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 $\beta$ and $\gamma$ 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 case of $\sum _i{\beta }_i=1$ the demand function equals $$q_i={\gamma }_i+\frac{{\beta }_i}{p_i}(y-\sum _j{\gamma }_j{p}_j)$$ where $y$ is total expenditure, and $p_i$ is the price of good $i$.

The Stone–Geary utility function was first derived by Roy C. Geary, in a comment on earlier work by Lawrence Klein and Herman Rubin. Richard Stone was the first to estimate the Linear Expenditure System.