Determining the Actual Structure of the Demand Function through the Nesting or Non-nesting BOX-COX Ideal Demand System

The main goal in this research is to survey and determine the actual structure of the demand function through the BOX-COX consumer goods demand system which includes various forms of demand functions. Using nested and non-nested methods the estimation of consumer demand function is done. Nonlinear seemingly unrelated regressions are also used for the periods of 1982- 2007 via the combined statistics of income groups in urban areas in order to calculate uncompensated price elasticity and expenditure elasticity associated with the demand function estimate. Results of nested and non-nested tests show that the BCDS and AIDS models are near performance. The elasticity figures resulted from the BCDS and AIDS models have also revealed that food group is an essential one, social affairs (clothing, health, leisure and education) are regarded as almost luxury, and miscellaneous group (transportation and others) is quite luxury. But the group of housing (housing and furniture), in the BCDS model is almost luxury and in the AIDS model considered as essential. The elasticity of demand was confirmed by the demand law and cross elasticity of demand has also shown that the food group compared with the social affairs is considered as supplementary and to the group of housing and miscellaneous is regarded as a substitute. The social affairs group compared with the miscellaneous group is supplementary and to the housing group is a substitute and finally the miscellaneous group is considered as a substitute to the housing group.