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Unformatted text preview: 5$6*",%7&89&"6:)%6,;%66&)<&=>$%=&8)&?9$%76 ,%&:",?6&$%=&,%?)>(
2 .@$>:+6A&58")&:",?,%7&$%=&%$8,)%$+&9$+89&,%6*"$%??);"$7(& Application: Measuring the responsiveness of demand to changes in prices and income. I. Elasticities II. A Note on Examples: Metro pricing Percentage Change Calculations !"#$%$&$'($)$&$* and national health insurance coverage.
II. A Note on Percentage Change Calculations B9&<)++)C,%7&<)">*+$&:");,=6&$&6)>&D*,?E&>89)=&)< The following formula provides a some quick method of approximating implications of +,"($$$.$&$'*$&$+/#01$2"3"4"$&$+/#01$567"89#4:"($ $::")@,>$8,%7&,>:+,?$8,)%6&)<&:"?%8$7&?9$%76A percentage changes: +,"$ &&F<& G&89%& ;$$ G
2 <477/="$7:9>"$:9="=$?@$AB$08$C40#9#@$8"D08"8$E011=$?@ Application: C9"&>$%6&H:"?%8$7&?9$%7&,%&/I( FBG
!"#$%$&$'($)$&$* is good for small percentage changes. This approximation B '$&$HAB B9,6&$::")@,>$8,)%&,6&7))=&<)"&6>$++&:"?%8$7&?9$%76( B* Application: $&$IFB +,"($$$.$&$'*$&$+/#01$2"3"4"$&$+/#01$567"89#4:"($ Let A = P, B = Q Then, C = PQ = Total Revenue = Total Expenditure, J,0#$,077"=$#/$#/#01$:"3"4"$&$#/#01$"67"89#4:"K +,"$ ;$$
Suppose price rises by 2% and quantity demanded falls by 5%: %ΔP = +2% %ΔQ = <477/="$7:9>"$:9="=$?@$AB$08$C40#9#@$8"D08"8$E011=$?@ 5% ApproximationG FBGWhat happens to total revenue = total expenditure? Approximation: $$ ; B '$&$HAB True change: P2 =1.02P1 Q2 =.95Q1 B *$&$IFB P2Q2 = (1.02 P1 )(.95 Q1 )= .969 P1Q1 True changeG$ This is a 3.1% decline in revenue. J,0#$,077"=$#/$#/#01$:"3"4"$&$#/#01$"67"89#4:"K III.$&$L;MA$'L$$$$*A$&$;NF$*L$ions, Calculation 'A Elasticity: Definitions, Interpretat
A. Definitions and Interpretations: An elasticity is a measure of the responsiveness of changes in one variable to changes in another variables. In particular, an elasticity ApproximationG $PO;NF$*one variable in response to a percentage change in measures the percentage change in $P&$;NQN$' * $ 'A*A$&$OL;MA$'L L LL another variable. The following table shows the definitions of the price elasticity of demand, the income elasticity of demand and the crossprice elasticity of demand. $$ +,9=$9=$0$IR;LB$8">19"$9$:"3"4"; ; True changeG$ 'A$&$L;MA$'L$$$$*A$&$;NF$*L$ 4 !"#$%&" 2&)/" 3.#$+)/)+45,( '"6#*7 '"()*)+),* 375851"&/"*+5,&51&,1,&+),*#.5/9#*:"5)*5;< 55555551"&/"*+5,&51&,1,&+),*#.5/9#*:"5)*52< #./%.#+),* = 2<585>?= = ;<585@A= 3758= ;<B= 2< 555555855@A=5B5?= 55555585@? 0*+"&1&"+#+) ,* 3(("/+5,(5# C= /9#*:"5)* 1&)/"5,(5D 0*/,6" 3.#$+)/)+45,( '"6#*7 365851"&/"*+5,&51&,1,&+),*#.5/9#*:"5)*5;< 5555555551"&/"*+5,&51&,1,&+),*#.5/9#*:"5)*5! = !585?= = ;<585E= 3758= ;<B= ! 55555585E=5B5?= 55555585F 3(("/+5,(5# C= /9#*:"5)* )*/,6" &,$$52&)/" 3.#$+)/)+45,( '"6#*7 3<45851"&/"*+5,&51&,1,&+),*#.5/9#*:"5)*5;< 5555555551"&/"*+5,&51&,1,&+),*#.5/9#*:"5)*524 = 24585>?= = ;<585G= 3<458= ;<B= 24 55555585G=5B5?= 55555585A 3(("/+5,* 7"6#*7 (,&5D5,(5# C= /9#*:" )*5245
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alculation of Elasticities: (1) Price Elasticity of Demand Suppose that: p1 = $8 and Q1 = 2 p2 = $7 and Q2 = 3 The Price Elasticity of Demand equals: 3 3 6)&'789:&';<*%(9:9(='$>'?&@*01'&A"*<%+ Suppose instead that we were looking at the same portion of the demand curve, but that 8 price had risen from $7 to $8 instead of falling from $8 to $7: !"##$%&'90%(&*1'()*('B&'B&8&'<$$C90D'*('()&'%*@&'#$8(9$0'$> Suppose that: !"#$%&#%&'()*%+#,p1 = $7 and Q1 = 3 p2 =$8andQ2 =2 ()&'1&@*01':"8E&F'G"('()*('#89:&')*1'89%&0'>8$@'.4'($'./ Then we would get: 90%(&*1'$>'>*<<90D'>8$@'./'($'.4+ !"##$%&'()*(+''#,''.4'*01'2,''5 ''''''''''#3''./'*01'23''3 In both cases, price changed by $1 and quantity 1$*% :(1$,6,7 .$% /',"% 012#23% 4560#% 0"1$+#*% /7% 89% changed by 1 unit. However, a $1 change i price ($6,;% % <'&#=#53% 1% change depending upon whether 0"1$+#*%n/7% 9%is a “different” percentage89% 0"1$+#% 6$% 4560#% 62% 1 the base of calculating the percentage is $8 or $7. Similarly, the 1 unit change >*6??#5#$,@%4#50#$,1+#%0"1$+#%*#4#$*6$+%(4'$%&"#,"#5%,"# in quantity is a 50% change in quantity when the base is 2 and only a 33% change in quantity when the base is /12#%'?%01)0()1,6$+%,"#%4#50#$,1+#%62%8A%'5%8B;%%C6D6)15)73%,"# 3. 