A dynamical model for real economy and finance

We have studied a discrete time dynamical model with four variables and delays, describing the interaction between a three-sector real economy and a financial market with four assets. Investors and financial intermediaries have heterogeneous beliefs. We show that complexity related to the evolution of state variables emerges and we investigate interdependence among economic fluctuations and assets volatility. By means of stability analysis we have found that real economy influences the existence of equilibrium prices in financial markets and that risky asset prices as well as capital per capita reach zero only when the elasticity of substitution between capital and labour is low enough. Bifurcation analysis shows that an increase of bond return would decrease the price of all the assets, conversely when the bond return decreases fluctuations and complex dynamics may arise. Due to the complexity of the model, computational tools are used to investigate long run dynamics, thus showing that for sufficiently high values of the interest rate bifurcations with repetitive structure emerge. In addition, we show how the total number of shares in each sector influences its price volatility. Finally, when fluctuations appear, economic policy intended to increase employment could stabilise the model only in sufficiently developed economies.