Answer to Question #220064 in Macroeconomics for Digi

Question

Assume the logarithmic transformation f a utility function, for the consumption of two commodities is given by
ln U = ln4 + 0.5ln X + 0.25lnY
(a) if the price of X is GHS2.50 and that of Y is GHS4.00, calculate the optimal combination for an income of GHS50.00.

Answer 1

ln U = ln4 + 0.5ln X + 0.25lnY

Solving this equation using logarithms

U = 4X^0.5Y^0.25

If X is GHS2.50 and Y is GHS4.00 thne

U= 4x2.50^0.5x 4.00^o.25

U=8.9

Solving for Y from the logarithmic transformation of a utility function

ln U = ln4 + 0.5ln X + 0.25lnY

Y= U⁴ / 256X²

But Y=50 and U = 8.9

50 = 8.9⁴ / 256 X²

X²=(50 X 256)/8.9⁴

X²= 2

X= + 1.4 OR -1.4