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 which the demand function equals

$q_i = \gamma_i %2B \frac{\beta_i}{p_i} (y - \sum_j \gamma_j p_j)$

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.

Source

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