The Stone–Geary utility function takes the form

U = ∏ i ( q i − γ i ) β i {\displaystyle U=\prod _{i}(q_{i}-\gamma _{i})^{\beta _{i}}}

where U {\displaystyle U} is utility, q i {\displaystyle q_{i}} is consumption of good i {\displaystyle i} , and β {\displaystyle \beta } and γ {\displaystyle \gamma } are parameters.

For γ i = 0 {\displaystyle \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 ∑ i β i = 1 {\displaystyle \sum _{i}\beta _{i}=1} the demand function equals

q i = γ i + β i p i ( y − ∑ j γ j p j ) {\displaystyle q_{i}=\gamma _{i}+{\frac {\beta _{i}}{p_{i}}}(y-\sum _{j}\gamma _{j}p_{j})}

where y {\displaystyle y} is total expenditure, and p i {\displaystyle p_{i}} is the price of good i {\displaystyle 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.