University of Toronto, Department of Economics, ECO 204 2009
‐
2010 S. Ajaz Hussain
ECO 204 2009
‐
2010
S. Ajaz Hussain
Elasticity: a Quick Review
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‐
mail
about typos or suggestions for improvements
_____________________________________________________________________________________
In this note we will do a very quick review of an “elasticity”. In ECO 100, most of you have
probably seen:
•
“Price Elasticity”
ሺ% ch
•
“Income Elasticity”
ሺ%
ange in ܳ / % change in Priceሻ
change in ܳ / % change in Incomeሻ
•
“Cross Price Elasticity”
ሺ% change in ܳ / % change in Price of Other Goodሻ
However, in ECO 204 and upper level economics/finance courses, you will see other types of
elasticities. As such, I am going to do a “general” discussion of elasticity. Let’s start by seeing
why we use elasticities. Economics and finance models often state a relationship between two
economic/financial variables. For example:
•
A company’s sales depends on price
•
A consumer’s consumption depends on income
•
A company’s output depends on labor input
In each case, a variable depends on (“is a function of”) another variable. We could describe
such relationships in general terms by sayin
riable
ݕ
is a function of the variable
ݔ
:
g that a va
ݕൌ ሺݔሻ
݂
Notice that as
ݔ
changes, it leads to changes in
ݕ
(if you’re in ECO 220, you may have seen that
just because
ݕ,ݔ
are related doesn’t mean that
ݔ
causes
changes in
ݕ
). We will often want to
know: how are changes in
ݕ
related to changes in
ݔ
? One way to answer this question is to look
at the elasticity of
ݕ
with respect to
ݔ
:
ܧ ൌ Elasticity of ݕ with respect to ݔ ൌ
% Δ ݕ
% Δ ݔ
1
ECO 204 (Draft) Elasticity: a Quick Review
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View Full DocumentUniversity of Toronto, Department of Economics, ECO 204 2009
‐
2010 S. Ajaz Hussain
Notice that
ܧ
can be positive, zero or negative
1
. The sign simply tells us whether
ݕ,ݔ
are
positively or negatively elated.
r
Example
: Suppose the
ݕ
variable is a company’s sales
ܳ
and the
ݔ
variable is the price
ܲ
of its
product. Then:
ܳൌ݂ሺܲሻ
ܧ ൌ Elasticity of ܳ with respect to ܲ ൌ
% Δ ܳ
% Δ ܲ
For most products, higher prices lead to lower sales: thus, th
ratio will be negative.
is
Remember that changes in
ݔ
are associated with changes in
ݕ
. As such, we’ll often want to
know how sensitive changes in
ݕ
are to changes in
ݔ
. For example, if
ݔ
changes by 10%, will
ݕ
change by more than 10%? Exactly 10%? Or less than 10%?
One way to answer this question is to see if the (absolute value of the) elasticity is larger than,
equal to
than 1.
, or less
Case 1:
ܧ1
ܧ ൌ Elasticity of ݕ with respect to ݔൌฬ
% Δ ݕ
% Δ ݔ
ฬ1
௬ௗ௦
ሱۛۛۛሮ % Δ ݕ % Δ ݔ
That is, if the elasticity is larger than 1, any percentage change in
ݔ
is associated with a larger
percent
ge in
ݕ
. In such cases, we say the elasticity is “elastic”.
age chan
Case 2:
ܧ൏1
ܧ ൌ Elasticity of ݕ with respect to ݔൌฬ
% Δ ݕ
% Δ ݔ
ฬ൏1
௬ௗ௦
ሱۛۛۛሮ % Δ ݕ ൏ % Δ ݔ
That is, if the elasticity is smaller than 1, any percentage change in
ݔ
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 Fall '08
 HUSSEIN
 Economics, Microeconomics, Supply And Demand, Department of Economics, S. Ajaz Hussain

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