ELASTICITY

Objectives/Key Topics

Upon completion of this unit, you should understand and be able to answer these questions:

1. How is the responsiveness of consumers to changes in various demand factors measured?

2. Elasticities – a. What are they?b. How are they calculated?c. What factors influence their values?d. How can they be used?

3. How is the responsiveness of producers to changes in supply factors measured?

Question

Suppose your cumulative GPA increases from 3.00 to 3.30 after this semester. What was the ‘percentage increase’ in your cumulative GPA?

Answer

in itia l va lue

x

x

100

303 00

100

10%

..

Question

What is likely to happen to the quantity demanded of gasoline if it were to increase in price by 20%?

Elasticity of D Definition (Meaning)

= A measure of responsiveness of D to changes in a factor that influences D

Two components1. Magnitude of change (number)2. Direction of change (sign)

= The number shows the magnitude of how much D will change due to a 1% change in a D factor

The sign shows whether the D factor and D are changing in the same or opposite directions + same direction- opposite direction

Elasticities of Demand

EQ,F = %ΔQdx/%ΔF = %ΔQ/%ΔF

Where,Qdx = the quantity demanded of X

F = a factor that affects Qdx

Notes:sign > 0 Qdx & F, ‘directly’ related

sign < 0 Qdx & F, ‘indirectly’ related

number > 1 %ΔQd, >%ΔF

Measures of Responsiveness of D to P Changes

1. Slope = unit ΔP/unit ΔQd

→ can be used to show unit Δ Qd caused by 1 unit ΔP

→ a problem with slope is that it depends on the ‘units’ of measurement

2. Elasticity = % Δ Qd/% ΔP→ shows % Δ Qd for each 1% ΔP→ does NOT depend on ‘units’ of measurement

Alternative elasticity calculation ‘formulas’:

1. Point=> calculate % changes as % of original values

2. Midpoint=> Calculate % changes as % of average of

original values and new values, = (original value + new value) / 2

Elasticity Calculation (point method)

%%

QF

QQ

x

FFx

QQFF

QQ

x FF

QFx FQ

QF

FQ

d

1 00

10 0

Types of Elasticities ( % / % ) Q Fxd

Type FE0 = own P PX

EC = cross P PY

EI = Income I

EA = advertising A

Elasticity Value Meanings (e.g.)

E0 = -2 for each 1% Px,Qd for X will by 2% in opposite direction

EC = +1/2 for each 1% PY,Qd for X will by 1/2% in same direction

EI = +.1 for each 1% I,Qd for X will by .1% in same direction

Own Price Elasticity of Demand

E QPQ Pxd

xx x,

%%

Negative according to the ‘law of demand’

E lastic E

Inelastic E

U nitary E

Q P

Q P

Q P

x x

x x

x x

:

:

:

,

,

,

1

1

1

Perfectly Elastic & Inelastic Demand

Price Price

Quantity

DD

D

Quantity

Perfectly Elastic Perfectly Inelastic

E0 Calculation (point formula)

QP

PQ

slope o f DPQ

x

x

x

x

x

x

1

E0 Calculation (example)

P Q

slopePQ

EQP

PQ

EPQ

at Q P

E

5 5

1 2

2

8 1

218

2 5

0 0

0

.

/

( )

,

( ) ( ) .

E0 and Linear D Curve

P

a

1/2a

Q

E0>1

E0=1

E0<1

Factors Affecting Own Price Elasticity

Available Substitutes The more substitutes available for the good, the

more elastic the demand. Time

Demand tends to be more inelastic in the short term than in the long term.

Time allows consumers to seek out available substitutes.

Expenditure Share Goods that comprise a small share of consumer’s

budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes.

Uses of E0

Calculate % change in P needed to bring about desired % change in Q sold

Calculate % change in Q sold that will result from a given % change in P

Predict how TR will Δ due to given % ΔP

Elasticity Equation

=>

EQP0

%%

Note: this is an equation with 3 variables => given values for 2 variables, can solve for value of 3rd variable

Example: %ΔQ = E0(%ΔP)

Example: %ΔP = (%ΔQ)/E0

Use of E0 (Example)

According to an FTC Report, AT&T’s own price elasticity of demand for long distance services is –8.64.

If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

Answer

Calls would increase by 25.92 percent!

E QP

Q

x Q

Q

Q Pxd

x

xd

xd

xd

x x, . %%

. %

( . ) %

% .

8 64

8 6 43 %

3 % 8 6 4

25 92 %

Question

If a firm wants to increase its dollar sales of a product, should it P or P?

Quote of the Day

“Students of Economics need to be taught, in business, sometimes you should raise your price, and sometimes you should lower your price.”

- CEO of Casey’s

E0 and TR

TR = P∙Q = total revenue (total $ sales)If E0 elastic (# > 1)

little P BIG Q TR little P BIG Q TR* (P)

If E0 inelastic (# < 1)

BIG P little Q TR* ( P) BIG P little Q TR

Max TR

Maximum R will be generated at midpoint of linear, down-sloping D curve

P

5.00

2.50

5 10Q

P=5-.5Q

Max TR

E0 and TR (Example)

Recall E0 = -.25 at P=1 and Q=8 for P=5 - .5Q

Given E0 is inelastic firm should be able to TR by P.

P Qd TR ($)

1 8 8.002 6 12.00

2.50 5 12.50* (= max TR)

Cross Price Elasticity of Demand

E QPQ Pxd

Yx Y,

%%

+ Substitutes

- Complements

Income Elasticity

E QMQ Mxd

x,

%%

+ Normal Good

- Inferior Good

Elasticity of Supply

E QP

law of S

Q P

xs

xXS

x,

%%

0

Elasticity Summary

Elasticities can be used to estimate:

Q if P or P or I orTR if P

dx

x y

x

?