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Income and Substitution II
Beware that thou forget not the LORD thy God
… lest when thou hast eaten and art full,
and hast built goodly houses, and dwelt therein
…thou say in thine heart, My power and the
might of mine hand hath gotten me this wealth.
Deuteronomy 8:1114, 17
The Economics Outline
1. The Slutsky Equation
The Mathematics Outline
1. The Envelope Theroem
The Slutsky Equation
The Slutsky Equation is the mathematical version of the income and substitution effects
discussion that we developed graphically in the previous lecture.
Remember, that we
started this discussion because we are interested in how the quantity demanded changes
as price changes, or the sign of
i
i
P
x
∂
*
∂
.
Going back to the identity
)
,
,...,
(
,
,...,
(
)
,
,...,
(
1
1
1
U
P
P
E
P
P
x
U
P
P
h
n
n
i
n
i
≡
, if we
differentiate both sides by
P
i
we get:
i
i
i
i
i
i
P
E
E
x
P
x
P
h
∂
∂
∂
∂
+
∂
∂
=
∂
∂
and rearranging terms we can write this term as:
i
i
i
i
i
i
P
E
E
x
P
h
P
x
∂
∂
∂
∂
−
∂
∂
=
∂
∂
Note:
The
i
subscripts denote the
i
th good hence we are talking about taking the
derivative of the price of good
i
.
These are called “own price” derivatives.
We
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This note was uploaded on 11/30/2011 for the course STAT 380 taught by Professor Stevens during the Spring '11 term at Brigham Young University, Hawaii.
 Spring '11
 Stevens

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