Gloria Jarne

Stability of vertically differentiated Cournot and Bertrand-type models when firms are boundedly rational

This paper compares the dynamic of Cournot and Bertrand duopolies with vertical product differentiation and under bounded rationality. We find that an increase in the product differentiation degree destabilizes the Nash equilibrium under quantity competition, while the Bertrand–Nash equilibrium becomes more stable. From a global dynamic analysis, we show that an increase in the firms’ adjustment speed constitutes a source of complexity in both models. There is a cascade of flip bifurcations leading to increasingly complex attractors, and there are global bifurcations generating complex basins of attraction.

Nonlinear Cournot and Bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations

In a differentiated triopoly model with heterogeneous firms, the local stability of the Nash equilibrium under both quantity and price competition is analyzed. We find that the presence of a firm following a gradient rule based on marginal profits, and a player with adaptive expectations, determines the local stability of the Nash equilibrium, regardless the competition type, while the effects of the degree of product differentiation on the stability depend on the nature of products. Moreover, the Nash equilibrium is more stable under quantity competition than under price competition.

On the dynamics of economic games based on product differentiation

Defining a micro-economics-based demand structure of differentiated products, we analyse the conditions for stability of the Cournot-Nash and the Bertrand-Nash equilibria. We find that, in the presence of both complements and substitute goods, the stability of the Nash equilibrium increases when goods tend to be independent. Moreover, the Nash equilibrium is also more stable under quantity competition than under price competition, regardless of whether goods are complements or substitutes.

ENDOGENOUS CYCLICAL GROWTH WITH A SIGMOIDAL DIFFUSION OF INNOVATIONS

The model we propose in this paper is an extension of the one described in Freeman et al. [Freeman, S., Hong, D. and Peled, D. (1999) Endogenous Cycles and Growth with Indivisible Technological Developments. Review of Economics Dynamics, 2, 403–432]. In our model, we incorporate the process of diffusion of major innovations and analyze macroeconomic effects on consumption, capital and aggregate output. Following Bresnahan and Trajtenberg [Bresnahan, T. and Trajtenberg, M. (1995) General Purpose Technologies: Engines of Growth?. Journal of Econometrics, 65, 83–108.], Helpman [Helpman, E. (ed.) (1998) General Purpose Technologies and Economic Growth. MIT Press] and Lipsey et al. [Lipsey, R.G., Carlaw, K. and Bekar, C. (2005) Economic Transformations: General Purpose Technologies and Long Term Economic Growth. Oxford University Press.] we assimilate major innovations with the emergence of certain GPTs, and we suggest that the diffusion process for these technologies, at a large scale, might follow an S-shaped pattern. The proposed model presents optimum stationary solutions which are cyclical and have a wave dynamic within each cycle. The cycles are characterized by certain co-movements in consumption, R&D investment, capital accumulation and output. Consideration of the innovation diffusion process highlights new aspects of endogenous cycles and long-run growth.

An Evolutionary Growth Model with Banking Activity

In this paper, we propose an evolutionary growth model in which an innovative production sector interacts with a simplified banking sector. We explore the relationships between long-term sources of growth (technological change), and short-term/mid-term factors (such as price dynamics and interest rates). The model suggests new explanations for the endogenous emergence of sharp crises with profound effects in the long run. An interesting aspect of the model is that these crises appear in a strictly private economy, in which everything produced is sold, there are no government distortions, and there are no exogenous shocks. The crises emerge from the interactions between uneven innovation rates and market reactivity. In fact, high reactivity in financial markets can amplify the (initially small) effects of innovative competition, leading to a destabilization of economic growth. Drawing on the model results we suggest some policy implications.

Rethinking Macroeconomic Policy within a Simple Dynamic Model: Simple Dynamic Model to Rethink Standard Policy

We propose a simple macro‐dynamic model to rethink standard policy prescriptions. Our model includes exogenous growth, endogenous capital accumulation and debt, demand‐driven production with a non‐linear IS curve, a dynamic Phillips curve, and fiscal and monetary policy instruments. It has multiple steady states with different stability properties, and it is analytically tractable to a significant extent. We complete the analytical results with simulations. We find alternative growth patterns, endogenous fluctuations, and demand‐driven level effects even in the long‐run. For certain steady states the model shows saddle‐path type instabilities, which lead us to reflect on fiscal and monetary policy standards.

Rethinking Macroeconomic Policy within a Simple Dynamic Model

We propose a simple macrodynamic model to rethink some standard policy prescriptions. Our model includes exogenous growth, endogenous investment, demand-driven production and employment, a dynamic Phillips curve, and fiscal and monetary policy instruments. The model has multiple steady states with different stability properties, and it is analytically tractable to a significant extent. Given the nonlinear nature of the model, we complete the analytical results with simulations. The model generates different growth patterns, endogenous fluctuations, and demand-driven level effects even in the long-run. It also reveals saddle-path type instabilities in which seemingly stable paths suddenly give way to increasing volatility. These results lead us to reflect on fiscal and monetary policy standards, and suggest new interpretations for the “Great Recession”.