Transcript Lec 4.ppt

Income Elasticity
(Normal Goods)
Elasticity
Elasticity
Income
Elasticity
(Normal Goods)

Elasticity is a measure of how responsive a dependent
variable is to a small change in an independent variable(s)

Elasticity is defined as a ratio of the percentage change in
the dependent variable to the percentage change in the
independent variable

Elasticity can be computed for any two related variables
Income Elasticity
Elasticity can be computed to show the effects of:
(Normal Goods)

a change in price on the quantity demanded [ “a change in
quantity demanded” is a movement on a demand function]

a change in income on the demand function for a good

a change in the price of a related good on the demand
function for a good

a change in the price on the quantity supplied

a change of any independent variable on a dependent
variable
Income Elasticity
(Normal Goods)
“Own” Price Elasticity

Income Elasticity
Sometimes called “price elasticity”
(Normal Goods)
 can be computed at a point on a demand function or
as an average [arc] between two points on a
demand function
 ep, h, e are common symbols used to represent price

elasticity
Price elasticity [ep] is related to revenue
 “How will a change in price effect the total
revenue?” is an important question.
Income
Elasticity
Elasticity as a measure of responsiveness
(Normal Goods)

The “law of demand” tells us that as the price of a good
increases the quantity that will be bought decreases but does
not tell us by how much.

ep [“own”price elasticity] is a measure of that information]

“If you change price by 5%, by what percent will the quantity
purchased change?
e
p
or,
% change in quantity demanded

