The Ramsey Model On Economic Growth And

1. Production Possibilities in Ramsey’s Formulation

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 repre- sentations 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 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.

Assumptions

Cor- respondence: C. The emergence of a new economic geography is indeed one of the major events in the economic literature of the last decade see Krugman, andFujita, Krugman and Venables,and Fujita and Thisse, Departing from the early regional science contributions, which are typically based on simple flow equations see Beckman,or more recently, Ten Raa,and Puu,the new economic geography models use general equilibrium frameworks with a refined specification of local and global market structures, and some precise assumptions on the mobility of production factors.

Their usefulness in explaining the mechanics of agglomeration, the formation of cities, the determinants and implications of migrations, and more generally, the dynamics of the distributions of people and goods over space and time is undeniable, so undeniable that this discipline has become increasingly popular in the recent years.

Two main characteristics of the new economic geography contributions quoted just above are: i the discrete space structure, and ii the absence of capital accumulation. Typ- ically, economic geographers use two-regions frameworks, mostly analogous to the two- country models usually invoked in The Ramsey Model On Economic Growth And theory. However, some continuous space exten- sions of these models have been already studied.

2. The Classical-Utilitarian Calculus

In a continuous space extension of his two-region model, Krugman shows that the economy always displays regional convergence, in contrast to the two-region version in which convergence and divergence are both possible. Mossay proves that continuous space is not incompatible with regional divergence using a different migration scheme. Click here Mossay, mi- grations additionally depend on idiosyncrasies in location taste, inducing a divergence force, which can balance the utility gradient force mentioned before.

As a consequence, regional divergence is a possible outcome in this model. Both models, however, ignore the role of capital accumulation in migrations: They both assume zero individual saving at any moment.

Indeed, the zero saving assumption is a common characteristic The Ramsey Model On Economic Growth And the new economic geography literature, especially in continuous space settings, with continue reading notable exception of Brito This strong assumption is done https://modernalternativemama.com/wp-content/custom/essay-service/buy-essays-online.php to ease the resolution of the models, which are yet very complex with the addition of the space dimension.

Nonetheless, as capital accumulation is not allowed, the new economic geography mod- els are losing a relevant determinant of migrations, and more importantly, an engine of growth. While a large part of growth theory is essentially based on capital accumulation, the new economic geography has mainly omitted this fundamental dimension so far.

It seems however clear that many economic geography problems eg. Thus, there is an urgent need to unify in some way the two disciplines, or at least to develop some junction models. This paper follows exactly this line of research. We study the Ramsey model with space.

Space is continuous and infinite, and optimal consumption and capital accumulation are space dependent. This is done in order to prevent the divergence of the objective integral function over an infinite space.

Convergence Dynamic

In this paper we will work in https://modernalternativemama.com/wp-content/custom/personal-statement/redneck-recording-process.php classical Benthamian case. We can do so by accounting for population density, which introduces a kind of spatial discounting therefore forcing the convergence of the objective integral function even under an infinite space configuration. Capital is perfectly mobile across space and of course, across time through intertemporal substitution, as usual in a Ramsey-like model.

Capital flows from the regions with low return to capital to the regions with high return.]

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Must-Read: Robert Solow: On the Irrelevance of the Ramsey Model July 10, Must-Read: Given the extraordinary number of potentially macro economically significant market failures for which there is evidence—both casual-observational and statistical—why would anyone ever have imagined that taking the representative-agent Ramsey model and adding one or two, or three frictions would not produce a degenerate research program? This diversity only intensifies my uncomfortable feeling that something is being put over on us, by ourselves. Why do so many of those research papers begin with a bow to the Ramsey model and cling to the basic outline? Quite the contrary: a story loses legitimacy and credibility when it is spliced to a simple, extreme, and on the face of it, irrelevant special case…. It could… be true that the bow to the Ramsey model is… a harmless way of providing some apparent intellectual unity…. That seems hardly worthy of grown-ups, especially because there is always a danger that some of the in-group come to believe the slogans, and it distorts their work….

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