Home » 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 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 I to spend on three goods x1 , x2 and x3, with unit prices p1 , p2 and p3respectively. Your taste can be represented by the utility function

u(x1,x2,x3) = x1a x2b x31-a-b

where a and b are between 0 and 1, and a + b < 1.

(a) What is your optimal choice for x1 , x2 and x3? Use the Lagrange Method.

(b) What are the shares of income spent on the three goods respectively?

(c) Derive your indirect utility function.

(e) If there are n goods and the utility function is:

u(x1,x2,…,xn) = x1a1 x2a2 ··· xn1- a1 -a2 -…- an-1

where a1, a2,…, an-1 are all between 0 and 1, and a1+a2+…+an-1 <1

The unit prices are p1 , p2 ,…, pn respectively.

Without calculations, write down the demand function for x1 and the share of income spent on it.

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