MSP-Model of the Economic Complex Adaptive System (ECAS): Economy as a Complex Adaptive System

Demand-Supply (Walrasian) Adjustment

This is stabilizing mechanism based on demand and supply interrelation: excess demand for the goods triggers the growth of price. Walras’s (1874) theory of general equilibrium in the modern formulation is based on three statements:

• 1.

  Walras’s law (aggregate demand equals to aggregate supply) is fulfiled;

• 2.

  Excess demand is homogeneous function of degree zero (excess demand does not depend on the choice of price scale);

• 3.

  Utility of goods consumed by any agent subject to budget constraint is maximal in equilibrium state.

Samuelson (1941) proposed equations describing the change of prices in response to excess demand for the goods.

A sign-preserving continuous function depends on excess demand for the n-th commodity. Equations (1) can be analyzed by means of comparative statics methods. Vector of equilibrium prices is the solution of the following system of equations:

After Walras’s system of general equilibrium was formulated rigorously the question about the existence and uniqueness of equilibrium arose. Wald (1951) proved that equality between the number of equations and the number of unknown variables in Walras’s system guarantees neither existence nor uniqueness of solution.

Arrow & Debreu (1954) used Brouwer’s fixed point theorem in order to explore the problem of existence of equilibrium states for this system. Hicks (1939) formulated the stability problem for equilibrium state (perfect and imperfect stability). The problem of uniqueness and stability of equilibrium was discussed in many works (Samuelson (1941; 1944); Metzler (1945); Arrow & Hurwicz (1958); Arrow, Block & Hurwicz (1959); McKenzie (1960); Morishima (1964); Dierker (1972); Varian (1975); Fisher (1975) and others). Samuelson (1944) proved that Hicksian conditions of stability generally do not guarantee in the general case the dynamical stability of equilibrium. Mosak (1944); Metzler (1945) and Morishima (1964) used the ‘gross substitution’ hypothesis as the necessary assumption that guarantees the existence of unique and stable equilibrium. It was proved also that the unique stable equilibrium exists if the economy has ‘dominant negative diagonal’ in Jacobi’ matrix of ‘excess demand’ functions. These ‘conditions of global stability’ imposed onto the properties of Jacobi’ matrix are not always suitable for the actual economy. Rader (1972) indicated that the ‘gross substitutability’ hypothesis contradicts to real situation at the markets of production factors. Arrow & Hurwicz (1958) noted that unstable equilibrium points can exist generally in economy free from these restrictive special ‘conditions’. Scarf (1960) considered some examples where the global equilibrium is unstable. Debreu (1970) proposed algorithm for the analysis of economy having multiple equilibrium points. The analysis of the problem of uniqueness and stability of general equilibrium is not finished.