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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.

1

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

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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