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Question 2

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Subject
Economics
School
University of Miami
Type
Homework
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Question two 1
Question two
Name of student
Name of professor
Name of course

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Question two 2
Question 2
Part a
Given that;
UA (XA, YA)=XA
1/3
YA
2/3
UB (XB, YB)=XB
2/3
YB
1/3
Finding the U'A
dUA/dXA =1/3 XA-
2/3
YA
2/3
dUA/dYA =2/3 XA
1/3
YA
1/3
Setting U'A =0, we have;
0 =1/3 XA-
2/3
YA
2/3
0=2/3 XA
1/3
YA
1/3
1/3 XA-
2/3
YA
2/
3=2/3 XA
1/3
YA
1/3
XA-
2/3
/ XA
1/3
=2 YA
1/3
/YA
2/
3
1/XA=2 YA
-1/
3
XA=1/2 YA
-1/
3
YA= 2XA
-3
Part b

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Question two 1 Question two Name of student Name of professor Name of course Question two Question 2 Part a Given that; UA (XA, YA)=XA1/3YA2/3 UB (XB, YB)=XB2/3YB1/3 Finding the U'A dUA/dXA =1/3 XA-2/3YA2/3 dUA/dYA =2/3 XA1/3YA1/3 Setting U'A =0, we have; 0 =1/3 XA-2/3YA2/3 0=2/3 XA1/3YA1/3 1/3 XA-2/3YA2/3=2/3 XA1/3YA1/3 XA-2/3/ XA1/3=2 YA1/3 /YA2/3 1/XA=2 YA-1/3 XA=1/2 YA-1/3 YA= 2XA-3 Part b 2 Question two General equilibrium allocation is given by; q*A=qA+PY.Y q*B=qB+PX.X trading at px=p for B and py=1 for A We have; q*A=qA+Y q*B=qB +P.X At WB=(0,10); XB2/3YB1/3=10 1/3 WB=(0,10)= 10 1/3 q*A=10 1/3+10 1/3 q*B=10 1/3+P. 10 1/3 10 1/3+10 1/3=10 1/3+P. 10 1/3 P=10 1/3/10 1/3=1 Part c From the general allocation equation for both A and B let replace p=1 q*A=qA+P.Y= qA+1.Y =10 1/3+10 1/3= 10 2/3 3 Question two 4 q*B=qB +P.X= qB+1.X= 10 1/3+10 1/3=10 2/3 The general allocation in part (b) is Pareto efficiency since it is impossible to make Anne better off without making Ben worse off. Name: Question 2 Description: trading at px=p for B and py=1 for A From the general allocation equation for both A and B let replace p=1 ...
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