Document Type: Original Article


1 Ph.D. candidate of Agricultural Economics, University of Payame Noor, Tehran, Iran

2 Associate Professor of Agricultural Economics, University of Payame Noor, Tehran, Iran

3 Professor of Agricultural Economics, Faculty of Agricultural Economics and Development, University of Tehran, Karaj, Iran

4 Assistant Professor of Agricultural Economics, Institute of Planning Research, Agricultural Economics and Rural Development, Tehran, Iran


The separability of consumer desires is a necessary condition for multi-stage budgeting and collectivization is consistent of commodity where costs are allocated between edible groups using price indices and intergroup allocations are made independent of other groups. In empirical studies of demand, the concept of separation is used to correctly estimate demand function and limit the number of parameters. For this purpose, data related to price index and cost of selected commodities (citrus fruits, cucurbits, and vegetables) derived from the Central Bank over 2016 in urban households of Iran were used. The results of the separability tests support the hypothesis that consumers first allocate their income to selected commodities in three groups (citrus fruits, cucurbits, and vegetables) and then approves the income allocation action between the types of its subgroups that are grouped. Also, the results of the system estimation showed that all groups had a negative intrinsic price elasticity. In the meantime, the price elasticity of the groups of citrus fruits (orange, tangerines, and lemon), cucurbits fruits (potato, tomato, and onion) and vegetables (the leafy ones) are equal to -0.83, -0.48 and -0.91, respectively. Given the income elasticity calculated for the three commodity groups, the second commodity group (potato, tomato, and onion) is more essential than the other commodity groups, which should be considered in government policies as to agricultural production and pricing.

Graphical Abstract


  • Weak separability (WS) allows the splitting of a utility function (technology) into many sub-utility functions.
  • Separability types include (symmetric and asymmetric separable structures), weak or strong separability.
  • Goods belonging to a group may be aggregated if the direct utility function is weakly separable.
  • Rotterdam modelbased on consumer demand theory and is sufficiently flexible to capture variations in consumer behavior


Alboghdady, M.A., & Alashry, M.K. (2010). The demand for meat in Egypt: An Almost Ideal estimation. African journal of Agricultural and Resources Economics, 4, 70-81.]In Persian [

Baccouche, R., & Laisney, F. (1991). Describing the separability properties of empirical demand systems. Journal of Applied Econometrics, 6, 181-206.

Barnett, W.A. (1979). Theoretical foundations for the Rotterdam model. Review of Economic Studies, 46,109-30.

Barnett, W.A., & Choi, S. (1989).  A monte carlo study of tests of blockwise weak separability. Journal of Business & Economic Statistics, 7, 362-77.

Barten, A. (1993). Consumer allocation models: Choice of functional form. Empirical Economics, 18, 129-158.

Blackorby, C., Primont, D., & Russell, R. R. (1978). Quality, separability, and functional structure: Theory and economic applications. New York: North Holland.

Brester, G.W., & Wohlgenant, M.K. (1991). Estimating interrelated demands for meats using new measures for ground beef and table cut beef. American Journal of Agricultural Economics, 72, 1182-1194.

Byron, R. P. (1970). A simple method for estimating demand systems under separable utility assumptions. Review of Economic Studies, 37,261-74.

Capps, J.R.O., & Love. H.A. (2002). Econometric considerations in the use of electronic scanner data to conduct consumer demand analysis. American Journal of Agricultural Economics, 84(3), 807-816.

Deaton, A., & Muellbauer, L. (1980). Economics and consumer behavior. Cambridge MA: Cambridge University Press.

Eales, I.S., & Unnevehr, L.J. (1988). Demand for beef and chicken products: Separability and structural change. American Journal of Agricultural Economics, 70,521-32

Erfani, A.R., Davoodi, P., Sadeqi, F. (2017). Grouping monetary assets in iran based on non-parametric analysis of money demad.  Journal of Economic Research, 52(4), 879-904 [In Persian].

Falsafian, A., & Ghahramanzadeh, M. (2011). Selection of a functional system for meat demand analysis in Iran, Journal of Food Industry Research, 22(2), 176-187[In Persian].

Goldman, S., & Uzawa, H. (1964). A note on separability in demand analysis. Econometrica, 32,387-398. [In Persian].

Gregory, A., & Veall, M. (1985). Formulating Wald tests on nonlinear restrictions. Econometrica, 53, 1465-1468.

Hanoch, G. (1975). Production and demand models with direct or indirect implicit additivity. Econometrica, 43, 395-419.

Hayes, D., Wahl, T., & Williams, G. (1990). Testing restrictions on a model of Japanese meat demand. American Journal of Agricultural Economics, 72, 556-66.

Jorgenson, D. W., & Lau, L. J. (1975). The structure of consumer preferences. Annals of Economic and Social Measurement, 4(1) ,49-101.

Judge, G., W. Griffiths, R. Hill, H. Lutekpohl, & Lee, T. (1986). The theory and practice of econometrics. New York: John Wiley & Sons.

Lee, L., Schulz-Ted, C., & Schroeder-Tian, X. (2011). Using weak separability and generalized composite commodity theorem in modeling ground beef demand- agricultural and applied economics association’s AAEA & NAREA Joint Annual Meeting. Pittsburgh, Pennsylvania, 24-26.

Leontief, W.W. (1974). Introduction to the theory of the internal structure of functional relationships. Econometrica, 15, 361-73.

Moschini, G., Moro, D., & Green, R.D, (1994). Maintaining and testing separability in demand systems. American Journal of Agricultural Economics, 76, 61-73.

Nayga, R. M., & Capps, Jr, O. (1994). Tests of weak separability in disaggregated meat products. American Journal of Agricultural Economics, 76, 800-808.

Nicol, C. (1991). The effect of expenditure aggregation on hypothesis tests in consumer demand systems. International Economic Review, 32, 405-16.

Phillips, P. C. B., & Park, J. Y. (1988). On the formulation of wald tests of non-linear restrictions, Econometrica, 56(5), 1065-1083.

Pudney, S. (1981). An empirical method of approximating the separable structure of consumer preferences. Review of Economic Studies, 48,561-77.

Raghfar, H. Kurdbacheh, H., & Khodayari Shahsavari, T. (2017). Inves tigating the food baskets in urban households of iran using system requirements equations. Social Welfare Journal, 17(65), 43-68.

Shabanzadeh, M., & Mahmoodi, A. (2016). Assessment of fruit and nut gathering, vegetables, grains and vegetable products: Application of generalized compounding theory. Journal of Agricultural Economics and Development, 29(4), 345-358. ]In Persian[

Sono, M. (1961). The effect of price changes on the demand and supply of separable goods. International Economic Review, 2, 239-271.

Theil, H. (1980). The system-wide approach to microeconomics. Chicago: The University of Chicago Press.