Stone–Geary utility function

The Stone-Geary utility function takes the form

$U=\prod _{i}(q_{i}-\gamma _{i})^{\beta _{i}}$

where U is utility, q_i is consumption of good i, and β and γ are parameters.

For $\gamma _{i}=0$, the Stone-Geary function reduces to the generalised Cobb-Douglas function.

The Stone-Geary utility function gives rise to the Linear Expenditure System, in which the demand function equals

$q_{i}=\gamma _{i}+{\frac {\beta _{i}}{p_{i}}}(y-\sum _{j}\gamma _{j}p_{j})$

The Stone-Geary utility function was first derived by Roy C. Geary in a comment on early work by Klein and Rubin. Stone was the first to estimate the Linear Expenditure System.

Source

J.P. Neary (1997), 'R.C. Geary's Contributions to Economic Theory', in D. Conniffe (ed.), R.C. Geary, 1893-1983: Irish Statistician, Oak Tree Press, Dublin