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Can you please solve 8 e knowing that the awnser to 8 d is found written below. Please also see attached question
Awnser to 8d:
U = (X1)^(1/2)*(X2)^(1/3)
We have budget constraint as, m = P1*X1+P2*X2
Let's set up the Lagrange maximizing function as below.
L = U(X1, X2) - λλ(P1X1+P2X2-m)
L = (X1)^(1/2)*(X2)^(1/3)- λλ(P1X1+P2X2-m)
Finding first order condition,
dL/dX1 = (0.5)*(X2)^(1/3)/(X1)^(1/2)-λλP1
dL/dX2 = (1/3)*(X1)^(1/2)/(X2)^(2/3)-λλP2
Equating these equations to zero to get,
(0.5)*(X2)^(1/3)/(X1)^(1/2)-λλP1 = 0
(1/3)*(X1)^(1/2)/(X2)^(2/3)-λλP2 = 0
(0.5)*(X2)^(1/3)/(X1)^(1/2)/P1 = (1/3)*(X1)^(1/2)/(X2)^(2/3)/P2
(3/2)*(X2/X1) = P1/P2
X1 = (1.5P2*X2)/P1
dL/dλλ = P1X1+P2X2-m=0
P1X1+P2X2 = m
P1*(1.5P2*X2)/P1+P2X2=m
2.5*P2X2=m
X2 = 0.4*m/P2
X1 = 0.6*m/P1
Hence, Marshallian demand function for good q and good 2 respectively are
X1 = 0.4*m/P1
X2 = 0.6*m/P2
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