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Exchange Economies Ps

This document contains two homework problems related to intermediate microeconomics concepts. The first problem modifies an exchange economy model from class and asks how changes to endowments or preferences impact equilibrium prices. The second problem defines Pareto efficiency and asks whether specific allocations of goods in an exchange economy are Pareto efficient or not.

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12 views

Exchange Economies Ps

This document contains two homework problems related to intermediate microeconomics concepts. The first problem modifies an exchange economy model from class and asks how changes to endowments or preferences impact equilibrium prices. The second problem defines Pareto efficiency and asks whether specific allocations of goods in an exchange economy are Pareto efficient or not.

Uploaded by

bobbyy222
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Intermediate Microeconomics - Exchange Economies Problem Set

1. Homework associated to Exchange Economy video


(a) Suppose we modify the exchange economy presented in the video such that now (x
0
A
, y
0
A
) =
(2, 0) and (x
0
B
, y
0
B
) = (0, 4) Recalculate the new equilibrium price p
e
X
. Compare it with
the previous one. What does this result tell us about the relationship between equilibrium
prices and endowments in an exchange economy?
(b) Suppose now that the endowment is the same as in (a) and there is a change in consumers
preferences such that now U
A
= x
1/2
A
y
A
and U
B
= x
1/2
B
y
B
. Note that now both consumers
preferences are relatively more inclined towards good y. Calculate the new equilibrium
price p
e
X
. What does this result tell us about the relationship between equilibrium prices
and preferences in an exchange economy?
2. Homework associated to First Welfare Theorem video
(a) Dene with your own words what is Pareto Eciency. (see section 15.3 in SF book)
(b) Lets take the exchange economy shown in the exchange economy videos with the only
dierence being that total initial endowment in the economy is given by (X
0
, Y
0
) =
(10, 10). Determine if each one of the following allocations are Pareto Ecient or not:
i. (x
A
, y
A
) = (4, 8) and (x
B
, y
B
) = (5, 2)
ii. (x
A
, y
A
) = (0, 0) and (x
B
, y
B
) = (10, 10)
iii. (x
A
, y
A
) and (x
B
, y
B
) are such that both consumers are maximizing utility at a given
set of prices (p
x
, p
y
) and we have that x
A
+x
B
= 10 and y
A
+y
B
= 10.
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