5.12 the almost ideal demand system The general form for the expenditure function of the almost ideal demand system (AIDS) is given by n

In E(

p1,…, pn, U) = a0 + a i=1 k

+ U

β0q i=1 n

αi In pi + 1 2a n

i=1 a

j=1 pk

βk,

γij In pi In pj For analytical ease, assume that the following restrictions apply:

n

γij = γji

, a.

a n

i=1

αi = 1, and a j=1 n

γij = a k=1

βk = 0.

Derive the AIDS functional form for a two-goods case.

b.

Given the previous restrictions, show that this expenditure function is homogeneous of degree 1 in all prices. This, along with the fact that this function resembles closely the actual data, makes it an ‘ideal’ function.

c.

Using the fact that sx = d In E

d In px

(see Problem 5.8), calculate the income share of each of the two goods.