Stone–Geary utility function explained

The Stone–Geary utility function takes the form

U = \prod _{i} (q _{i-\gamma} ^{\beta _{i}} ^{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 equalsq _{i} = \gamma _{i} + (\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]

Further reading

• Book: Neary, J. Peter . J. Peter Neary . http://www.ucd.ie/economic/staff/pneary/pdf/geary97.pdf . 1997 . R.C. Geary's Contributions to Economic Theory . D. . Conniffe . R.C. Geary, 1893–1983: Irish Statistician . Oak Tree Press . Dublin . dead . https://web.archive.org/web/20050325205914/http://www.ucd.ie/economic/staff/pneary/pdf/geary97.pdf . 2005-03-25 .
• Book: Silberberg, Eugene . Wing . Suen . The Structure of Economics: A Mathematical Analysis . Boston . Irwin McGraw-Hill . Third . 2001 . 0-07-234352-4 . Empirical Estimation and Functional Forms . 357–363 . https://books.google.com/books?id=7y9lQgAACAAJ&pg=PA357 .

Notes and References

1. Book: Varian, Hal . Hal Varian . Microeconomic Analysis . New York . Norton . Third . 1992 . 0-393-95735-7 . 212 . Estimating consumer demands . https://books.google.com/books?id=m20iQAAACAAJ&pg=PA210 .
2. Roy C. . Geary . A Note on ‘A Constant-Utility Index of the Cost of Living’ . . 18 . 2 . 65–66 . 1950 . 2296107 .
3. L. R. . Klein . H. . Rubin . A Constant-Utility Index of the Cost of Living . . 15 . 2 . 1947–1948 . 84–87 . 2295996 .
4. Richard . Stone . Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand . . 64 . 255 . 1954 . 511–527 . 2227743 .