Main Properties of MSP-ECAS-Model: Application to the European Economy

Main Properties of MSP-ECAS-Model: Application to the European Economy

DOI: 10.4018/978-1-5225-2170-9.ch002
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Evolutionary Branches, Long-Term Equilibrium And Temporal Equilibrium States Of Ecas

MSP-modeling opens new possibilities for deeper understanding of the Economic System. MSP-model of ECAS reveals existing implicitly nontrivial economic interrelations between economic indicators. We consider below two cases: 1) MSP-model with constant parameters (Chapter 2 and 3) MSP-model with changing parameters (Chapter 4). Surely MSP-model with constant parameters simplifies of course the economic reality but this model gives important qualitative description of the economy as the complex system which evolves cyclically through a sequence of discontinuous cycles with different durations.

MSP-model with constant parameters introduces into economics new fundamental notion – “evolutionary branch” - locus of temporal equilibrium states of the Economic System in the plane 978-1-5225-2170-9.ch002.m01. The fact of existence of such special curves is surprising. We can rewrite equations (19)-(20) from the Introduction for “evolutionary branches” via “productivity of capital” 978-1-5225-2170-9.ch002.m02 and “capacity utilization rate” 978-1-5225-2170-9.ch002.m03.

“Upper Evolutionary Branch” for economic system:


“Lower Evolutionary Branch” for economic system:


Symbol 978-1-5225-2170-9.ch002.m08 designates productivity of capital in the point of long-term equilibrium (Point 1 in Figure 2). The following interrelations are fulfilled:

978-1-5225-2170-9.ch002.m09 or 978-1-5225-2170-9.ch002.m10(3)

Efficiency of economic system depends on productivity of capital (equations (1)-(2)):

“Upper Evolutionary Branch” of economic system:

; (4)

“Lower Evolutionary Branch” of economic system:

; (5)

Productivity of capital equals tangent of angle of inclination 978-1-5225-2170-9.ch002.m13 of radius-vector in the plane 978-1-5225-2170-9.ch002.m14:


Parameter 978-1-5225-2170-9.ch002.m16 influences onto the geometric shape of “evolutionary branches”. According to formula (30) from the Introduction this parameter equals to ratio of length of two line segments along Z-axis.


There are two types of the economic systems:

  • Type 1: The systems with 978-1-5225-2170-9.ch002.m18 (or 978-1-5225-2170-9.ch002.m19). These systems evolve via sequence of evolutionary cycles.

  • Type 2: The systems with 978-1-5225-2170-9.ch002.m20 (or 978-1-5225-2170-9.ch002.m21). These systems evolve non-cyclically.

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