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Cobb-Douglas Utility - Eventually!

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  • Alan A. Powell
  • Keith R. McLaren
  • K.R. Pearson
  • Maureen T.Rimmer

Abstract

Consider the following two opinions, both of which can be found in the literature of consumer demand systems: (a) As the real income of a consumer becomes indefinitely large, re-mixing the consumption bundle becomes irrelevant: having chosen the ultimately satisfying budget shares at any given set of relative prices, the superlatively wealthy continue to allocate additional income in the same proportions. With very large and increasing per capita income, ultimately the utility function becomes indistinguishable from Cobb-Douglas. (b) Consumer demand systems in which the income elasticities monotonically approach one (from above, in the case of luxuries; from below, in the case of necessities) are unsatisfactory both theoretically and empirically. For instance, a necessity with a low (less than 1) income elasticity may very well become less elastic with further increases in income. The issue is important for CGE modelers because explicit direct additivity (as in the linear expenditure system [LES]) is often the modeler's default choice: this leaves us firmly in the world of (a). Hanoch's implicit direct additivity exhibits very flexible Engel properties. Rimmer and Powell's AIDADS system belongs to this class. Within such a system it is possible to satisfy the motivations underlying both (a) and (b), as illustrated by the Engel (income) elasticities for a 3-commodity AIDADS system shown in Figure 1 below. Whilst the system eventually converges to Cobb-Douglas, some income elasticities can be effectively zero at any imaginable actual income level. Inferiority can also be accommodated over a range of incomes. This paper discusses the above in more detail, strengthening the case for implicit direct additivity. An experimental calibration of a database to the AIDADS system is illustrated with modifications made to the ORANI-G teaching model. A technical appendix establishes the effectively global regularity of AIDADS. Related computer files may be found here.

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Bibliographic Info

Paper provided by Victoria University, Centre of Policy Studies/IMPACT Centre in its series Centre of Policy Studies/IMPACT Centre Working Papers with number ip-80.

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Date of creation: Jun 2002
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Handle: RePEc:cop:wpaper:ip-80

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Related research

Keywords: consumer demand system; applied general equilibrium; separability; implicitly directly additive preferences; effectively global regularity; Cobb-Douglas; calibration; AIDADS;

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References

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  1. Russel J. Cooper & Keith R. McLaren, 1992. "An Empirically Oriented Demand System with Improved Regularity Properties," Canadian Journal of Economics, Canadian Economics Association, vol. 25(3), pages 652-68, August.
  2. Maureen T. Rimmer & Alan A. Powell, 1994. "Engel Flexibility in Household Budget Studies: Non-parametric Evidence versus Standard Functional Forms," Centre of Policy Studies/IMPACT Centre Working Papers op-79, Victoria University, Centre of Policy Studies/IMPACT Centre.
  3. Harrison, W Jill & Pearson, K R, 1996. "Computing Solutions for Large General Equilibrium Models Using GEMPACK," Computational Economics, Society for Computational Economics, vol. 9(2), pages 83-127, May.
  4. John Cranfield & Paul Preckel & James Eales & Thomas Hertel, 2000. "On the estimation of 'an implicitly additive demand system'," Applied Economics, Taylor & Francis Journals, vol. 32(15), pages 1907-1915.
  5. W. Jill Harrison & K.R. Pearson & Alan A. Powell & E. John Small, 1993. "Solving Applied General Equilibrium Models Represented as a Mixture of Linearized and Levels Equation," Centre of Policy Studies/IMPACT Centre Working Papers ip-61, Victoria University, Centre of Policy Studies/IMPACT Centre.
  6. Maureen T. Rimmer & Alan A. Powell, 1992. "Demand Patterns Across the Development Spectrum: Estimates for the AIDADS System," Centre of Policy Studies/IMPACT Centre Working Papers op-75, Victoria University, Centre of Policy Studies/IMPACT Centre.
  7. Mark Horridge, 2000. "ORANI-G: A General Equilibrium Model of the Australian Economy," Centre of Policy Studies/IMPACT Centre Working Papers op-93, Victoria University, Centre of Policy Studies/IMPACT Centre.
  8. Maureen T. Rimmer & Alan A. Powell, 1992. "An Implicitly Directly Additive Demand System: Estimates for Australia," Centre of Policy Studies/IMPACT Centre Working Papers op-73, Victoria University, Centre of Policy Studies/IMPACT Centre.
  9. Coyle, William T. & Mark Gehlhar & Thomas W. Hertel & Zhi Wang & Wusheng Yu, 1998. "Understanding the Determinants of structural Change in World Food Markets," GTAP Working Papers 260, Center for Global Trade Analysis, Department of Agricultural Economics, Purdue University.
  10. Alan A. Powell, 1992. "Sato's Insight on the Relationship between the Frisch 'Parameter' and the Average Elasticity of Substitution," Centre of Policy Studies/IMPACT Centre Working Papers g-99, Victoria University, Centre of Policy Studies/IMPACT Centre.
  11. Cooper, Russel J & McLaren, Keith R & Parameswaran, Priya, 1994. "A System of Demand Equations Satisfying Effectively Global Curvature Conditions," The Economic Record, The Economic Society of Australia, vol. 70(208), pages 26-35, March.
  12. John A.L. Cranfield & Thomas W. Hertel & James S. Eales & Paul V. Preckel, 1998. "Changes in the Structure of Global Food Demand," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 80(5), pages 1042-1050.
  13. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  14. Gary K.K. Wong & Keith R. McLaren, 2002. "Regular and Estimable Inverse Demand Systems: A Distance Function Approach," Monash Econometrics and Business Statistics Working Papers 6/02, Monash University, Department of Econometrics and Business Statistics.
  15. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
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Citations

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Cited by:
  1. Paul Preckel & J. A. L. Cranfield & Thomas Hertel, 2010. "A modified, implicit, directly additive demand system," Applied Economics, Taylor & Francis Journals, vol. 42(2), pages 143-155.
  2. Gelan, Ayele Ulfata, 2007. "Does food aid have disincentive effects on local production? A general equilibrium perspective on food aid in Ethiopia," Food Policy, Elsevier, vol. 32(4), pages 436-458, August.
  3. Preckel, Paul V. & Cranfield, John A.L. & Hertel, Thomas W., 2005. "Implicit Additive Preferences: A Further Generalization Of The Ces," 2005 Annual meeting, July 24-27, Providence, RI 19373, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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