Competitive market for multiple firms and economic crisis

Abstract

Abstract:The origin of economic crises is a key problem for economics. We present a model of long-run competitive markets to show that the multiplicity of behaviors in an economic system, over a long time scale, emerge as statistical regularities (perfectly competitive markets obey Bose-Einstein statistics and purely monopolistic-competitive markets obey Boltzmann statistics) and that how interaction among firms influences the evolutionary of competitive markets. It has been widely accepted that perfect competition is most efficient. Our study shows that the perfectly competitive system, as an extreme case of competitive markets, is most efficient but not stable, and gives rise to economic crises as society reaches full employment. In the economic crisis revealed by our model, many firms condense (collapse) into the lowest supply level (zero supply, namely bankruptcy status), in analogy to Bose-Einstein condensation. This curious phenomenon arises because perfect competition (homogeneous competitions) equals symmetric (indistinguishable) investment direction, a fact abhorred by nature. Therefore, we urge the promotion of monopolistic competition (heterogeneous competitions) rather than perfect competition. To provide early warning of economic crises, we introduce a resolving index of investment, which approaches zero in the run-up to an economic crisis. On the other hand, our model discloses, as a profound conclusion, that the technological level for a long-run social or economic system is proportional to the freedom (disorder) of this system; in other words, technology equals the entropy of system. As an application of this new concept, we give a possible answer to the Needham question: "Why was it that despite the immense achievements of traditional China it had been in Europe and not in China that the scientific and industrial revolutions occurred?"

Exponential structure of income inequality: evidence from 67 countries

“…Because the firm consists of labor and capital, the Cobb-Douglas aggregate production function (or GDP) of neoclassical economics can be written in the form (Tao 2010(Tao , 2016):…”

Golden-Rule Level of the Employment

“…. ; n. Similar to statistical physics in which the internal energy UðN p ; SÞ can be written as a function of the number of particles, N p and the entropy S, Tao 10,17 suggested that the total revenue (or gross value of output) of N¯rms (or agents), Å, can be written as a function of N and the technological progress T ; that is,…”

“…This means that the improvement of technological progress of a society is due to the degree of freedom that social members have experienced. 10,17 Equation (16) clearly predicts the revenue distribution among agents (or¯rms) in a competitive economy. Hence, we can compare it with the household income (like the revenue of self-employed¯rm) data.…”

“…Indeed, there have been many relevant papers in the literature. [5][6][7][8][9][10][11][12][13][14][15][16] Even so, we still have little understanding for the relationship between statistical equilibrium and general equilibria. Recently, Tao 12 made an e®ect to clarify the relationship.…”

The IncomeGini of Fairness

“…", about fairness and about opportunities, versus corruption and crony economics [1][2][3][4][5][6][7] (see footnote a). Clearly, there are other economical and sociological functions and indicators that are valuable in describing nations [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] and freedom 8 and democracy 6 are in°uencing lives much more. Yet, the income distribution, and the distributions derived from that, the \wealth distribution" and the \control on the°ow of wealth distribution", are clearly among the basic most in-°u ential quantities and should be researched on.…”