# Finance: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,[1] 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,[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

1. Varian, Hal (1992). "Estimating consumer demands". Microeconomic Analysis (Third ed.). New York: Norton. pp. 212. ISBN 0-393-95735-7.
2. Geary, Roy C. (1950). "A Note on ‘A Constant-Utility Index of the Cost of Living’". Review of Economic Studies 18 (2): 65–66.
3. Klein, L. R.; Rubin, H. (1947–8). "A Constant-Utility Index of the Cost of Living". Review of Economic Studies 15 (2): 84–87.
4. Stone, Richard (1954). "Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand". Economic Journal 64 (255): 511–527.