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. 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, in a comment on earlier work by Lawrence Klein and Herman Rubin. Richard Stone was the first to estimate the Linear Expenditure System.

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.