Answer to Question #82798 in Microeconomics for Robert

Question

The utility function is:
u(x,y)=32x^0.5+y
The marginal utilities are:
MUx=16x^-.5 MUy= 1 How do I derive the demand functions for x and y?
Thank you!

Answer 1

u(x,y) = 32x^0.5 + y, MUx = 16x^(-0.5), MUy = 1.

In equilibrium MUx/Px = MUy/Py and the budget constraint is Px*x + Py*y = I.

So, 16x^(-0.5)/Px = 1/Py,

16/(Px*x^0.5) = 1/Py,

Px*x^0.5 = 16Py,

x^0.5 = 16Py/Px,

x = 256Py^2/Px^2 - the demand function for x.

As Px*x + Py*y = I, then:

Px*x + Px*x^0.5*y/16 = I,

y = 16*(I - Px*x)/(Px*x^0.5) - the demand function for y.