On the dynamics of capital accumulation across space

We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations with the corresponding boundary conditions. Then, we study the roles of initial capital and technology distributions over space in various scenarios.economics, economic geography, parabolic differential equations, optimal control

Age-structured Human Capital and Spatial Total Factor Productivity Dynamics

This paper models total factor productivity (TFP) in space and proposes an empirical model for TFP interdependence across spatial locations. The interdependence is assumed to occur due to age-structured human capital dynamics. A semi-parametric spatial vector autoregressive framework is suggested for modeling spatial TFP dynamics where the role of demographic state and technological change are explicitly incorporated in the model to influence their spatial TFP co-movements. Empirical scrutiny in case of Asian countries suggests that cross-country human capital differences in their accumulation and appropriation pattern significantly influenced TFP volatility interdependence. The finding of complementarity in TFP in spatial locations calls for joint policy program for improving aggregate and individual country welfare.Total factor productivity, Spatial growth, Non-linearity, Human capital, Age-structure, Semi-parametric VAR

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.

Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model

We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature to derive the Pontryagin conditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic system gives rise to an ill-posed problem in the sense of Hadamard (1923). We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly different from those of the non-spatial linear Ramsey model due to the spatial dynamics induced by capital mobility.Ramsey model, Economic geography, parabolic equations, optimal control

Marxism

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