Question

A consumer has the utility function over goods X and Y, U(X; Y) = X^1/3Y^1/2

Let the price of good x be given by P_x, let the price of good y be given by P_y,

and let income be given by I.

1. Derive the consumer’s generalized demand function for good X.
2. Solve for the Marshallian Demand for X and Y using P_x, and P_y (there are no numbers—use the notation).
3. c. Is good Y normal or inferior? Explain precisely.

Answer 1

Page Nor 1 Answet- Given data A optimal bundle condition, MUX/Px = MUY/PY NYI3*x^4/px x^ V8 / 2* Jy * py solve Sorx, 3px 1 X= 2* y* py &x generalized demand Sunctions budget constraint, 1 = Px*x+pyxy I = (2x * Py (3px) * Px + pyty = 2y* Py/3 + Pyty = Qyt Py + 3 pyty In spyty solve dosy

Y = 31 SPY Page No. 2 (marshallin demand of y) = 3 * Px* x + 2 Px* x & Step I = SPx*X solve for x, 2. X = 21/5px {marshallian demand of xk Y = 31/5PY DERIVATIVE of demand of y with respect to I And check it is positive or negative. Positive DERIVATIVE means good is normal And negative DERIVATIVE means. Good is inferior.

Page No - 3 DY = 3/5py, DI SO PERIVATIVE is positive, so good y is normal good