3.1 Kaldor-Kalecki model with a steady equilibrium Consider the following model of an aggregate economy: 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. The transformations Y = y + Y $^{∗}$, K = k + K $^{∗}$, applied to (3.5), give us the system We also investigate the idealized macroeconomic model with foreign capital investment, 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 Y ′ = α [ I ( Y, K ) − S ( Y, K )] , K ′ = I ( Y, K ) − δK, (3.4) Y ′ = α [(1 − s ) Y − aY 3 + bK ] , K ′ = Y − aY $^{3}$+ bK − δK, (3.5) Y ∗ = √ δ (1 − s ) + bs aδ , K ∗ = s δ √ δ (1 − s ) + bs aδ , y ′ = α [ ( 2( s − 1) − 3 bs δ ) y + bk − ay 3 − 3 √ aδ (1 − s ) + abs δ y 2 ] , k ′ = ( 3 s − 2 − 3 bs δ ) y + ( b − δ ) k − ay 3 − 3 aδ (1 − s ) + abs δ y $^{2}$. (3.6) S ′ = αY + pS ( k − Y $^{2}$) , Y ′ = v ( S + F ) , F ′ = mS − rY, (3.7) 8 3.2 A model with a business cycle