The Stone-Geary utility function has the form

Where bi ≥ 0 and  The a1 ≥ 0 are often interpreted as ‘subsistence’ levels of the respective commodities.

(a) Derive the associated expenditure and indirect utility functions. Note that the former is linear in utility, whereas the latter is proportional to the amount of ‘discretionary income’, 

(b) Show that b1 measures the share of this ‘discretionary income’ that will be spent on ‘discretionary’ purchases of good x1 in excess of the subsistence level a1.

 

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