Question

An individual has preferences over housing, x (measured in square metres), and other goods, y, represented by utility function u(x,y) = x4y. Her disposable income is $75000, and the price of housing is $1000/m2, while that of other goods is py = $1.

b) [5 marks] The government decides to subsidize housing at a rate of 20%. Find the resulting optimal bundle and utility level.

Answer 1

As Cobb Douglas utility function

U = X^a * Y^b,

Then optimal bundles

X* = aM/(a+b)*Px ,

Y* = bM/(a+b)*Py

So here, a = 4, b= 1, Px = 1000, Py = 1

B) now new price of x

Px' = 800

( As Px falls by 20%)

So new X* = 4*75,000/(1+4)*800

= 300,000/4000

= 75

from BC : XPx + YPy = M

Y* = (75,000 - 75*800)/1

= 15,000

So optimal bundle

(X,Y)* = (75, 15,000)

U = 75⁴*15,000 =