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

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