Question #82798

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!

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!

Expert's answer

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.

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