Question

An individual derives utility from​ games, g (y−​axis), and toy​ airplanes, a​(x−​axis), described by the utility function​ U(g,a) = g^0.6a^0.4. The price per game is​ $20 and the price of toy airplanes is​ $10. Using the slope of the income consumption curve​ (ICC), determine whether games and toy airplanes are normal or inferior goods when income increases from​ $100 to​ $200.

A. Both goods are normal goods with an ICC slope of 4/3.

B. Both goods are inferior goods with an ICC slope of -4/3.

C. Both goods are inferior goods with an ICC slope of -3/4

D. Both goods are normal goods with an ICC slope of 3/4

Answer 1

We've been given a utility function and a constraint. We need to first find utility maximizing quantities of g and a. For that we will have to take lagrangian.

For income 100-

using equation 3, we get

100-20g-10*4g/3=0

g=3

a=4*3/3=4

For income 200, the condition will become

L(g,a,lambda)=g^.6a^.4+lambda(200-20g-10a)

rest everything remains same as income 100 except

dL/dlambda=200-20g-10a=0...…………(3)

a/g=4/3, same as before.

using 3, we get

200-20g-10*4g/3=0

g=6.

a=4*6/3=8

So, when income increased from 100 to 200, the consumption of both goods increased. And hence, both are normal goods.

The ICC curve is a line passing from points (3,4) and (6,8). The slope of this line is 4/3

Hence, option A is correct.