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  1. 2 Przegląd Statystyczny

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  1. 2 Kiedrowski R.

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  1. 2 2007

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1

THE STABILITY OF CLASSICAL EQUILIBRIUM IN A MULTI-PRODUCT ECONOMY WITH FIXED CAPITAL

100%
Kiedrowski R.
Przegląd Statystyczny
|
2007
|
vol. 54
|
issue 4
62-91
EN
The work is a continuation of another paper of the author published recently in 'Przeglad Statystyczny'. It is devoted to a deterministic dynamic model of classical inspiration in which 'n' firms are owned by one representative owner, called capitalist. The model is aimed to describe mathematically the process of accumulation of capital by the capitalist and its distribution among enterprises based on profitability differentials. Decisions on capital allocation in the firms determine their stocks of fixed capital and hence production capacities. The firms themselves decide on prices and production (capital utilization) in response to disequilibria between supply and demand. Their decisions in turn affect profit rates. While in the previous work a detailed description of the model and its long-run equilibrium have been presented, the issue of the present study is the stability of this equilibrium which is related to the old problem of profit rates equalization, described already in the works of the classics - Smith, Ricardo and Marx. Since the long-run classical equilibrium is a state of homothetical growth of an economy with constant prices and equal profit rates, the stability is defined by relative variables, describing proportions between prices and outputs of different goods and proportions of stocks of fixed capital in different firms. Hence the exact subject of the analysis is stability of proportions. The paper contains a mathematical proof of the local asymptotic stability of the classical equilibrium. The general idea of the proof comes from French authors G. Dumenil and D. Levy who have proved stability of classical equilibrium in similar models. Nevertheless, the proof contains also same new essential elements which have been introduced because of the specific structure of the investigated model.
2

A MODEL OF CLASSICAL CAPITAL ALLOCATION IN A MULTI-PRODUCT ECONOMY WITH FIXED CAPITAL

100%
Kiedrowski R.
Przegląd Statystyczny
|
2007
|
vol. 54
|
issue 3
63-91
EN
The paper is devoted to presentation of a dynamic multi-product deterministic model of classical inspiration in which decentralized decisions of economic agents are based on adjustements to different kinds of disequilibria. It is assumed that there are 'n' firms producing 'n' different goods. The goods can be used as well for consumption, current inputs and investment purposes. The firms decide on prices and production levels (capacity utilization) on the basis of disequilibria between supply and demand (inventories of unsold commodities) and on the diffenences between real and target capacity utilization rates. They pay wages to their employees who spend them immediately on consumption goods. Special attention is paid to the process of capital accumulation which is controlled by one representative owner of all firms, named for simplicity a capitalist. In each period the capitalist decides on the value of accumulation taking into account total calculated (expected) profit, average capacity utilization rate and the average interest rate, correlated with inflation rate. Having decided about the total amount of accumulation the capitalist distributes it between enterprises according to their profit rates differentials. Although the accumulation of capital in a certain firm is described in financial terms, it uniquely determines the increase of fixed capital (productive capacity) in subsequent period. It is provided that a long-term classical equilibrium exists in the considered economy. In this equilibrium prices are constant, all profit rates are equal while all physical variables as fixed capital, output or consumption of each good grow at the same constant rate. Moreover, the equilibrium growth rate does nor depend on the analytical forms of worker's and capitalist's consumption functions, and hence the same rate of growth can be achieved for various structures of fixed capital and output adjusted to different consumption patterns
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