Question
Jamal has utility functionU B (X 1 ,X 2 )=(X 1 +2)(X 2 +3) . He also has incomem , and faces pricesP 1 andP
Jamal has utility functionU
B
(X
1
,X
2
)=(X
1
+2)(X
2
+3)
. He also has incomem
, and faces pricesP
1
andP
2
for goods 1 and 2 respectively.
What is Jamal's budget constraint?
P
1
X
1
+P
2
X
2
=m
(P
1
+P
2
)(X
1
+X
2
)=m
P
1
+P
2
=m
P
1
X
1
+P
2
X
2
+m=0
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Problem PS2.3.2
1 point possible (graded)
What is Jamal's MRS of good 1 for good 2?
(Hint: The inverse MRS and negative MRS are not listed as answers below.)
X
1
X
2
+3X
1
+2X
2
+6
dX
2
dX
1
X
2
+3
X
1
+2
X
2
X
1
Jamal's MRS cannot be calculated from the provided information
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Problem PS2.3.3
1 point possible (graded)
What is Jamal's optimal choice of goods 1 and 2 as functions of his income and prices?
(Assume an interior solution.)
X
1
=m+2P
1
3P
2
2P
1
,X
2
=m2P
1
+3P
2
2P
2
X
1
=m3P
1
+2P
2
3P
1
,X
2
=m+3P
1
2P
2
3P
2
X
1
=m3P
1
+2P
2
2P
2
,X
2
=m+3P
1
2P
2
2P
1
X
1
=m+2P
1
3P
2
3P
2
,X
2
=m2P
1
+3P
2
3P
1
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Problem PS2.3.4
1 point possible (graded)
Korra has utility functionU
A
(X
1
,X
2
)=[(X
1
+2)(X
2
+3)]
2
. She has the same income as Jamal, and faces the same prices. Find her optimal consumption bundle.
(Assume an interior solution.)
X
1
=m+2P
1
3P
2
2P
1
,X
2
=m2P
1
+3P
2
2P
2
X
1
=m3P
1
+2P
2
3P
1
,X
2
=m+3P
1
2P
2
3P
2
X
1
=m3P
1
+2P
2
2P
2
,X
2
=m+3P
1
2P
2
2P
1
X
1
=m+2P
1
3P
2
3P
2
,X
2
=m2P
1
+3P
2
3P
1
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Problem PS2.3.5
1 point possible (graded)
A third consumer, Larry has preferencesU
C
(X
1
,X
2
)=(X
1
+2)
2
(X
2
+3)
and the same income as Jamal and Korra. Find his optimal consumption bundle.
(Assume an interior solution.)
X
1
=2m+6P
2
2P
1
3P
1
,X
2
=m+2P
1
6P
2
3P
2
X
1
=2m+2P
2
6P
1
3P
1
,X
2
=m+6P
1
2P
2
3P
2
X
1
=2m6P
2
+2P
1
3P
1
,X
2
=m2P
1
+6P
2
3P
2
X
1
=2m2P
2
+6P
1
3P
1
,X
2
=m6P
1
+2P
2
3P
2
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Problem PS2.3.6
1 point possible (graded)
How does Larry's consumption differ from Korra's?
(Assume interior solutions.)
Larry consumes moreX
1
and moreX
2
at the same prices.
Larry consumes lessX
1
and moreX
2
at the same prices.
Larry consumes lessX
1
and lessX
2
at the same prices.
Larry consumes moreX
1
and lessX
2
at the same prices.
It does not differ. Larry consumes the same amount ofX
1
and the same amount ofX
2
at the same prices.
The answer cannot be determined from the provided information
None of these options
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