Judith Natalia Ariza Archila
2102143
Parcial Final Microeconomía III
1.
q2=x12+x2
→x2=x1
2+x2
2
M´axx1x1
2
S.a(x1)2x2
2=¯
U
2x1+x1
2+x2
2=w1
2+w2
2
δ=x1x1
2+λ1(¯
UB−(x1)2x2
2) + λ2w1
2+w2
2−2x1+x1
2+x2
2
∂δ
∂x1=x1
2−λ12x1x2
2−2λ2= 0
∂δ
∂x2=x1−λ2(1) = 0
∂δ
∂x2
2
=−λ12x2−2λ2= 0
Despejar
•λ2=x1
•x1
2−λ12x1x2
2−2λ2= 0
λ1(x1)2=λ2
λ1(x1)2=x1
λ1=x1
(x1)2
λ1=1
x1
Aplicando la ley de samuelson
x1
2
x1+2x1x2
2
(x1)2= 1
x1
2
x1+2x2
2
x1= 1
−x1
2+x2
2
x1= 1
x2
x1= 1
x2=x1
2.
3.
e2lny =eln4000000ly
eln(y2)=eln(4000000ly)
y2= 4000000ly
y= (4000000ly)1
2
y= 2000ly 1
2
Cmgy =1000
ly
1
2
=ly
1000 = ly ∗ly 1
2
1000 = ly 3
2
ly = 100→
Trabajo
y= 2000ly 1
2
y= 2000 ∗(100) 1
2
y= 20000→
Papel
x= 2000lx 1
2(y−yo)a
x= 2000lx 1
2(20000 −38000)−0.1
x=2000lx
1
2
−18000 1
10
x
´
=1000
−18000 1
10
∗lx 1
2
1
