Stone-Geary utility function

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The Stone-Geary utility function takes the form

U = \prod_{i} (q_i-\gamma_i)^{\beta_{i}}

where U is utility, qi is consumption of good i, and β and γ are parameters.

For γi = 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 pi 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.

[edit] Source

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