% change in price
ep

%DQ
%DP
At a point on a demand function this can be
calculated by:
Q
Q22 -Q
Q11 = D Q
ep =
Q1
=
P2 P-2 P
-1 P=1 D P
P1
DQ
Q1
DP
P1
+2
D
Q
ep =
[2/3 = .66667]
31
Q
=
D
-2P
P71
% DQ = 67%
% DP = -28.5%
[-2/7=-.28571]
Price decreases from $7 to $5
Px
P1 = $7
P2 = $5
A
D P = -2
[rounded]
The “own” price elasticity of demand
at a price of $7 is -2.3
P2- P1 = 5 - 7 = D P = -2
D Q = +2
.
-2.3
This is “point” price elasticity. It is calculated at a point
on a demand function. It is not influenced by the direction
or magnitude of the price change.
B
Q1 = 3
=
Q2 = 5
Q2 - Q1 = 5 - 3 = D Q = +2
D
There is a problem! If the
price changes from $5 to
$7 the coefficient of
elasticity is different!
Qx/ut
ep =
D-2
Q
[-2/5 = -.4]
5Q1
=
D+2P
% DQ = -40%
% DP = 40%
= -1
[this is called “unitary elasticity]
[+2/5 = .4]
P51
When the price increases from $5 to $7, the ep = -1 [“unitary”]
In the previous slide, when the price decreased from $7 to $5, ep
The point price elasticity is
different at every point!
There is an
easier way!
Px
P2 = $7
P1 = $5
A
ep = -2.3
D P = +2
B
D Q = -2
Q2= 3
= -2.3
Q1= 5
ep = -1
D
Qx/ut
By rearranging terms
An easier way!
DQ
Q1
DQ
P1
ep =
DQ
=
Q1
*
P1
D P
P1
ep
Q2= 5
P2- P1 = 5 - 7 = D P = -2
Q2 - Q1 = 5 - 3 = D Q = +2
Then,
DQ
DP
=
+2
-2
DP
*
P1
Q1
this is the
slope of the
demand function
Given that when:
P1 = $7,
Q1 = 3
P2 = $5,
=
DQ
this is a point on
the demand
function
= -1
DQ
= -1
DP
P71
* Q
31
P1 = $7,
= -2.33
Q1 = 3
On linear demand functions the
slope remains constant so you
just put in P and Q
This is the slope of the demand Q = f(P)
The following information was
given
P1 = $7,
P2 = $5,
Q1 = 3
Q2= 5
$7
The slope of the demand function
DQ
DP
+2
=
-2
A
B
$5
Q2 - Q1 = 5 - 3 = D Q = +2
P2- P1 = 5 - 7 = D P = -2
[Q = f(P)] is
Q = f (P)
Px
= -1
The equation for the demand
function we have been using is
Q = 10 - 1P. A table can be
constructed.
Px must decrease
by 5.
What is the Q
intercept?
Q increases by 5
3
5
D
/
Q
Q=x 10ut
The slope [-1] indicates that for every
1 unit increase in Q, Px will decrease by 1.
Since Px must decrease by 5, Q must
increase by 5
Q = 10 when Px = 0
The slope-intercept form
Q = a10+ -m1 P
The slope is -1
The intercept is 10
For a simple demand function: Q = 10 - 1P
price
quantity
$0
10
$1
9
$2
8
$3
7
$4
6
$5
5
$6
4
$7
3
$8
2
$9
1
$10
0
ep
0
-.11
-.25
-.43
-.67
-1.
-1.5
-2.3
-4.
-9
undefined
Total
Revenue
using our formula,
ep =
DQ
P1
D P * Q1
the slope is -1, price is 7
P71
DQ
ep = (-1) * Q1 = -2.3
3
DP
at a price of $7, Q = 3
Calculate
Q=1
ep
at P = $9
ep = (-1)
9
1
= -9
Calculate ep for all other
price and quantity
combinations.
For a simple demand function: Q = 10 - 1P
price
quantity
$0
10
$1
9
$2
8
$3
7
$4
6
$5
5
$6
4
$7
3
$8
2
$9
1
$10
0
ep
0
-.11
-.25
-.43
-.67
-1.
-1.5
-2.3
-4.
-9
undefined
Total
Revenue
0
Notice that at higher prices
the absolute value of the price
elasticity of demand, ep, is
greater.
Total revenue is price times
quantity; TR = PQ.
Where the total revenue [TR]
is a maximum, ep  is equal
to 1
9
16
21
24
25
24
In the range where ep < 1, [less
than 1 or “inelastic”], TR increases as
price increases, TR decreases as P
decreases.
21
16
9
0
In the range where ep > 1,
[greater than 1 or “elastic”], TR
decreases as price increases, TR
increases as P decreases.
To solve the problem of a point elasticity that is different for every price quantity
combination on a demand function, an arc price elasticity can be used. This arc price
elasticity is an average or midpoint elasticity between any two prices. Typically,
the two points selected would be representative of the usual range of prices in the
time frame under consideration.
The formula to calculate the average or arc price
elasticity is:
DQ
P1 + P2
ep =
*
P1 + P2 =
12
P1 = $7,
P2 = $5,
Q1 = 3
Q2= 5
Q1 + Q2
= 8
Q2 - Q1 = 5 - 3 = D Q = +2
P2- P1 = 5 - 7 = D P = -2
ep =
DQ
-1
DP
The average
*
P1 12
+ P2
Px
$7
Q1 + Q2
DP
The average or arc ep between
$5 and $7 is calculated,
A
Slope of demand
B
$5
ep between $5 and $7 is -1.5
DP
= - 1
D
= - 1.5
Q1 8+ Q2
DQ
3
5
Qx/ut
Given: Q = 120 - 4 P
Price
$ 10
$ 20
$ 25
$ 28
Quantity
e
p
TR
Calculate the point ep at each
price on the table.
Calculate the TR at each price
on the table.
Calculate arc ep at between
$10 and $20.
Calculate arc ep at between
$25 and $28.
Calculate arc ep at between $20 and $28.
Graph the demand function [labeling all axis and functions], identify
which ranges on the demand function are price elastic and which are
price inelastic.
Given: Q = 120 - 4 P
Price
Quantity
ep
TR
$ 10
80
-.5
$800
$ 20
40
-2
$800
$ 25
20
-5
$500
$ 28
8
-14
$224
Calculate the point ep at each
price on the table.
Calculate the TR at each price
on the table. TR = PQ
Calculate arc ep at between
$10 and $20.
ep = -1
Calculate arc ep at between
$25 and $28.
ep = -7.6
ep = -4
Calculate arc ep at between $20 and $28.
Graph the demand function [labeling all axis and functions], identify
which ranges on the demand function are price elastic and which are
price inelastic. At what price will TR by maximized?
P = $15
Graphing Q = 120 - 4 P,
TR is a maximum
where ep is -1 or TR’s
slope = 0
Price
When ep is -1 TR is a maximum.
When | ep | > 1 [elastic], TR and P
move in opposite directions. (P has
a negative slope, TR a positive slope.) 30
The top “half” of the demand
function is elastic.
| ep | > 1 [elastic]
ep = -1
| ep | < 1
When | ep | < 1 [inelastic], TR and P
move in the same direction. (P and TR 15
both have a negative slope.)
Arc or average ep is the average
elasticity between two point [or prices]
point
ep is the elasticity at a point or price.
TR
inelastic
60
120 Q/ut
The bottom “half” of the demand
function is inelastic.
Price elasticity of demand describes
how responsive buyers are to change
in the price of the good. The more “elastic,” the more responsive to DP.
Determinants of Price Elasticity

Income Elasticity
(Normal
Goods)
Availability of substitutes
[greater
availability of substitutes
makes a good relatively more elastic]

