UCLA
Economics 11 – Fall 2006
Professor Mazzocco
ANSWER KEY
Problem Set 2
Due by October 19 before 11:30am.
1)
Robinson is the only person in an island, and has an endowment of 100 units of X
and 120 units of Y. His utility function is U=lnX+lnY
a)
Find the marginal utility of X and Y.
b)
Find the marginal rate of substitution when Robinson consumes all his
endowment.
c)
Suppose now that Robinson finds that he is not alone on the Island, so now he can
trade goods with other people. Find the relative prices P
X
/P
Y
above which
Robinson decides to sell X and to buy Y (Hint: think about the relative price at
which if he trades a small amount he stays on the same indifference curve).
Explain.
Answer
a)
MU
X
=1/X
MU
Y
=1/Y
b)
2
.
1
100
120
/
1
/
1
/
/
=
=
=
=
∂
∂
∂
∂
=
X
Y
Y
X
Y
U
X
U
MRS
c)
He will be willing to sell good X and buy Y only if:
2
.
1
≥
Y
X
P
P
2)
Joe has a weekly endowment of 60 dollars that he spends buying games (G) and
music cds (M). The price of each game is 20 dollars; the price of each cd is 10
dollars. Joe’s utility is given by: U=G
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
 cunningham
 Economics, Utility, Substitute good

Click to edit the document details