1 demand and supply: elasticity principles microeconomics professor dalton econ 202 – spring 2013...
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Demand and Supply:Elasticity
Principles MicroeconomicsProfessor Dalton
ECON 202 – Spring 2013Boise State University
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Elasticity
Elasticity - measure of responsiveness
Measures how much a dependent variable changes due to a change in an independent variable
Elasticity = %Δ X / %Δ Y • Elasticity can be computed for any two
related variables
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Elasticity Measures
Elasticities economists are interested in:• a change in price on the quantity demanded• 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
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Price Elasticity of Demand
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.
The price elasticity of demand, ε, is a measure of that information
“If you change price by 5%, by what percent will the quantity purchased change?
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ε % Q
% P
At a point on a demand function this can be calculated by:
ε =
Q2 - Q1
Q1
P2 - P1
P1
Q2 - Q1 = Q
P2 - P1 = P=
QQ1
PP1
Price Elasticity of Demand
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Q
Q1
P
P1
ε =
Price decreases from $7 to $5
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Px
Qx/t
D
$5B
5
$7A
P1 =
P2 =
P2- P1 = 5 - 7 = P = -2P = -2
Q1 = Q2 =
Q2 - Q1 = 5 - 3 = Q = +2
Q = +2
+2
7
3[2/3 = .66667]
[-2/7=-.28571]
= % Q = 67%
% P = -28.5%= -2.3 [rounded]
The “own” price elasticity of demandat a price of $7 is -2.3
This is “point” price elasticity. It is calculated at a pointon a demand function. It is not influenced by the directionor magnitude of the price change.
.
There is a problem! If theprice changes from $5 to$7 the coefficient of elasticity is different!
-2
7
3
Px
Qx/t
D
$5B
5
$7A
Q
Q1
P
P1
ε =
When the price increases from $5 to $7,
P1 =
P2 =P = +2
+2
5
Q1=Q2=
Q = -2
-2
5 = % Q = -40%
% P = 40%= -1 [this is called “unitary elasticity]
the ε = -1 [“unitary”]
ep = -1
In the previous slide, when the price decreased from $7 to $5, ε = -2.3
ep = -2.3The point price elasticity is different at every point!
There is an easier way!
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An easier way!
Q1PP1
ε =
QQ1 =
Q
Q1
P1
P*
By rearranging terms
=P1
Q1*
Q
Pthis is the slope of thedemand function
this is a point onthe demandfunction
Q P1
Q1
= *Pε
Given that when:P1 = $7, Q1 = 3
P2 = $5, Q2= 5
P2- P1 = 5 - 7 = P = -2
Q2 - Q1 = 5 - 3 = Q = +2
Then,Q
P +2 -2
= = -1
This is the slope of the demand Q = f(P)
-1
P1 = $7, Q1 = 3
7
3= -2.33
On linear demand functions the slope remains constant so you just put in P and Q
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Use of Price Elasticity
Ruffin and Gregory [Principles of Economics, Addison-Wesley, 1997, p 101] report that:• short run εof gasoline is = .15 (inelastic)• long run εof gasoline is = .78 (inelastic)• short run εof electricity is = . 13
(inelastic)• long run εof electricity is = 1.89 (elastic)
Why is the long run elasticity greater than short run?
What are the determinants of elasticity?
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Determinants of Price Elasticity
Availability of substitutes• greater availability of substitutes makes a good
more elastic Proportion of budget expended on good
• higher proportion – more elastic Time to adjust to the price changes
• longer time period means more adjustments possible and increases elasticity
Price elasticity for “brands” tends to be more elastic than for the category
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P
Q/t
D1
D1 is a “perfectly elastic”demand function.
ε % Q
% P
For an infinitesimally smallchange in price, Q changes by infinity.
= undefined
perfectly elasticε = undefined
.
Buyers are very responsive to price changes. An infinitely small change in pricechanges Q by infinity.
D2
perfectlyinelasticε = 0
D2 is a “perfectly inelastic” demand function, no matter howmuch the price changes the same amount is bought. Buyersare not responsive to price changes! ε = 0, perfectly inelastic.
0
P 0= 0
.
As the demand function becomes more horizontal, [buyers are more responsiveto price changes],ε approaches infinity.
De
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Income Elasticity
Income elasticity [ey] is a measure of the effect of an income change on demand.
When ey > 0, the good is a normal or superior good an increase in income increases demand, a decrease in income decreases demand.
0 < ey < 1 is a normal good
1 < ey is a superior good
When ey < 0, the good is an inferior good
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Examples of Income Elasticity
normal goods, [0 < ey < 1 ], (between 0 and 1) • coffee, beef, Coca-Cola, food, Physicians’
services, hamburgers, . . .
Superior goods, [ ey > 1], (greater than 1)
• movie tickets, foreign travel, wine, new cars, . .
Inferior goods, [ey < 0], (negative)
• “top ramen,” flour, lard, beans, . . .
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Cross-Price Elasticity
Cross-price elasticity [exy] is a measure of how responsive the demand for a good is to changes in the prices of related goods.
Given a change in the price of good Y, what is the effect on the demand for good X?
exy is defined as:
PQ
ey
xxy
%
%
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Cross-Price Elasticity
In the case of beef and pork•the ebp is not the same as epb
•ebp is the % change in the demand for beef with respect to a % change in the price of pork
•epb is the % change in the demand for pork with respect to a % change in the price of beef
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The cross elasticity of the demand for beef with respect to the
price of pork, ebeef-pork or ebp can be calculated:
ebp =% Q of beef
%P of pork
An increase in the price of pork,
+ Pp
“causes” an increase in the demand for beef.
+ Qb+ebppositive
cross elasticity is positive
ebp =% Q of beef
%P of pork
A decrease in the price of pork,
- Pp
“causes” a decrease in the demand for beef.
- Qb+ebppositive
If goods are substitutes, exy will be positive. The greater the coefficient, the more likely they are good substitutes.
Cross-Price Elasticity
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Cross-Price Elasticity
•exy > 0 suggests substitutes, the higher the coefficient the better the substitute
•exy < 0 suggests the goods are complements, the greater the absolute value the more complimentary the goods are
•exy = 0 suggests the goods are not related
•exy can be used to define markets in legal proceedings
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Elasticity of Supply
Elasticity of supply is a measure of how responsive sellers are to changes in the price of the good.
Elasticity of supply [es] is defined:
seQuantity Supplied
price%
%
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Q /t
P
Given a supply function,
supply
at a price [P1], Q1 is produced and offeredfor sale.
P1
Q1
At a higher price [P2],
P2
a largerquantity, Q2, will be producedand offered for sale.
Q2
+P
+Q
The increase in price [ P ], inducesa larger quantity goods [ Q]for sale.
The more responsive sellers are to
P, the greater the absolute value of es.
[The supply function is “flatter”ormore elastic]
Elasticity of supply
es = %Qsupplied
%P
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Q /ut
PThe supply function is amodel of sellers behavior.
Sellers behavior is influenced by:1. technology
2. prices of inputs3. time for adjustment
market periodshort runlong runvery long run
4. expectations 5. anything that influences costs of production
taxesregulations, . . .
Se
a perfectly elastic supply [es is undefined.]
Sia perfectly inelasticsupply, es = 0
as supply approaches horizontal es
approaches infinity
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Elasticity
Price elasticity of demand • elastic, inelastic or unitary elasticity
Income elasticity • superior, normal, and inferior
Cross-Price elasticity• complements/substitutes
Price elasticity of supply• Elastic, inelastic