Portion of the expenditures on the good to the total budget
[lower portion tends to increase relative elasticity]

Time to adjust to the price changes [longer time period means
there are more adjustment possible and increases relative
elasticity

Price elasticity for “brands” is tends to be more elastic than for
the category of goods
An applicationIncome
of priceElasticity
elasticity.
(Normal Goods)
The price elasticity of demand for milk is estimated between -.35 and -.5.
Using -.5 as a reasonable figure, there are several important observations that
can be made.
What effect does a
10% increase in the Pmilk
have on the quantity that
individuals are willing to buy?
To solve for % D Q
Multiply both sides by +10%
ep
Since ep = -.5
e
%DQ
-5%(-.5
= p
(+10%)x
) =% D Q
A 10% increase in the price of milk would
reduce the quantity demanded by about
5%.
If price were decreased by 5%, what
would be the effect on quantity
A 10% increase
demanded?
in P reduces Q
by 5%
% +10%
DP

%DQ
%DP
x (+10%)
Pmilk
P2
P1
+10%
-5%
Q2 Q1
Dmilk
Qmilk
%DQ
ep 
%DP
The price elasticity of demand is a measure of
the % D Q that will be “caused” by a % D P.
If the price elasticity of demand for air travel was estimated at -2.5, what
effect would a 5% decrease in price have on quantity demanded ?
-2.5 =
%DQ
%
DP
- 5%
= +12.5% change in quantity demanded
If the price elasticity of demand for softdrink was estimated at -.8, what
effect would a 6% increase in price have on quantity demanded ?
-.8 =
%DQ
%+6%
DP
= -4.8% decrease in quantity demanded
If the price elasticity of demand for milk were -.5, the effects
of a price change on total revenue [TR] can also be estimated.
Since ,
%DQ
ep 
%DP
When |ep| < 1, demand is “inelastic. “ This means that
the % D Q < % D P. Since the % price
decrease is greater than the % increase in Q,
TR [TR = PQ] will decrease.
When |ep| < 1, a price decrease will decrease TR; a price increase will
increase TR, Price and TR “move in the same direction.” [inelastic demand
with respect to price]
When |ep| > 1, demand is “elastic.” This means that the % D Q > % D P.
When the % price decrease is less than the % increase in Q,
TR [TR = PQ] will increase.
When |ep| > 1, a price decrease will increase TR; a price increase will
decrease TR, price and TR “move in opposite directions.” [elastic demand
wrt price]
Graphically this can be shown
TR
TR = PQ, so the maximum TR is the
rectangle 0Q1 EP1
Price and
TR move in
opposite
directions
As price rises into the elastic range
the TR will decrease. Notice that
in this range the slope of demand
P
is negative, the slope of TR is
positive
TR is a maximum
TR
elastic
price rises
P1
0
at the midpoint, ep = -1
+TR
(P2 Q2) is less
P2
E
than
Loss in
(P
1 Q
1)
TR
when
DP
Q2
Q1
D
Q/ut
When price elasticity of demand is
inelastic
TR
TR is a maximum
A price decrease will result in
a decrease in TR [PQ]. notice that
both TR and Demand have a
negative slope in the inelastic
range of the demand function.
Price and TR “move in the same P
direction.”
A price decrease will reduce
TR; a price increase will
increase TR. Note that
this information is useful
but does not provide
information about profits!
TR
at the midpoint, ep = -1
P1
P0
0
E
inelastic
TR = P1 Q1
[Maximum]
results
in a smaller PQ
[TR]
Q1
D
Q0
Q/ut
“Own” Price Elasticity of Demand

ep

ep will be negative because the demand function is negatively sloped.

A linear demand function will have unitary elasticity at its “midpoint.” AT
THIS POINT TR IS A MAXIMUM!
A linear demand function will be more “elastic” at higher prices and tends
to be more “inelastic” in the lower price ranges

is a measure of the responsiveness of buyers to changes in the price
of the good.
Fall '97
Economics 205Principles of Microeconomics
Slide 24
Examples

Goods that are relatively price elastic



lamb, restaurant meals, china/glassware, jewelry, air travel
[LR], new cars, Fords
in the long run, |ep| tends to be greater
Goods that are relatively price inelastic


electricity, gasoline, eggs, medical care, shoes, milk
in the short run, |ep| tends to be less
Fall '97
Economics 205Principles of Microeconomics
Slide 26
Reference: Principles of Economics, 6/e by Karl Cas,
Ray Fair
Slides prepared by: Fernando Quijano and Yvonn
Quijano
Fall '97
Economics 205Principles of Microeconomics
Slide 27