9%($6,%0"1$+#%6$%:(1$,6,7%62%1%EFG%0"1$+#%6$%:(1$,6,7%&"#$ ,"#%/12#%62%H%1$*%'$)7%1%IIG%0"1$+#%6$%:(1$,6,7%&"#$%,"# of demand when Note that this problem arises because we are measuring the elasticity there /12#%62%I; are big proportional or percentage changes. J',#%e would be dividing the change in price /#01(2#%by&#% 15# ,"1,% ,"62% 45'/)#D% 1562#2% or quantity nearly identical bases, and w D#12(56$+% ,"#% #)12,606,7% '?% *#D1$*% &"#$%nearly identical. For example, consider a percentage and proportional changes would be ,"#5#% 15#% /6+ 45'4'5,6'$1)%'5%4#50#$,1+#%0"1$+#2;% drop in price from P1 = $8.00toP2 =$7.99. Inthiscase,Q1 =2andQ2 =2.01. The percentage
change in price is .125%, the percentage increase in quantity is .5%, and the elasticity of demand is estimated to be 4.00. If, on the other hand, price had increased from $7.99 to $8.00, then quantity demanded would have declined from 2.01 to 2.00. In this cases, the percentage change in quantity demanded would have been .4975% and the percentage change in price .12502%, yielding an elasticity of 3.979, a value nearly identical to that calculated from the price fall.) Example: If were looking at small changes (say a change in price by .01 or one penny), "/*$4) &$) 51&"7) ) <#%(&%') (/&') &') "*++0) (/) %&0=5#&$( #1)6,*$(&(&'7))8/)9#1%,+*)9#1)(/)*1")+*'(&"&(:)0&;&0')(/9#1%,+*7 "/*$4)&$)6,*$(&(:)3:)(/)*;1*4)6,*$(&(:)(#)"*+",+*()(/ 51#5#1(&#$*+)"/*$4)&$)6,*$(&(:)0%*$00)*$0)(/)"/*$4Economists calculate what is called an arc elasticity of demand when there are "big" &$)51&")3:)(/)*;1*4)51&")(#)"*+",+*()(/)51#5#1(&#$*+ percentage changes in prices or quantities. The formula for the arc elasticity divides the change &$) 51&"7) ) <#%(&%') to calculate the proportional change in "/*$4)in quantity by the average quantity (/&') &') "*++0) (/) %&0=5#&$( quantity the change in price by price to calculate 9#1%,+*7 demanded andprice. Sometimes this isthe averagemidpoint formula.the proportional change in called the <,55#')(/*(>))))?@)A)B)))C@)A)D)
)))))))))))))))))?D)A)E)))CD)A)F <,55#')(/*(>))))?@= 2 P2=7 Q2=3 )A)B)))C@)A)D) Suppose that: P1 = 8 Q1 G;1*4)51&")A))HIB)J)IEK)L)D)A)IE7MN G;1*4)6,*$(&(:)A))HD)J)FK)L)D)A)D7M)) quantity= (2+3)/2=2.5 Average price = ($8 + $7) / 2)A)E)))C )A)F )))))))))))))))))? = $7.50 Average
D D T elasticity of demand &')"#%5,(0)*')9#++#.'> 8/)arc he arc elasticityof demand is computed as follows: G;1*4)51&")A))HIB)J)IEK)L)D)A)IE7MN G;1*4)6,*$(&(:)A))HD)J)FK)L)D)A)D7M)) 7 8/)arc elasticity of demand &')"#%5,(0)*')9#++#.'>
The arc elasticity of demand represents an average elasticity of demand over the relevant portion of the demand curve. (You should verify that you get the same arc elasticity, 7 starting from a price of $7 increasing to $8 and a reduction in quantity demanded from 3 to 2.) The price elasticity of demand varies along a linear demand curve. In the following graph, the $1 change in price always leads to a 1 unit change in quantity. But a $1 change in price is a 12.5% change in price when initial price is $8 and a 33% change in price when the initial price is $3. Likewise the 1 unit change in quantity is a 50% change in quantity when the initial quantity is 2 and a 14% change in quantity when the initial change in quantity is 7. Since the price elasticity of demand varies all along a straight line demand curve, is it possible to compare the price elasticity of demand of two straight line demand curves? Answer: Yes. We can compare the elasticity of two demand curves at a common price and quantity (i.e., where the demand curves intersect). At the point of intersection, the curve, which is flatter is more elastic. is a 50% change in quantity when the initial quantity is 2 and a 14% change in quantity when the initial change in quantity is 7. Since the price elasticity of demand varies all along a straight 13 line demand curve, is it possible to compare the price elasticity of demand of two straight line demand curves? Answer: Yes. We can compare the elasticity of two demand curves at a common price and quantity (i.e., where the demand curves intersect). At the point of intersection, the curve which is flatter is more elastic. © Bryan L. Boulier, 2010. All rights reserved. ...
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