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Cobb-Douglas Utility - Eventually!

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

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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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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  1. 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.
  2. 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.
  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. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
  11. Powell, Alan A., 1992. "Sato's insight on the relationship between the Frisch 'parameter' and the average elasticity of substitution," Economics Letters, Elsevier, vol. 40(2), pages 173-175, October.
  12. Cranfield, John & James Eales & Thomas W. Hertel & Paul Preckel, 1998. "Changes in the Structure of Global Food Demand," GTAP Working Papers 295, Center for Global Trade Analysis, Department of Agricultural Economics, Purdue University.
  13. 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.
  14. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
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