Finance:Stone–Geary utility function

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The Stone–Geary utility function takes the form

[math]U = \prod_{i} (q_i-\gamma_i)^{\beta_{i}}[/math]

where [math]U[/math] is utility, [math]q_i[/math] is consumption of good [math]i[/math], and [math]\beta[/math] and [math]\gamma[/math] are parameters.

For [math]\gamma_i = 0[/math], the Stone–Geary function reduces to the generalised Cobb–Douglas function.

The Stone–Geary utility function gives rise to the Linear Expenditure System,[1] in which the demand function equals

[math]q_i = \gamma_i + \frac{\beta_i}{p_i} (y - \sum_j \gamma_j p_j) [/math]

where [math]y[/math] is total expenditure, and [math]p_i[/math] is the price of good [math]i[/math].

The Stone–Geary utility function was first derived by Roy C. Geary,[2] in a comment on earlier work by Lawrence Klein and Herman Rubin.[3] Richard Stone was the first to estimate the Linear Expenditure System.[4]


  1. Varian, Hal (1992). "Estimating consumer demands". Microeconomic Analysis (Third ed.). New York: Norton. pp. 212. ISBN 0-393-95735-7. 
  2. Geary, Roy C. (1950). "A Note on ‘A Constant-Utility Index of the Cost of Living’". Review of Economic Studies 18 (2): 65–66. 
  3. Klein, L. R.; Rubin, H. (1947–8). "A Constant-Utility Index of the Cost of Living". Review of Economic Studies 15 (2): 84–87. 
  4. Stone, Richard (1954). "Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand". Economic Journal 64 (255): 511–527. 

Further reading[edit]–Geary utility function was the original source. Read more.