4.10 stone–Geary utility Suppose individuals require a certain level of food (x) to remain alive. Let this amount be given by x0. Once x0 is purchased, individuals obtain utility from food and other goods (y) of the form U(x, y) = (x − x0)αy

β, where α + β = 1.

a.

Show that if I > px x0 then the individual will maximise utility by spending α (I – pxx0) + px x0 on good x and β(I – px x0) on good y. Interpret this result.

b.

How do the ratios px x/I and py/I change as income increases in this problem?