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

• Authors: Kiedrowski R.
• Languages of publication: PL

Abstracts

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.

Keywords

EN

CAPITAL ACCUMULATION & DISTRIBUTION; CAPITAL ALLOCATIONS; EQUILIBRIUM STABILITY; PROFIT RATES EQUALIZATION

Discipline

• ECONOMICS: ECONOMICS

• Publisher: Główny Urząd Statystyczny
• Journal: Przegląd Statystyczny
• Year: 2007
• Volume: 54
• Issue: 4
• Pages: 62-91
• Document type: ARTICLE

Contributors

author

Kiedrowski R.

• R. Kiedrowski, Akademia Ekonomiczna w Poznaniu, Katedra Ekonomii Matematycznej, al. Niepodleglosci 10, 60-967 Poznan, Poland

Identifiers

CEJSH db identifier

08PLAAAA03697446