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Answered Same Day Sep 28, 2021

Solution

Komalavalli answered on Sep 30 2021

157 Votes

a)
We have N number of partial derivatives for utility u
)
Let us assume V =u(x1)
MUx1 = ∂V/∂ x1 = ∂u/∂ x1=0
The partial derivative with respect to x1 indicates Marginal utility of good x1. MUx1 tells us the amount of an additional utility we get by consuming extra unit of good x1.
c)
If u is homogenous degree of 1
The homogeneity of u means that
u(t x1, ……., t xn) = t1u'(x1, ……., xn) for all (x1, ……., xn)
t ui’(t x1, ……., t xn) = t1ui’(x1, ……., xn)
Dividing both sides by t we get
ui’(t x1, ……., t xn) = ui’(x1, ……., xn)
Therefore ui’ is homogenous of degree 0
d)
Total consumer Expenditure E = px+qy
e)
V = c
E = px+qy --------------(1)
By rea
anging equation 1, we get
q*y = E –P*x
y = (E –P*x)/q
By taking partial derivative of above equation with respect to x , we get
y'(x)= –P /q
f)
Min E = px+qy
Subject to V = u(x,y)
L = px+qy + λ (u(x,y) – V)
∂L/∂x = p + λ ∂u(x,y)/∂x =0
MUx = p + λ ∂u(x,y)/∂x =0
MUx = λ ∂u(x,y)/∂x = -p
∂L/∂y= q + λ ∂u(x,y)/∂y =0
MUy = λ ∂u(x,y)/∂y = -q
g)
Marginal rate of substitution is MRS...

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