u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4 initial prices px,py and final prices p′x,p′y. For THE problem,...

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u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4 initial prices px,py and final prices p′x,p′y. For THE problem,...

u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4

initial prices px,py and final prices p′x,p′y. For THE problem, you are to find:

(a) the optimal choice at the initial prices (b) the optimal choice at the final prices

(c) the change = optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect

business economics

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Answer 1

Answer #1

A) now preferences are perfect substitutes

MRS = MUx/MUy = 1/3

Px/Py = 1/2

So as MRS < Px/Py

MUx/Px < MUy/Py

So only Y is consumed, thus Y* = M/Py

Y* = 12/2 = 6

M : income

(X*, Y*) = ( 0, 6)

B) new price ratio = Px`/Py`

= 1/4

So now MRS > new price ratio

So only X is consumed

X* = M/Px`

X* = 12/1 = 12

(X*, Y* ) = (12,0)

c) now change in X = 12 units

Change in Y = - 6 units

as preferences are perfect substitutes,so only substitution effect exists

income effect is zero

SE in X = +12

SE in Y = -6

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Answer 2

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u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4 initial prices px,py and final prices p′x,p′y. For THE problem,...