content_image/319213.jpg content_image/319215.jpg content_image/319214.jpg content_image/319216.jpg content_image/319217.jpg
## 3.1 Kaldor-Kalecki model with a steady equilibrium 

Consider the following model of an aggregate economy: 

<img src='content_image/319213.jpg'>

where Y is income, K is capital stock, I is gross investment, and S is savings. Income changes pro- portionally to the excess demand in the goods market, and the second equation is a standard capital accumulation equation. The constant depreciation rate δ and the adjustment coefficient α are positive. This model was studied in detail in [58] and [88]. It admits a stable equilibrium under certain conditions on the functions involved. 

Let us consider the following specification of system (3.4) with I ( Y, K ) = Y − aY $^{3}$+ bK, S ( Y, K ) = sY, 

where the constant parameters satisfy a > 0 , b < 0 , 0 < s < 1 and 0 < δ < 1 . 

One can see that a steady state of (3.5) with positive coordinates 

exists only if δs < δ + bs. 

<img src='content_image/319215.jpg'>

<img src='content_image/319214.jpg'>

The transformations Y = y + Y $^{∗}$, K = k + K $^{∗}$, applied to (3.5), give us the system 

<img src='content_image/319216.jpg'>

## 3.2 A model with a business cycle 

We also investigate the idealized macroeconomic model with foreign capital investment, 

<img src='content_image/319217.jpg'>

where S ( t ) are savings of households, Y ( t ) is Gross Domestic Product (GDP), F ( t ) is foreign capital inflow, k is potential GDP, and t is time. If k is set to 1, then Y, S, F are measured as multiples of potential output. The parameters represent corresponding ratios: α is the variation of the marginal 

