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Microeconomics
Problem Set 4 Questions
Due February 17
th
, 2010
Winter 2010 ECON 100A
THIS PROBLEM SET IS CONTAINS NON MIDTERM MATERIAL, BUT SINCE THE CLASS IS
CUMULATIVE THE PROBLEM SET WOULD BE GOOD PRACTICE FOR THE MIDTERM
Professor Michael Noel
University of California San Diego
1.
Explain what happens to the individual’s happiness as price falls along
a.
A downward sloping ordinary demand curve for good X.
Utility increases as price falls.
b.
A Hicksian or compensated demand curve for good X.
Utility is unchanged.
2.
This question is about income and substitution effects, and in a mathematical way.
a.
Write down the Slutsky equation for the effect of a change in the price of good X on the
consumption of good X.
See your class notes.
∂
x/
∂
p
x
=
∂
x
h
/
∂
p
x
– (
∂
x/
∂
E)x*
b.
Under what conditions will the ordinary demand curve for X be downward sloping?
Explain
your answer CAREFULLY by referring to the equation above.
Be sure to tell me the signs of
any expression in the Slutsky equation that you know and why you know it.
The ordinary Marshallian demand curve is downward sloping if
∂
x/
∂
p
x
< 0. We know that the
slope of the Hicksian (
∂
x
h
/
∂
p
x
, SE only) is always negative (or zero). So we need that
∂
x
h
/
∂
p
x
– (
∂
x/
∂
E)x* < 0, or that
∂
x
h
/
∂
p
x
< (
∂
x/
∂
E)x*. This occurs if the good is normal (so the right
hand side is positive) or that it is negative (inferior) but not more negative than the left hand
side. In other words, the good must either be normal or it must be inferior but not so inferior
that the IE would dominate the SE.
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A consumer gets utility from two goods, X and Z.
X and Z are normal goods and are gross
substitutes for the consumer.
Using budget lines and indifference curves, Explain and Illustrate the
income and substitution effects of an increase in the price of X.
Z
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 Winter '08
 staff
 Microeconomics

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