Lecture 5:Elasticity of Demand and SupplyText: Chapter 5 ( pages 101105!CASNRResponsiveness of the Quantity Demanded to Price ChangesEarlier, we indicated that, ceteris parius, the !uantity of a product demanded will vary inversely to the price of that product"#hat is, the direction of change in !uantity demanded following a price change is clear"$hat is not %nown is the e&tent y which !uantity demanded will respond to a price change"#o measure the responsiveness of the !uantity demanded to change in price, we use a measure called "#$CE EL%ST$C$T& '( DE)%*D+',n "rice Elasticity of Demand#he price elasticity of demand is a measure of the responsiveness of !uantity demanded to a price change',n "rice Elasticity of Demand' #he percentage change in the !uantity demanded relative to a percentage change in its own price"(or a smooth )differentiale* demand curve, the price elasticity of demand is given y QPPQPPQQED==QPPQED=-sing "rice Elasticity of DemandElasticity is a pure ratio independent of units"Since price and !uantity demanded generally move in opposite direction, the sign of the elasticity coefficient is generally negative"+nterpretation' +f ED , - ."/.' A one percent increasein price results in a ."/.0 decrease in !uantity demanded',n "rice Elasticity of Demand (ED!.uantity ./.1"rice "/"1 ED1 1.2. 1133 -.2 )14-.2*5)1.241* , - 3"36&1.2 , - 26 .23 -23 ).4-23*&)1334.* , - 3"36&23 , - .2 113 -63)14-63*&)2346* , - 3"3.2&1."2 , - 3"7A numerical e&ampleClassifications of ',n "rice Elasticity of Demand:$nelastic demand ( 0ED0 1 1 !:a change in price rings aout a relatively smaller change in !uantity demanded )e&" gasoline*"#otal Revenue , PQ rises as a result of a price increase-nitary elastic demand ( 0ED0 2 1 !:a change in price rings aout an e!uivalent change in !uantity demanded"#R, PQ remains the same as a result of a price increaseElastic demand ( 0ED0 3 1 !:a change in price rings aout a relatively larger change in !uantity demanded )e&" e&pensive wine*"#R , PQ falls as a result of a price increase"rice Elasticity of Demand 4Total #e5enue and EDPrice +nelastic Demand8 ED 8 9 1 Price Elastic Demand 8 ED8 : 1 PP Q Q T#T#"rice Elasticity along Linear Demand Cur5esLinear Demand Cur5e: Q = a bPPrice elasticity of this demandEd 2 (6Q7 6P!(P7Q! 2 ; b(P7Q!Any downward sloping demand curve has a corresponding inverse demand curve"$n5erse linear Demand Cur5e: P = a/b (1/b!QPQ3a/2 aa/ba/2bMAt P= a/b,Ed , ; < at P = 0, Ed , 3< at P= a/2b,Ed , ;1+n the region of the demand curve to the left of the mid-point =, demand is elastic, that is 8 9 Ed 1 1+n the region to the right of the mid-point =, demand is inelastic, 1 1 Ed 9 3Constant Elasticity Demand Cur5eAnother commonly used demand curve is the constant elasticity demand curve, given y Q = aP-b(or this demand curve, the price elasticity of demand is Ed 2 (6Q7 6P!(P7Q! 2 ; b#hus, the price elasticity of demand is always the same (-b! on every point of this demand curve" >owever, such a demand curve could e elastic, or inelastic, or unit-elastic )depending on the value of b* " ?wn Price Elasticity of Demand )ED*Calculating ?wn Price Elasticity of Demand from a Demand (unction'@sing calculus' Aiven a demand function'Qb 2 100 : ;0 Pb : /0 Pc < +005I, where, Qb , Quantity demanded of eer in illion B-pac%s, Pb , Price of eer per B-pac% )C2*, Pc , Price of a pac% of chips )C1*, and I , Annual household income )C.2,333*"Qb , 133 D 73E)2* D .3E)1* F "332E).2333* , 22 #a%ing partial derivative of the demand function with respect to price and sustituting values for P and Q we get' QPPQEd =/./. " .222* 73 ) = = =QPPQEdPrice Elasticity of Demand for some Commodities in the @S"roduct',n "rice Elasticity (Demand!#ur%ey - 1"2B=argarine - 3"G6Heef - 3"B6Cheese - 3"6BPotatoes - 3"73Hread - 3"12Cross "rice Elasticity of DemandShows the percentage change in the !uantity demanded of good I in response to a change in the price of good 5"EDYX = % Change in QDY /% change in PXAlgeraically'Read as the cross-price elasticity of demand for commodity Iwith respect to commodity 5"-nits of & demanded "rice of = ED&=>>>>>>>>>>>B3C1363 C1. )-.34.