The Stone–Geary utility function takes the form

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

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

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

The Stone–Geary utility function gives rise to the Linear Expenditure System.^[1] In case of ${\displaystyle \sum _{i}\beta _{i}=1}$ the demand function equals

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

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

The Stone–Geary utility function was first derived by Roy C. Geary,^[2] in a comment on earlier work by Lawrence Klein and Herman Rubin.^[3] Richard Stone was the first to estimate the Linear Expenditure System.^[4]

References

Further reading

• Neary, J. Peter (1997). "R.C. Geary's Contributions to Economic Theory" (PDF). In Conniffe, D. (ed.). R.C. Geary, 1893–1983: Irish Statistician. Dublin: Oak Tree Press. Archived from the original (PDF) on 2005-03-25.
• Silberberg, Eugene; Suen, Wing (2001). "Empirical Estimation and Functional Forms". The Structure of Economics: A Mathematical Analysis (Third ed.). Boston: Irwin McGraw-Hill. pp. 357–363. ISBN 0-07-234352-4.