Question

Suppose the utility function of an individual is
U=X^{1/4} Y^{3/4} and income is I=4000. If price of
X is P_{x}=4 and price of Y is Py=1.

The optimal consumption bundle for this individual is:

a) X=50, Y=1000

b) X=150, Y=2000

c) X=250, Y=3000

d) X=350, Y=4000

e) None of above

Answer #1

Answer 1

Maximize: X^{1/4}Y^{3/4}

Subject to: 4X + Y = 4000 -----------------(1)

Legrange is given by:

L = X^{1/4}Y^{3/4} + u(4000 - 4X + Y), where u =
Legrange multiplier

First Order condition:

Dividing above conditions we get :

Y/(3X) => 4 => Y = 12X

Putting this in (1) we get:

4X + 12X = 4000

**=> X = 250**

=> Y = 12*250 =

**=> Y = 3000**

Hence, the correct answer is **(c) X=250,
Y=3000**

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