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Markets
Taxes
Detour A.2: Elasticity
De&nition
The elasticity of a variable measures the percentage change of its value as
a result of an increase of the value of another variable by 1
%
.
Elasticity
:
=
Δ
y
y
Δ
x
x
=
Δ
y
Δ
x
&
x
y
,
where
Δ
x
, respectively
Δ
y
denote the change of
x
, respectively
y
.
Ani Guerdjikova
ECON 313
Fall 2007
35 / 59
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Taxes
Example
Elasticity of demand
Suppose that the elasticity of demand for gas is
&
0
,
3. Then, a 5
%
increase of gas price leads to a 1
,
5
%
decrease of demand for gas:
Δ
y
y
=
&
0
,
3
Δ
x
x
=
=
&
0
,
3
±
0
,
05
=
=
&
0
,
015
Ani Guerdjikova
ECON 313
Fall 2007
36 / 59
Markets
Taxes
The elasticity of a function
f
(
x
) =
y
is given as:
Elasticity
:
=
f
(
x
0
)
&
f
(
x
)
f
(
x
)
x
0
&
x
x
=
f
(
x
0
)
&
f
(
x
)
x
0
&
x
±
x
f
(
x
)
If
f
is di/erentiable at
x
,
df
(
x
)
dx
:
=
lim
x
0
!
x
f
(
x
0
)
&
f
(
x
)
x
0
&
x
,
the elasticity of
f
at point
x
can be written as:
Elasticity
:
=
df
(
x
)
dx
±
x
f
(
x
)
Ani Guerdjikova
ECON 313
Fall 2007
37 ± 59
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Price Adjustment
1.
Tatonnement
Price adjustment process:
p
t
+
1
>
p
t
if
D
(
p
t
)
>
S
(
p
t
)
p
t
+
1
=
p
t
if
D
(
p
t
) =
S
(
p
t
)
p
t
+
1
<
p
t
if
D
(
p
t
)
<
S
(
p
t
)
.
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This note was uploaded on 04/30/2008 for the course ECON 3130 taught by Professor Masson during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 MASSON
 Microeconomics

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