microeconomics concept

7/29/2019 microeconomics concept

1/5

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


2/5

Elasticity 2


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


3/5

Elasticity 3


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


4/5

Elasticity 4


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


5/5

Elasticity 5


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

microeconomics concept

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