 Econ Ordnl Utlty 4 Exmle: Lner Demnd Curve Exmle: onts of Interest Suose nverse demnd s lner = bx x = /b / b We clculte dx /d = - / b Own-rce elstcty of demnd s ε = dx x d = ( ) b b = / ε = - = bx ε = 0 Observe tht = 0 ε = = 0 0 = ε = = ε = - = ε = = / b / b ε = 0 x Econ Ordnl Utlty 5 4

5 Exmle: Summry Imortnt Secl Cses Wht s the elstcty of horzontl demnd curve? ε = own-rce elstc / ε = own-rce unt elstc own-rce nelstc Wht s the elstcty of vertcl demnd curve ε = 0 /b /b x Econ Ordnl Utlty 8 Income Elstcty of Demnd Income Effects Grhclly We re lso nterested n demnd chnges s ncome chnges We use Income Elstcty to mesure t, where Income Elstcty for Good s defned s: x references m Engle Curve ε m dx m = x dm m m m m x x Econ Ordnl Utlty 9 Econ Ordnl Utlty 0 5

6 Grhcl Income Elstcty (cont) Norml nd Inferor Goods x references Income Offer Curve m m x m m m Engle Curve x For most goods demnd ncreses s ncome ncreses Tht s ε m > 0 And the Engle curve s sloed forwrd Such goods re clled Norml Goods However, demnd for some goods decreses s ncome ncreses Tht s ε m < 0 And the Engle curve s sloed bckwrd Such goods re clled Inferor Goods Note tht some goods my be both Norml nd Inferor n dfferent rce rnges Econ Ordnl Utlty Econ Ordnl Utlty Inferor to Wht? Wht exctly s n nferor good, nd wht s t nferor to? Exmle: the Yugo Very che cr: Sold for ~ $4,000 n the US n 986 oor qulty nd very smll Sold modertely well n the US Stll n roducton n Serb Who do you thnk bought the crs? Wht do you thnk hened when ther ncome ncresed? Inferor to Wht? To other goods vlble Norml, Inferor nd Gffen Goods A Norml Good cnnot be Gffen Good -or- All Gffen Goods re Inferor goods (Cn you see why?) However, most Inferor Goods re not Gffen Goods Econ Ordnl Utlty 3 Econ Ordnl Utlty 4 6

7 Cn ll goods be nferor? All goods cnnot be Inferor, tht s At lest one good must be Norml Why? x Cross-rce Elstcty of Demnd Fnlly, we re nterested n how demnd chnges s other rces chnge We use Cross-rce Elstcty to mesure t, where Cross-rce Elstcty for Good reltve to the rce of good j s defned s: j dx ε j = x d j m m x Are there ny references tht wll result n consumton decresng for both goods when ncome ncreses? Econ Ordnl Utlty 5 Econ Ordnl Utlty 6 Substtutes nd Comlements If consumers see two goods s close substtutes for ech other, wht sgn wll the cross-rce elstcty of demnd hve? ε j > 0 If consumers see two goods s comlements for ech other, wht sgn wll the cross-rce elstcty of demnd hve? ε j < 0 Exmles erfect Comlements/Substtutes Homothetc references x = A ε Wht mkes ths nterestng? Econ Ordnl Utlty 7 Econ Ordnl Utlty 8 7