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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. |
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| | For <math>\gamma_i = 0</math>, the Stone-Geary function reduces to the generalised [[Cobb-Douglas]] function. |
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| | The Stone–Geary utility function gives rise to the Linear Expenditure System, 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>. |
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| | 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. |
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| | ==Sources== |
| | *[[J. Peter Neary]], [http://www.ucd.ie/economic/staff/pneary/pdf/geary97.pdf 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] |
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| | {{DEFAULTSORT:Stone-Geary utility function}} |
| | [[Category:Utility]] |
The Stone–Geary utility function takes the form
where is utility, is consumption of good , and and are parameters.
For , 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
where is total expenditure, and is the price of good .
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