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,^[1] 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 $p_{i}$ is the price of good $i$ .

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. 210–213 [p. 212]. ISBN 0-393-95735-7. {{cite book}}: External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)
^ Geary, Roy C. (1950). "A Note on 'A Constant-Utility Index of the Cost of Living'". Review of Economic Studies. 18 (2): 65–66. JSTOR 2296107.
^ Klein, L. R.; Rubin, H. (1947–8). "A Constant-Utility Index of the Cost of Living". Review of Economic Studies. 15 (2): 84–87. JSTOR 2295996. {{cite journal}}: Check date values in: |year= (help)CS1 maint: year (link)
^ Stone, Richard (1954). "Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand". Economic Journal. 64 (255): 511–527. JSTOR 2227743.

Neary, J. Peter (1997). "R.C. Geary's Contributions to Economic Theory". In Conniffe, D. (ed.). R.C. Geary, 1893–1983: Irish Statistician. Dublin: Oak Tree Press. {{cite book}}: External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)
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. {{cite book}}: External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)