Practice Problem 1
Riccardo M. Masolo
April 6, 2008
1 Question 3: Pareto Eﬃciency
a The set of feasible alternatives, maintaining the same assumptions as in
Question 2 for what concerns nonnegative consumption and possibility of
wasting goods, is:
X
=
{
((
x
1
,y
1
)
,
(
x
2
,y
2
)) :
x
1
,x
2
,y
1
,y
2
≥
0
and x
1
+
x
2
≤
10
.
5
, y
1
+
y
2
≤
6
}
b The set of Pareto Eﬃcient alternatives can be characterized noticing how
only agent one ”enjoys” good
y
. So any allocation such that all of good
y
is
consumed by agent 1 and good
x
is not wasted will be part of the PE set:
PE
=
{
((
x
1
,y
1
)
,
(
x
2
,y
2
)) :
x
1
,x
2
≥
0
y
1
= 6
, y
2
= 0
, and x
1
+
x
2
= 10
.
5
}
c Right from the deﬁnition of UPS in your notes one can describe it as:
UPS
=
{
(
u
1
,u
2
) :
u
1
=
1
3
x
1
+
y
2
1
, u
2
= 5
x
2
for some
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 SARVER
 Microeconomics, KaldorHicks efficiency, Vilfredo Pareto, Riccardo M. Masolo

Click to edit the document details