Stone–Geary utility function

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.[1] 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,[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

  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

  • Neary, J. Peter (1997). "R.C. Geary's Contributions to Economic Theory" (PDF). In Conniffe, D. (ed.). R.C. Geary, 1893–1983: Irish Statistician. Dublin: Oak Tree Press. Archived from the original (PDF) on 2005-03-25.
  • 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.