1. Suppose that a consumer’s utility function for goods x , y and z is expressed according to the Cobb–Douglas utility function U ( x , y , z ) = x 0.5 y 0.5(1 + z )0.5 . Prices are given by px = 1,...

1. Suppose that a consumer’s utility function for goods
x,
y
and
z
is expressed according to the Cobb–Douglas utility function
U(x,
y,
z) =
x
0.5y
0.5(1 +
z)0.5.
Prices are given by
px
= 1,
py
= 4, and
pz
= 8. Consumer income is given by
I
= 8.

a. Determine the utility maximising quantity of\ good
z
consumed.

b. Explain why this quantity of good
z
is optimal?

c. Determine the minimum income required for the consumer to purchase product
z.