## Acta Univ. Agric. Silvic. Mendelianae Brun. 2005, 53, 173-188

## Linear models of income patterns in consumer demand for foods and evaluation of its elasticity

The paper is focused on the use of the linear constructions for developing of Engel’s demand models in the field of the food-consumer demand. In the theoretical part of the paper, the linear approximations of this demand models are analysed on the bases of the linear interpolation. In the same part of this text, the hyperbolic elasticity function was defined for the linear Engel model. The behaviour of the hyperbolic elasticity function and its properties were consequently investigated too. The behaviour of the determined elasticity function was investigated according to the values of the intercept point and the direction parameter in the original linear Engel model. The obtained theoretical findings were tested using the real data of Czech Statistical Office. The developed linear Engel model was explicitly dynamised, because the achieved database was formed into the time series. With respect to the two variables definitions of the hyperbolic function in the theoretical part of the text, the determined dynamic model of the Engel demand for food was transformed into the form with parametric intercept point:*re*_{t}^{*} = *A*_{t} + 0.0946 · *rm*_{t}^{*},

where the values of absolute member are defined as:*A*_{t} = 1773.0973 + 9.3064 · *t* – 0.3023 · *t*^{2}; (*t* = 1, 2, ... 32).

The value of At in the parametric linear model of Engel consumer demand for food was during the observed period (1995–2002) always positive. Thus, the hyperbolic elasticity function achieved the elasticity coefficients from the interval:

η_{t} ∈〈+0; +1).

Within quantitative analysis of Engel demand for food in the Czech Republic during the given time period, it was founded, that income elasticity of food expenditures of the average Czech household was moved between +0.4080 and +0.4511. The Czech-household demand for food is thus income inelastic with the normal income reactions.

### Keywords

total real expenditures for food, real incomes, linear-dynamic Engel model, parametric linear Engel model, elasticity function.