*&)134B3* , - 1"BByxxyxx ydYXQPPQPPQQEy==Cross Price Elasticity of Demand )Edyx*Calculating Cross Price Elasticity of Demand from a Demand (unction'@sing calculus' Aiven a demand function'Qb 2 100 : ;0 Pb : /0 Pc < +005I, where, Qb , Quantity demanded of eer in illion B-pac%s, Pb , Price of eer per B-pac% )C2*, Pc , Price of a pac% of chips )C1*, and + , Annual household income )C.2,333*"Qb 2 100 : ;0?(5! : /0?(1! < +005?(/5000! 2 55 #a%ing partial derivative of the demand function for eer with respect to price of chips and sustituting values for Pc and Q we get' yxxydyxQPPQE =7B7B " 3221* .3 ) = = =bccbdbcQPPQEClassification of Crossprice elasticity of Demand$nterpretation:+f Edyx , - 3"7B' A one percent increasein price of chips results in a 3"7B0 decrease in !uantity demanded of eerClassification:$f (Edyx 3 0!:implies that as the price of good X increases, the !uantity demanded of Aood Y also increases"#hus, Y and X are su@stitutes in consumption )e&" chic%en and por%*"$f (Edyx 1 0!:implies that as the price of good X increases, the !uantity demanded of Aood Y decreases"#hus Y J X are Complements in consumption )e&" ear and chips*"$f (Edyx 2 0!:implies that the price of good X has no effect on !uantity demanded of Aood Y"#hus, Y J X are $ndependent in consumption )e&" read and co%e*$ncome Elasticityof Demand (EI!Shows the percentage change in the !uantity demanded of good I in response to a percentage change in +ncome" EI = % Change in QY /% change in IAlgeraically'-nits of & demanded $ncome E$

133C1.33123 C1B33 )234633*&)1.334133* , 1"2yy yIQIIQIIQQEy==+ncome Elasticity of Demand )EI*Calculating +ncome Elasticity of Demand from a Demand (unction'@sing calculus' Aiven a demand function'Qb 2 100 : ;0 Pb : /0 Pc < +005I, where, Qb , Quantity demanded of eer in illion B-pac%s, P

, Price of eer per B-pac% )C2*, Pc , Price of a pac% of chips )C1*, and I , Annual household income )C.2,333*".@ 2 100 : ;0?(5! : /0?(1! < +005?(/5000! 2 55 #a%ing partial derivative of the demand function with respect to income and sustituting values for Q and I we get' yyIQIIQE =././ " .22.2333* 332 " 3 ) = = =bbIQIIQE$ncome Elasticityof Demand (E$!$nterpretation'+f EI , ."./' A one percent increase income results in a ."./0 increase in !uantity demanded of eerClassification:+f EI : 3, then the good is considered a normal good )e&" eef*"+f EI 9 3, then the good is considered an inferior good )e&" ramen noodles*>igh income elasticity of demand for lu&ury goodsKow income elasticity of demand for necessary goods$ncome Elasticity of Demandfor Some Commodities in the -S"roduct$ncome Elasticityof Demand#otal food 3"71(ood away from home 3"27(resh fruits 3".2(ish 3".3Heef 3"13Por% 3"36=anagerial decisions and elasticitiesIou are a mar%eting manager and your costs have increased )energy, salaries* reducing your net revenues" Iou thin% aout increasing your price ut need to %now the effect on sales, total and net revenues"Iou are a supermar%et manager and you want to offer a 130 price cut in margarine this wee%" Iou want to %now how much more margarine you need to have to satisfy your clients"Example of price elasticity useIour supermar%et is selling 1333 containers of margarine a wee% at C 1"23 each" Iou %now that the own price elasticity for margarine is D3"G" +f you decide to reduce the price y 130, how many more margarine containers would you e selling that wee%LExample++Since E, Q4Q 4 P4P , -3"G, andP4P,-3"13Q4Q, -3"G E- 3"13Q,-3"GE-3"13 E 1333 , G3 more margarine containers to e sold$hat would e the total revenue gainLRevenue without price reduction, 1333E1"23 , 1233New revenue, 13G3 E1"72 , 162G$as it a good decisionLE&ample using Price Elasticity of Demand Elasticity of Demand for Heef' Ed 2 8 0+ABHeef disappeared in !uarter 7 of .33M , B"B6 ill" KsHeef disappeared in !uarter 6 of .33M , B"62 ill" Ks0 change in E!" Quant" Dem" , NQ4Q , )B"62-B"B6*4B"B6 , 8 3"3.MEd , )NQ4Q * 4)NP4P *; 3"B/ , ; 3"3.M 4)NP4P *NP4P , ; 3"3.M4 ; 3"B/, 3"367 +f price of eef in !uarter 7 of .313 is .// cents4l, then forecasted eef price for !uarter 6 of .313 is P? 2 /BB < 0+0C;D/BB 2 /BB