Analysis of Consumption on the Goods and Services Market in the Cybernetic Model of Selected Country

The paper analyses the consumption on the goods and services market in the cybernetic model of Czechia. The theoretical basis is given by the consumption function in the short-term, the macroeconomic multiplier of the two-sector economy and the cybernetic model with the goods and services market. All the above-mentioned theory is applied to the real conditions of the selected country, which is the Czech Republic.


Introduction
A real economy is a complex system that can be simplified into an economic model with inputs, outputs, and links inside. Exogenous inputs are most often considered as autonomous components of consumption, investment, government purchases, exports and imports. The key output is then the amount of product.
One of the most important input and output parts is consumption. There is the input autonomous consumption and the output total consumption as part of the gross domestic product. This article analyses autonomous and total consumption in a two-sector economy.

Consumption in the Short-Term
The theory of consumption function is very well explored in the professional literature of the 20 th and 21 st centuries [1][2][3].
Consumption function in the short-term is based on Keynesian theory. It is a relation between consumption and macroeconomic product. Mathematically expressed, these two variables are dependent and independent variable. The equation of the function is as follows in the formula (1).
Where: C is the total consumption, C0 autonomous consumption, c × Y induced consumption, c marginal propensity to consume, Y product.

Macroeconomic Multiplier of the Two-Sector Economy
The so-called Keynesian multiplication process uses the property of consumption function and especially of the post-induced consumption through the marginal propensity to consume. "The Keynesian multiplier process is the economist's paradigmatic positive feedback loop, in which an initial departure from full-employment equilibrium cumulates instead of being corrected" [4]. The principle of multiplication is infinite and weakening repetition of the original impulse, which is the change in autonomous expenditures. Mathematical evaluation of the strength of the effect is given by the formula (2).
autonomous consumption, I0 autonomous investments, G0 autonomous government purchases, NX net export, c marginal propensity to consume.

Cybernetic Model with the Goods and Services Market
"Cybernetics allows expression of the dependence of output change Y on exogenous input changes (C0+I0+G0+NX)" [5]. Cybernetic model with the goods and services market has following parameters: A constant price level is assumed, which can be achieved by calculations with input parameters at constant prices. The graphical interpretation of the above is shown in Fig. 1.

Consumption in Selected Country
Under the conditions of the Czech Republic, objective time series can begin in 1993 when Czechia and Slovakia became independent. In this case, the relevant data can be traced back to 1996 as shown in Table 1. Table 1. Consumption and product data of the Czech Republic (in CZK million, constant prices) [7].
By fitting the regression line with these points, an accurate consumption function with R 2 = 0.9781 is obtained. The parameters of this consumption function are c = 0.5137 and C0 = 683545 (Fig. 2). The complete consumption function is given in equation (3).
Where: C is the total consumption, C0 autonomous consumption, c × Y induced consumption, c marginal propensity to consume, Y product.

Fig. 2. Consumption Function in the Czech Republic.
Source: Author.

Macroeconomic Multipliers in Selected Country
The Keynesian multiplier is naturally based on the values of the consumption function, autonomous consumption and the marginal propensity to consume. For the Czech Republic, the calculation method (4) and the value of the multiplier (5) apply.
Where: Y is the product (GDP), C0 autonomous consumption, I0 autonomous investments, G0 autonomous government purchases, NX net export, c marginal propensity to consume.

Cybernetic Model of Selected Country
The cybernetic model of the Czech Republic is supplemented by specific values of autonomous consumption C0 = 683545, and marginal propensity to consume c = 0.5137. This means that the change in any autonomous expenditures (autonomous investments, autonomous government spending, net exports) will be 2.0563 times in the economy. Fig. 3 shows an actual cybernetic model of the Czech Republic with the goods and services market.

Complex Dataset of Selected Country
Czechia can be described from the point of view of consumption, Keynesian multiplier and cyber model by the parameters in Table 2.
Individual quantities were determined as follows:  Yreal data,  Creal data,  C0 + I0 + G0 + NX as the total input of cybernetic model,  C0 as one parameter of the consumption function,  I0 + G0 + NX as the difference between cybernetic model and consumption function data.