Suppose you have a total income of I to spend on three goods x 1 , x 2 and x 3 , with unit prices p 1 , p 2 and p 3 respectively.

Suppose you have a total income of
to spend on three goods
,
, with unit prices
respectively. Your taste can be represented by the utility function
u(x
,x
) = x
x
1-a-b
where
are between 0 and 1, and
+
< 1.
(a) What is your optimal choice for
? Use the Lagrange Method.
(b) What are the shares of income spent on the three goods respectively?
(c) Derive your indirect utility function.
(d) Derive your expenditure function.
(e) If there are n goods and the utility function is:
u(x
,…,x
n
a1
a2
··· x
1- a1 -a2 -…- an-1
, a
,…, a
n-1
are all between 0 and 1, and
+a
+…+a
<1
The unit prices are
,…,
respectively.
Without calculations, write down the demand function for
and the share of income spent on it.