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Fall 2020
Intermediate Microeconomics
Homework 3
Exercise 1:
An economy with no production technologies has two individuals. There are
two goods, good x and good y. Individual A owns 60 units of good x and 90
units of good y. Individual B owns 40 units of good X and 10 of good Y . A’s
preferences can be represented by the following utility function:
UA (xA ; yA ) = smallestfxA ; yA g:
B’s preferences can be represented by the following utility function:
2
UB (xB ; yB ) = 2xB (yB ) :
a. Draw an Edgeworth box where you can represent the amounts of both goods
that each individual owns. Also show three indi¤erence curves for each of the
two individuals.
b. Find all Pareto e¢ cient allocations both analytically and graphically (you
don’t need calculus, just take a good look at the indi¤erence curves).
c. If prices are px = A + 1 and py = 2, where A is the last digit of your Student
ID#, …nd what each individual would want to consume.
d. Are prices in (c) General Equiblibrium prices? Explain why.
Exercise 2:
An economy with no production technologies has two individuals. There are
two goods, good x and good y. Individual A owns 30 units of good 1 and 60
units of good 2. Individual B owns 60 units of good 1 and 30 of good 2. A’s
preferences can be represented by the following utility function:
UA (xA ; yA ) = ln(xA ) + ln(yA ):
B’s preferences can be represented by the following utility function:
uB (xB ; yB ) = 2xB + 9yB :
a. Draw an Edgeworth box where you can represent the amounts of both goods
that each individual has. Also show three indi¤erence curves for each of the two
individuals.
1
b. If prices are px = 1 and py = 1, …nd what each individual would want to
consume.
c. If py = 1 and individual 2 can choose any price px desired, what would be
the optimal choice? Also …nd what each individual would end up consuming.
d. Are prices in (b) or (c) General Equiblibrium prices?
Exercise 3:
For the Endowment Economy described in Exercise 1, assume that the initial
endowments are:
!A
x = 20(
where
ID#.
= 1+
p
B2
2
B
B
+ 1); ! A
y = 40; ! x = 30; ! y = 60
2
;
8B + 16, and B is the 2nd -to-last digit of your Student
a. Solve for the General Equilibrium relative price p .
b. Determine the General Equilibrium allocation (xA ; yA ; xB ; yB )
Exercise 4:
For the Endowment Economy described in Exercise 2,
a. Explain why any relative price p < 2=9 would lead to an excess supply of
good Y:
b. Explain why a relative price of p = 2=9 demand for good X by A is greater
than aggregate supply.
c. Solve for the General Equilibrium price p ; knowing –from parts (a) and
(b)– that it must be the case that p > 2=9:
d. Show your results from part (c) in an Edgeworth Box where the General
Equilibrium allocation is clearly marked along with all other e¢ cient allocations.
2
Fall 2020
Intermediate Microeconomics
Student Name:___________________
Student ID________
Homework 3
Front Page
Selected Answers:
Exercise 1.c.
The amount of good y that consumer B wants to consume is:
yB = ___________
Exercise 2.c.
If consumer B is the monopolist, then the price of good x selected is:
pm
x = ___________
Exercise 3.
The General Equilibrium relative price (p = px =py ) is:
p = ___________
Exercise 4.a.
If the relative price is p = 1=15 then aggregate demand for good y is::
YD = ___________
Exercise 4.b.
If the relative price is p = 2=9 then aggregate demand for good x is at the very
least equal to:
XD = ___________
3
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