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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 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,^[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

^ Varian, Hal (1992). "Estimating consumer demands". Microeconomic Analysis (Third ed.). New York: Norton. pp. 212. ISBN 0-393-95735-7.
^ Geary, Roy C. (1950). "A Note on 'A Constant-Utility Index of the Cost of Living'". Review of Economic Studies. 18 (2): 65–66. JSTOR 2296107.
^ Klein, L. R.; Rubin, H. (1947–1948). "A Constant-Utility Index of the Cost of Living". Review of Economic Studies. 15 (2): 84–87. JSTOR 2295996.
^ Stone, Richard (1954). "Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand". Economic Journal. 64 (255): 511–527. JSTOR 2227743.

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.