Finance:Stone–Geary utility function
The Stone–Geary utility function takes the form
- [math]\displaystyle{ U = \prod_{i} (q_i-\gamma_i)^{\beta_{i}} }[/math]
where [math]\displaystyle{ U }[/math] is utility, [math]\displaystyle{ q_i }[/math] is consumption of good [math]\displaystyle{ i }[/math], and [math]\displaystyle{ \beta }[/math] and [math]\displaystyle{ \gamma }[/math] are parameters.
For [math]\displaystyle{ \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 case of [math]\displaystyle{ \sum_i \beta_i =1 }[/math] the demand function equals
- [math]\displaystyle{ q_i = \gamma_i + \frac{\beta_i}{p_i} (y - \sum_j \gamma_j p_j) }[/math]
where [math]\displaystyle{ y }[/math] is total expenditure, and [math]\displaystyle{ p_i }[/math] is the price of good [math]\displaystyle{ 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]
References
- ↑ Varian, Hal (1992). "Estimating consumer demands". Microeconomic Analysis (Third ed.). New York: Norton. pp. 212. ISBN 0-393-95735-7. https://books.google.com/books?id=m20iQAAACAAJ&pg=PA210.
- ↑ Geary, Roy C. (1950). "A Note on ‘A Constant-Utility Index of the Cost of Living’". Review of Economic Studies 18 (2): 65–66.
- ↑ Klein, L. R.; Rubin, H. (1947–1948). "A Constant-Utility Index of the Cost of Living". Review of Economic Studies 15 (2): 84–87.
- ↑ 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
- Neary, J. Peter (1997). "R.C. Geary's Contributions to Economic Theory". in Conniffe, D.. R.C. Geary, 1893–1983: Irish Statistician. Dublin: Oak Tree Press. http://www.ucd.ie/economic/staff/pneary/pdf/geary97.pdf.
- Silberberg, Eugene; Suen, Wing (2001). "Empirical Estimation and Functional Forms". The Structure of Economics: A Mathematical Analysis (Third ed.). Boston: Irwin McGraw-Hill. pp. 357–363. ISBN 0-07-234352-4. https://books.google.com/books?id=7y9lQgAACAAJ&pg=PA357.
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