The macro equilibrium implies that s i and
The macro equilibrium implies that s=i and this YO-01027 implies that the property share is endogenously given by:
In the above nonlinear system there are 10 unknowns g, β, Ω, Q, r, π, R, Er, i and α in 10 equations ((3.3), (3.5)–(3.7), (4.1) and (5.1)–(5.5)).
The robustness of the model The system can be formulated in a more compact way in matrix form as:orwhere all the variables included in vector x represent deviations from steady state values. Some eigenvalues of this system are complex conjugate and have unitary modulus, λ =1, while the remaining are less than 1. Thus the fixed point has properties similar to the Neimark bifurcation, with limit cycles being generated (see Kuznetsov, 2004). For instance, one might wonder what happens if the propensity to consume out of wealth (c) increases. It is worth noting that this is the only channel through which an increase in wealth can affect the dynamics of the system. Furthermore, the nature of this increase is such to allow a macro inference of inequality. In the above linearized model, an increase in c makes the system unstable, because λ becomes greater than 1. In other words, inequality can feed instability. The same holds true if one increases the values of χ2, χ3, θ1 and θ2. In other words, whenever the weight of rent increases, not only inequality rises but also the system can become unstable.
Concluding remarks The model generates persistent and bounded dynamics, where the stylized facts characterizing the present state of the economy can be considered just a phase of these fluctuations. Within this perspective, changes in the wealth ratio (β) are not accompanied by changes in capital ratio, v, which is assumed to be fixed. Furthermore, α, the property share, and β, the wealth-output ratio, can be either positively or negatively related. Their links do not depend only on the hypotheses underlying the model but also on the values of the parameters chosen and the monetary policy pursued. Yet, the macro inference of inequality from the study of wealth dynamics still holds. The model can be extended in several ways. A first line would be to allow rent to affect production as happens in the classical authors. In order to accomplish this target, at least a two sector model must be considered. In the second place, the role of monetary and financial aspects could be enriched. The introduction of a cash flow in the investment function, along with the possibility of speculative debt according to a Minskian approach can be pursued (see Ferri, 2016). Thirdly, the impact of these variables on inequality should be deepened, for instance by considering heterogeneity between families holding wealth. Finally, the labour market variables should be explicitly taken into consideration. These enrichments can also allow to pursue more ambitious aims such as to better investigate how the medium-run dynamics can influence the long-run rate of growth. In fact, inequality not only can impact on fluctuations but it may also interfere with growth through the role of institutions and technical change that become essential players (see Cristini et al., 2015).
Introduction More recently, Dutt (1994) reexamines the question of long-run stability of modern economies through a dynamic model of capital accumulation and income distribution. This model gives two long-run equilibrium solutions. The first equilibrium, which is a saddlepoint, takes place when the economy is operating with excess capacity; given the instability of this equilibrium solution, it is possible that the economy will move over time with increasing capital accumulation and wage share until it reaches full capacity utilisation. The second long-run equilibrium solution, which is usually stable, is obtained when the economy is operating at full capacity utilisation. By incorporating technological change into the model through the ‘learning-by-doing’ hypothesis, his model allows for oscillations around the long-run equilibrium, with the economy alternating between periods of full and excess capacity. Lima (2004) extends Dutt\'s (1994) model by defining technological innovation as a non-linear function of distributive shares (wages and profits), with the latter determining both the incentive to innovate and the availability of funding needed to undertake it. Such an extension allows for the existence of a stable solution in an economy with excess capacity.