Question

I really need no calculatin mistakes, especially for the fourth one. This question is so important to me. Hope somebody helps me :)

One consumer is choosing to maximize U(X,Y)=XY under a budget constraint of PxX+PyY=M.

(Px,Py,M)=(4,2,24).

(1) What does formula Px/Py=2 imply?

(2) Draw a budget line.

(3) Draw an indiscriminate curve that conforms to a given utility function.

(4) What is the optimal consumption (X*,Y*).

(5) Calculate the income elasticity of demand for X goods.

Answer 1

1)px/py=2

It implies that, Consumer can buy twice of good y as much of good x ,with same budget.

2) if Consumer spend all income on x,then x=24/4=6

If Consumer spend on income on y, then y=24/2=12

C)

D) Utility maximizing condition:

MUx/Px= MUy/Py

Y/4=X/2

Y=2X

Budget constraint:,

24=4X+2Y

24=4X+2*2X=4X+4X=8X

X*=24/8=3

Y*=2X=2*3=6

5)

Utility maximizing condition:

MUx/Px= MUy/Py

Y/4=X/2

Y=2X

M=4X+2*2X=8X

X=M/8

∆X/∆M=1/8( derivative of demand of x with respect to M)

Income elasticity of X=(∆X/∆M)*(M/X)=(1/8)*(24/3)=1