Overlapping distribution method

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

Sources

• J. Peter Neary, J. Peter Neary (1997), 'R.C. Geary's Contributions to Economic Theory', in D. Conniffe (ed.), R.C. Geary, 1893-1983: Irish Statistician, Oak Tree Press, Dublin