Question

Consider the following five utility functions.

G(x,y) = x² + 3 y²

H(x,y) =ln(x) + ln(2y)

L(x,y) = x^1/2 + y^1/2

U(x,y) =x y

W(x,y) = (4x+2y)²

Z(x,y) = min(3x ,y)

In the case of which function or functions can the Method of Lagrange be used to find the complete solution to the consumer's utility maximization problem?

a.

H

b.

U

c.

G

d.

Z

e.

L

f.

W

g.

None.

Answer 1

The lagrangean works when the utility function is concave and where there is no possibility of a corner solution and also the function must be differentiable.

G function is convex since sum of two convex functions. So not applicable

H function is concave since sum of two concave functions. So lagrangean method works.

L function also concave since sum of two concave functions. So lagrangean method works.

U function is Cobb doughlas and quasi concave. So applicable.

W not applicable since we usually have corner solutions.

Z lagrangean not applicable since not differentiable.