Economics 11: Microeconomic Theory 1
Professor Christian Hellwig
Practice Problems Week 4
Answers
1)
Joseph likes roses (R) and tulips (T) equally, and views them as perfect substitutes in
proportion 1 to 1. The price of a rose is $3, the price of a tulip is $5, and Joseph has $30
to expend in flowers.
a) How much of each flower will Joseph buy?
b) Now, suppose that the price of a rose rises to $6. How does the consumption of Joseph
change?
c) What are the Joseph’s demands for roses and tulips (they must be functions of income
and prices)?
d) By how much should Joseph’s income increase to compensate him for the rise in the
price of roses?
a)
His preferences can be represented by U = R + T. If roses are cheaper he will
consume only roses. Therefore, R = 30/3 = 10 and T = 0. Utility is 10.
b)
Since tulips are now cheaper he will buy only tulips. R = 0 and T = 30/5 = 6.
Utility is 6.
c)
There are three cases:
1)
If p
r
< p
t
: R = I / p
r
and T = 0
2)
If p
r
> p
t
: R = 0 and T = I / p
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 Spring '08
 cunningham
 Economics, following utility function, expenditure function

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