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.