Evolution and jump in a Walrasian framework

Abstract

Lower profit rates play an importan role in the evolution of an ownership private economy. We argue that if managers look to maximize profits rates, then the decision to change, to those branches, or technologies, that offer higher rates of profits, plays an important role in the characterization of economies. If managers choose to produce according to those technologies that promise higher profit rates, then along the time, the distribution of the firms over the set of available technologies change, and therefore the economic fundamentals change. Under conditions of imperfect information, the imitation of the most successful firms plays can a decisive role in deciding how to produce. Along a path of Walrasian equilibria, regular economies can become singular and if this occurs, big changes must be expected after decisions of the firms for the next period.

A dynamic for production economies with multiple equilibria

“…Then the equilibria prices, in the first market, are given by p = 1/2, 1, 2. These equilibria correspond with (1/2, 1), (1,1) and (2,1) in the global economy. 3.…”

“…Definition 1. Given an economy ω, we say that the vector demand x = (x 1 1 , x 1 2 ), (x 2 1 , x 2 2 ) and the system price p = (p 1 , p 2 ) is a Walrasian equilibrium if:…”

“…3 Theorem 1. Let (ω 1 1 , ω), (ω, ω 2 2 ), f be a mirror symmetric Shpley-Shubik economy and set φ 1 (p) = (f ) −1 (p). Then, if ω 1 2 = ω = ω 2 1 , φ(1) + 2φ (1) > ω and φ(1) < min{ω 1 1 , ω 2 2 } the economy has at least three equilibria prices.…”

“…Let (ω 1 1 , ω), (ω, ω 2 2 ), f be a mirror symmetric Shpley-Shubik economy and set φ 1 (p) = (f ) −1 (p). Then, if ω 1 2 = ω = ω 2 1 , φ(1) + 2φ (1) > ω and φ(1) < min{ω 1 1 , ω 2 2 } the economy has at least three equilibria prices. One at price p 2 = 1, another in some p 3 > 1 and one more in 3 In the original Theorem is assumed that the endowments are ω 1 = (ω 1 1 , 0), and ω 2 = (0, ω 2 2 ).…”

“…Given that (p, 1) is an equilibrium for the economy E N * , last equation has the following economical interpretation: the value of the individual excess demand for the first good of the second consumer equals the value of the net output of the commodity 1 minus the income of the consumer 1 plus φ 1 (p −1 ) + ω 1 1 p, i.e.,…”