Stone–Geary utility function

The Stone–Geary utility function takes the form U=∏i(qi−γi)βi where U is utility, qi is consumption of good i, and β and γ are parameters.

For γi=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 ∑iβi=1 the demand function equals qi=γi+βipi(y−∑jγjpj) where y is total expenditure, and pi 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. https://books.google.com/books?id=m20iQAAACAAJ&pg=PA210.
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. (1947–1948). "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.

## Further reading

* Neary, J. Peter (1997). "R.C. Geary's Contributions to Economic Theory". in Conniffe, D.. R.C. Geary, 1893–1983: Irish Statistician. Dublin: Oak Tree Press. http://www.ucd.ie/economic/staff/pneary/pdf/geary97.pdf.
* 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. https://books.google.com/books?id=7y9lQgAACAAJ&pg=PA357.

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