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Lecture 7
Hicks Decomposition example
Market Demand
Price elasticity of demand
Income elasticity of demand
Consumer surplus
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View Full Document Hicks Decomposition: Example
•
U(X,Y) = XY
•
p
x
= p
y
= 2
•
Income = I = 4
•
MUx = Y; MUy = X
•
Two equations for equilibrium:
–
pxX + pyY = 4 => 2X + 2Y = 4
–
°±
²
°±
³
=
´
µ
´
¶
⇒
·
¸
=
2
2
= 1
⇒ ¹
=
º
= 1 => U(X,Y) = 1
•
Let the price of X decline to 1
•
Two equations for equilibrium:
–
pxX + pyY = 4 => X + 2Y = 4
–
°±
²
°±
³
=
´
µ
´
¶
⇒
·
¸
=
1
2
⇒ ¹
=
»º
•
Substituting:
–
2Y + 2Y = 4 => Y = 1 and X = 2Y = 2
1
2
1
X
Y
A
B
Hicks Decomposition, cont.
•
Find tangency of first indifference curve
and a line with the slope of
the second budget constraint:
XY = 1 and a line with slope ½
Slope of tangent = (1)MRS.
•
Conditions:
–
MRS = ½ = Y/X => 2Y = X
–
XY = 1 => 2YY = 2Y
2
= 1 => Y
2
= ½ => Y = √
1/2
–
X = 2√
1/2 ( = point C on the graph)
–
Substitution Effect: 2√
1/2
– 1
–
Income Effect: 2 
2√
1/2
2
1
X
Y
A
B
C
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This note was uploaded on 01/17/2012 for the course ECON 100A taught by Professor Safarzadeh during the Fall '09 term at UC Irvine.
 Fall '09
 SAFARZADEH
 Economics, Consumer Surplus, Income Elasticity, Price Elasticity

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