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Econ 3104
Midterm I. Problems from previous exams
1.
A farmer produces just two goods, potatoes,
X
, and milk,
Y
. These are also the only two
goods he consumes. Furthermore, he does not have income from any other source. Let
X
be the
quantity of potatoes he produces and
!
Y
be the quantity of milk he produces. Potatoes can be
bought and sold in the market at a price
p
x
and milk can be bought and sold at a price
p
y
.
Draw four separate diagrams. In each diagram draw the present budget set the farmer has
and also the budget set he will face in each of the following cases. (Thus, the first diagram will
depict the present situation as well as case (a) below, the second diagram will depict the
present situation and case (b) below etc.). Assume that in each case the quantities of milk and
of potatoes produced by the farmer remain unchanged. Be sure to label precisely all important
points in each diagram.
(a) The price of milk increases while the price of potatoes remains the same.
(b) The price of potatoes and the price of milk increase by 10%.
(c) The government pays the farmer
s
cents in subsidy for each gallon of milk
he produces
.
(d) The government pays the farmer
s
cents in subsidy for each gallon of milk
he sells.
(
Notice the difference between parts (c) and (d)).
2.
A consumer who consumes just two goods likes each as long as he does not have too
much of it. Once the quantities of each exceed certain amounts, he starts to dislike each.
Furthermore, the preferences of this consumer are convex. Draw an indifference curve diagram
that represents these preferences.
3.
A student can read the books
A
,
B
,
C
and
D
. His preferences over these books are
expressed by the following pairwise comparisons.
A
!
B
A
!
C
C
!
B
D
!
C
B
!
D
D
!
A
A
"
A
B
"
B
C
"
C
D
"
D
(a) Are these preferences complete? Are they reflexive? Briefly explain your answers. (No
explanation, no credit).
(b) Can these preferences be represented numerically by a utility function? If yes, provide
such a function. If not, explain why.
4.
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 Spring '08
 KATZ

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