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Stone–Geary utility function

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The Stone–Geary utility function takes the form

U = ∏ i ( q i − γ i ) β i {\displaystyle U=\prod _{i}(q_{i}-\gamma _{i})^{\beta _{i}}}

where U {\displaystyle U} is utility, q i {\displaystyle q_{i}} is consumption of good i {\displaystyle i} , and β {\displaystyle \beta } and γ {\displaystyle \gamma } are parameters.

For γ i = 0 {\displaystyle \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. In case of ∑ i β i = 1 {\displaystyle \sum _{i}\beta _{i}=1} the demand function equals

q i = γ i + β i p i ( y − ∑ j γ j p j ) {\displaystyle q_{i}=\gamma _{i}+{\frac {\beta _{i}}{p_{i}}}(y-\sum _{j}\gamma _{j}p_{j})}

where y {\displaystyle y} is total expenditure, and p i {\displaystyle p_{i}} is the price of good i {\displaystyle 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.

References

  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. JSTOR 2296107.
  3. Klein, L. R.; Rubin, H. (1947–1948). "A Constant-Utility Index of the Cost of Living". Review of Economic Studies. 15 (2): 84–87. JSTOR 2295996.
  4. 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.

Further reading

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