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 which 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.

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