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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 . AÃ¢â‚¬â„¢s
preferences can be represented by the following utility function:
UA (xA ; yA ) = smallestfxA ; yA g:
BÃ¢â‚¬â„¢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 indiÃ‚Â¤erence curves for each of the
two individuals.
b. Find all Pareto eÃ‚Â¢ cient allocations both analytically and graphically (you
donÃ¢â‚¬â„¢t need calculus, just take a good look at the indiÃ‚Â¤erence curves).
c. If prices are px = A + 1 and py = 2, where A is the last digit of your Student
ID#, Ã¢â‚¬Â¦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. AÃ¢â‚¬â„¢s
preferences can be represented by the following utility function:
UA (xA ; yA ) = ln(xA ) + ln(yA ):
BÃ¢â‚¬â„¢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 indiÃ‚Â¤erence curves for each of the two
individuals.
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b. If prices are px = 1 and py = 1, Ã¢â‚¬Â¦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 Ã¢â‚¬Â¦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 Ã¢â‚¬â€œfrom parts (a) and (b)Ã¢â‚¬â€œ 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 eÃ‚Â¢ cient allocations.
2
Fall 2020
Intermediate Microeconomics
Student Name:___________________
Student ID________
Homework 3
Front Page
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 = ___________
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