The Dynamics of Growth and Distribution in a Spatially Heterogeneous World

This paper tries to reconcile growth and geographical economics by dealing directly with capital accumulation through time and space and by seeing growth convergence and spatial agglomeration as jointly generated by dynamic processes displaying pattern formation. It presents a centralized economy in which a Bergson-Samuelson- Millian central planner finds a flow of optimal distributions of consumption, subject to a spatial-temporal capital accumulation budget constraint. The main conclusions are: first, if the behavioral parameters are symmetric, but there is an asymmetric distribution of the capital stock, then the long run asymptotic distribution will be spatially homogeneous; second, if there is homogeneous distribution of the capital stock, but there is an asymmetric shock in any parameter, then the economy will converge towards a spatially heterogeneous asymptotic state; third, spatially heterogeneous asymptotic states will only emerge exogenously, not endogenously; fourth, the spatial propagation mechanism can give birth, when the production function is close to linear, to a Turing instability, which implies that for some parameter values, a conditionally stable spacetime distribution should display spatial pattern formation.Optimal growth and distribution; Spatial growth; Optimal control of partial differential equations; Traveling waves; Fourier transforms; Turing instability.

Using data visualization to deduce faces expressions

Conferência Internacional, realizada na Turquia, de 6-8 de setembro de 2018.Collect and examine in real time multi modal sensor data of a human face, is an important problem in computer vision, with applications in medical and monitoring analysis, entertainment and security. Although its advances, there are still many open issues in terms of the identification of the facial expression. Different algorithms and approaches have been developed to find out patterns and characteristics that can help the automatic expression identification. One way to study data is through data visualizations. Data visualization turns numbers and letters into aesthetically pleasing visuals, making it easy to recognize patterns and find exceptions. In this article, we use information visualization as a tool to analyse data points and find out possible existing patterns in four different facial expressions.info:eu-repo/semantics/publishedVersio

Equilibrium asset prices and bubbles in a continuous time OLG model

In a Yaari-Blanchard overlapping generations endowment economy, and drawing on the equivalence between Radner (R) and Arrow-Debreu (AD) equi- libria, we prove that equilibrium AD prices have an explicit representation as a double integral equation. This allows for an analytic characterization of the relationship between life-cycle and cohort heterogeneity and asset prices. For a simple distribution, we prove that bubbles may exist, and derive conditions for ruling them out.overlapping generations, asset pricing, bubbles, integral equations, LambertW function

Non-Smooth Dynamics and Multiple Equilibria in a Cournt-Ramsey Model with Endogenous Markups

We consider a Ramsey model with a continuum of Cournotian industries where free entry generates an endogenous markup. The model produces two different regimes, monopoly and oligopoly, resulting in non-smooth dynamics. We analyze the global dynamics of the model, demonstrating the model may exhibit heteroclinic orbits connecting multiple equilibria. Small transitory changes in parameters can lead to large permanent effects and there can be a Rostovian poverty trap separating a low-capital and high-markup equilibrium from a high-capital low-markup equilibrium. The paper applies recent results from applied mathematics for non-smooth dynamic systems.Endogenous markups; Non-smooth dynamics; Discontinuity induced bifurcations; Heteroclinic orbits.

Local and global indeterminacy in two-sector models of endogenous growth

In this paper we consider a two-sector endogenous growth model where the productions of the final good and human capital require economy-wide external effects. Assuming constant returns to scale at the private and social levels, we show that local and global indeterminacy of equilibrium paths are compatible with any values for the elasticity of intertemporal substitution in consumption and any sign for the capital intensity difference across the two sectors.Two-sector model, endogenous growth, economy-wide externalities, local and global indeterminacy

Adaptive collocation methods for the numerical solution of differential models

A PDE integration algorithm that associates a Method of Lines (MOL) strategy based on finite differences or high resolution space discretizations, with a collocation strategy based on increasing level one or two-dimensional dyadic grids is presented. It reveals potential either as a grid generation procedure for predefined steep localised functions, and as an integration scheme for moving steep gradient PDE problems, namely 1D and 2D Burgers equations. Therefore, it copes satisfactorily with an example characterized by a steep 2D travelling wave and an example characterised by a forming steep travelling shock, which confirms its flexibility in dealing with diverse types of problems, with reasonable demands of computational effort

Fiscal policy, entry and capital accumulation: Hump-shaped responses

In this paper we consider the entry and exit of firms in a Ramsey model with capital and an endogenous labour supply. At the firm level, there is a fixed cost combined with increasing marginal cost, which gives a standard U-shaped cost curve with optimal firm size. The costs of entry (exit) are quadratic in the flow of new firms. The number of firms becomes a second state variable and the entry dynamics gives rise to a richer set of dynamics than in the standard case: in particular, there is likely to be a hump shaped response of output to a fiscal shock with maximum impact after impact and before steady-state is reached. Output and capital per firm are also likely to be hump shaped

On Sustainable Endogenous Growth under Intertemporally Depedendent Preferences

In this paper we study an endogenous growth model with habit-formation and address two questions that are, to the best of our knowledge, new for the sustainable endogenous growth literature: first, does the process of habit-formation in relation to the consumption of manufactured goods influence the stock of environmental capital? Second, does habit-formation affect the long-term rate of economic growth? Using a simple structure of an endogenous growth models, we first show that there may be multiple equilibrium, not all stable. Second, we prove that the presence of habits in relation to the manufactured goods lowers the steady state level of environmental capital. However the effect on the endogenous growth rate depends on the intertemporal elasticity of consumption substitution. In particular, an increase in the strength of habits will result in a higher endogenous output growth rate if the substitution between intertemporal consumption is elastic. On the other hand, a change in preferences towards a cleaner environment increases the steady state level of natural capital. But the presence of habits reduces the effectiveness of any public policy that is meant to increase the social value of environment in utility

Business Cycles with Endogenous Mark-ups

Endogenous mark-ups have been a matter of interest in macroeconomics, especially from the middle 1990’s onwards. However, the complexity of this class of models, does not allow general ualitative conclusions in most cases, and there is plenty of room for investigation, especially in the reasons driving the emergence of multiple equilibria and non-saddle-point dynamics. In this article we extend a simple dynamic general equilibrium model to include the possibility of strategic interaction between producers in each industry, and entry affects the level of macroeconomic efficiency through an endogenous mark-up. We demonstrate multiple equilibria is a likely outcome even in an exogenous labour-supply framework. A pair of equilibria exists (a stable and an unstable one) and they are connected through a heteroclinic orbit. When we allow labour supply to vary, a third equilibrium may emerge if the government is present in the economy, and local indeterminacy may existEndogenous mark-ups, Multiple equilibria, Local dynamics