Question
Asked Sep 28, 2019
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Jane has utility function u(x,y)=x4y5. The price of x is px, the price of y is py, and Jane’s income is W. What is the expression of her consumption of y as a function of prices and income (her optimal consumption is determined by the tangency rule)?

Qy(px,py,W)= 9W/5py.

Qy(px,py,W)= 5W/9py.

Qy(px,py,W)= 4W/3py.

Qy(px,py,W)= 5W/4py.

Qy(px,py,W)= 4W/5py.

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Expert Answer

Step 1

Given- U=X4Y5

MUx can be found by differentiating U in terms of x

So, MUx= 4X3Y5

MUy can be found by differentiating U in terms of y

So, MUy= 5 X4Y4

The slope of IC = MUx/MUy =  4X3Y5/ 5 X4Y4 = 4Y/5X

Step 2

We know budget line is represented as:

W= xPx+yPy -----------1

At the tangency of budget line and IC, MUx/MUy=Px/Py= 4Y/5X

Dividing equation 1 by Py

W/Py=x Px/Py + Y

Y= W/Py – X*4Y/5X

Y= ...

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Macroeconomic models

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