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Elasticity
Econ 2106 Principles of Microeconomics
Dr. Jon Mansfield Micro Lecture 2
1 . El a s t i ci t y - s e n s i t i v i t y , r e s p o n s i v e n e s s
Can Be Calculated for Any Variable in the Demand Function. Examples: Price, Income, Advertising, etc.
Compare Percentage Changes to Avoid a Units Problem in Measurement
D e f i n i t i o n : e p = ( % Q) / ( % P) = ( Q / Q) / ( P / P) = ( Q / P) ( P / Q)
A r c El a s t i c i t y P o i n t El a s t i ci t y
Discrete Range Point on the Demand Curve
ep = (( Q2 - Q1) / Q) / ((P2 - P1) / P) ep = (Q / P ) ( P / Q )
ep = [ (Q2 - Q1) / (Q1 + Q2) / 2] / [ (P2 - P1) / (P1 + P2) /2]
Linear demand curve (price form): P = a + bQ
b = (P / Q ) and (1 / b) = (Q / P )
ep = (Q / P ) ( P / Q)
ep = [ ( Q2 - Q1 ) / ( Q1 + Q 2) ] / [ ( P2 - P1 ) / ( P1 + P 2 ) ]
ep = ( 1 / b ) [ P / ( P - a) / b ] = [ P / ( P - a ) ]
V a l u e s
You should be able to work through the derivation of both elasticity formulas.
|ep| > 1 Elastic % Q > % P
|ep| < 1 Inelastic % Q < % P
|ep| = 1 Unit Elastic % Q = % P
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Elasticity 2
Econ 2106 Principles of Microeconomics
Dr. Jon Mansfield
2 . D o w n w a r d - s lo p i n g L i n e a r D e m a n d Cu r v e
Demand Function P = 12 - Q (or Q = 12 - P)
Total Revenue Function (TR) TR = (P)(Q) = (12 - Q)(Q) = 12Q - Q2
Average Revenue Function (AR) AR = TR / Q = [(P)(Q)] / Q = P
Marginal Revenue Function (MR) MR = (TR) / (Q) = (TR2 - TR1) / (Q2 - Q1)
MR using calculus (MRc) MRc = TR / Q = 12 - 2Q
Calculate the elasticities using the formulas.
As the price decreases from 12, what happens with both types of elasticities?
Q P TR MR MRc Ar c e las t i c i t y
ep = [ ( Q2 - Q1 ) / ( Q 1 + Q 2 ) ] / [ ( P2 - P1 ) / ( P 1 + P 2 ) ]
P o i n t e l a s t i c i t y
ep = [ P / ( P - a ) ]
0 12 0 - 12 - -
1 11 11 11 10 -23 -11
2 10 20 9 8
3 9 27 7 6
4 8 32 5 4
5 7 35 3 2
6 6 36 1 0
7 5 35 -1 -2
8 4 32 -3 -4
9 3 27 -5 -6
10 2 20 -7 -8
11 1 11 -9 -10
12 0 0 -11 -12
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Elasticity 3
Econ 2106 Principles of Microeconomics
Dr. Jon Mansfield
Based on the information and table above, graph the Demand and Marginal Revenue functions on one diagram and the
Total Revenue function directly beneath.
12
P $
Q
D
126
40
TR $
Q126
6
P = 12 - Q
MR = 12 - 2Q
TR = 12Q - Q2
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Elasticity 4
Econ 2106 Principles of Microeconomics
Dr. Jon Mansfield
3 . P r i ce Elas t i c i t y and To ta l Revenu e : The Pr i ce Ef fec t an d Quan t i t y E f fec t o f a P r i ce Chang e .
4 . W h a t i s t h e s i g n i f i c a n c e o f v e r t i c a l a n d h o r i z o n t a l d e m a n d c u r v e s ?
P
Q
Demand
P1
P2
Q1 Q2
A
Barea A
area
B
C
D
ep = 0 ep =
D
D
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Elasticity 5
Econ 2106 Principles of Microeconomics
Dr. Jon Mansfield
5 . H o w s e n s i t i v e i s t h e a m o u n t d e m a n d e d t o a c h a n g e i n p r i c e ? T h i s is p r i m a r i l y d e t e r m i n e d b y :
Elastic
number of substitute goods
importance in consumers budget
product durability
time period under consideration
6 . O the r Elas t i c i t i es
I n c o m e El a s t i ci t y o f D e m a n d Cr o s s El a s t i ci t y o f D e m a n d
eI = ( % QX) / ( % I ) (= ( QX / I) (I / QX)) eC = ( % QX) / ( % PY) (= ( QX / PY) (PY / QX))
eI > 0 Normal Good eC > 0 Substitute Goods
eI < 0 Inferior Good eC < 0 Complementary Goods