Exponential model of the Engel curve: Application within the income elasticity analysis of the Czech households' demand for meat and meat products

Abstract

The paper is focused on the economic and mathematical analysis of the Engel demand model in the exponential form: <i>q</i> = <i>a</i><sub>0</sub> × e<sup><i>a</i>1/<i>X</i></sup>.Properties of this exponential model are studied with respect to its application possibilities in the field of evaluation of the income elasticity of the Czech households’ demand for meat and meat products. According to the used database of the consumer behaviour of the average Czech household from 1995 to 2000 (CZSO-HES), the analysed exponential model of the Engel curve attained the following parameters:, <i>Q<sub>t</sub></i> = <i>A<sub>t</sub></i> × e<sup>–17336.8908<i>/Xt</i></sup>, where <i> A<sub>t</sub></i> = 44,6019 × e<sup>1,1119×10–4 × <i>t</i>2</sup> and <i>t</i> = 1, 2, …, 24. For the analysis of the income-demand elasticity of the developed exponential form, the model offers the static hyperbolic function: η (<i>X<sub>t</sub></i>) = 17 336.8908/<i>X</i><sub>t</sub>. The derived hyperbolic function of the income-demand elasticity falls digressively and the simulated values tend to the zero level. In analysed time period (1995–2000), the income-demand reactions were simulated in the elastic form with the values from 1.3866 to 1.1340. The average level of the analysed income- demand elasticity between the observed years reached the value of 1.2121, thus the 1% rise in the real level of the quarter households’ incomes per capita led to the average increase in the average Czech household’s demand for meat and meat products, including fish and fish products, of about 1.21%.