Question

3. Suppose that a consumer has a utility function
u(*x _{1}*,

please do step by step and show the graph

Answer #1

Perfect substitute preference

U = X1 + X2

MRS = MU1/MU2 = 1

Initially , P1/P2 = 1/2

Now as, *MRS > P1/P2*

*MU1/P1> MU2/P2*

*Only X1 is consumed*

*so X1* = M/P1= 10/1 = 10*

**(X1, X2) = (10,0)**

**.**

**after price change,** P1'/P2' = 4/2 =
2

*so MRS < P1'/P2'*

*MU1/P1' < MU2/P2'*

*only 2 is consumed*

*X2*' = 10/2 = 5*

*(X1, X2)*' = (0,5)*

*now for CV : the
income should be increased in a way that original utility level is
restored at new price levels*

*so U1 = 10*

*U2 = 5*

So, let new income level = M"

Then, 0 + M"/P2 = U1

M" = 10*2 = 20

**CV = M"-M**

**= 20-10**

**= 10**

**_________________________**

**now EV** ,let new income = M'

EV = M-M'

So, at original prices, new utility should be maintained

So, M'/1 = U2 = 5

M' = 5

**EV = 10-5 = 5**

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