arXiv subjects

Kensuke Ohtake

Publications and source records attributed to Kensuke Ohtake.

8 recordsLinked to original sources

arXiv2025

Unique global solution of an integral-differential equation of Footloose Entrepreneur model in new economic geography

This paper studies the Footloose Entrepreneur model in new economic geography in continuous space. In an appropriate function space, the model is formulated as an initial value problem for an infinite-dimensional ordinary differential equation. A unique global solution is constructed based on the Banach fixed point theorem. The stability of a homogeneous stationary solution is then investigated and numerical simulations of the asymptotic behavior of the solution are performed. Numerical solutions starting near the unstable homogeneous stationary solution converge to spike-shaped stationary solutions, and the number of spikes decreases with decreasing transport costs and strengthening preference for variety.

econ.TH↗

arXiv2024

Pattern formation by advection-diffusion in new economic geography

This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility function and an advection-diffusion equation that expresses population migration. It is found that diffusion stabilizes a homogeneous stationary solution when transport costs are sufficiently low, and it also inhibits the monotonic facilitation of agglomeration caused by lower transport costs in some cases. When the homogeneous stationary solution is unstable, numerical simulations show spatial patterns with multiple urban areas. Insights into the relation between agglomeration and control parameters (transport costs and preference for variety of consumers) gained from the large-time behavior of solutions confirm the validity of the analysis of linearized equations.

econ.TH↗

arXiv2023

City formation by dual migration of firms and workers

The Core-Periphery model in the new economic geography, which considers the single migration of workers driven by real wage inequality among regions, is extended to incorporate the migration of firms driven by real profit inequality among regions. In this dual-migration model, the behavior of solutions is qualitatively similar to that of single-migration models. That is, 1) spatially homogeneous population distributions become destabilized and eventually form several cities where both firms and workers agglomerate; 2) the number of cities decreases as transport costs decrease. These results provide a more general theoretical justification for the use of single migration models.

econ.TH↗

arXiv2023

A micro-founded comparison of fiscal policies between indirect and direct job creation

The purpose of this paper is to provide a micro-economic foundation for an argument that the direct employment by the government is more desirable than the government purchase of private goods to eliminate unemployment. A general equilibrium model with monopolistic competition is devised, and the effects of policies (government purchase, tax rate operation, and government employment) on macroeconomic variables (consumption, price, and profit) are investigated. It is shown that 1) the government purchase is inflationary in the sense that additional effective demand by the government not only increases private employment but also raises prices; 2) the government employment can achieve full employment without causing a rise in prices.

econ.TH↗

arXiv2022

Agglomeration and welfare of the Krugman model in a continuous space

Two spatial equilibria, agglomeration and dispersion, in a continuous space core-periphery model are examined to discuss which equilibrium is socially preferred. It is shown that when transport cost is lower than a critical value, the agglomeration equilibrium is preferable in the sense of Scitovszky, while when the transport cost is above the critical value, the two equilibria can not be ordered in the sense of Scitovszky.

econ.TH↗

arXiv2022

Continuous space core-periphery model with transport costs in differentiated agriculture

The core-periphery model with transport costs in differentiated agriculture is extended to continuous space. A homogeneous stationary solution is unstable but exhibits redispersion that it is stabilized by sufficiently low manufacturing transport costs or sufficiently strong preference for manufacturing variety. It is numerically observed that a solution starting from around the unstable homogeneous solution eventually forms a spike-like agglomeration. Furthermore, the redispersion also appears in the sense that the number of the spikes goes from decreasing to increasing as the manufacturing transport costs decrease. It is also observed that lower agricultural transport costs and stronger preference for agricultural variety promote agglomeration.

econ.TH↗

arXiv2021

Agglomeration triggered by the effect of the number of regions: A model in NEG with a quadratic subutility

We extend the mathematical model proposed by Ottaviano-Tabuchi-Thisse (2002) to a multi-regional case and investigate the stability of the homogeneous stationary solution of the model in a one-dimensional periodic space. When the number of regions is two and three, the homogeneous stationary solution is stable under sufficiently high transport cost. On the other hand, when the number of regions is a multiple of four, the homogeneous stationary solution is unstable under any values of the transport cost.

econ.TH↗

arXiv2021

A continuous space model of new economic geography with a quasi-linear log utility function

We consider the extension of a tractable NEG model with a quasi-linear log utility to continuous space, and investigate the behavior of its solution mathematically. The model is a system of nonlinear integral and differential equations describing the market equilibrium and the time evolution of the spatial distribution of population density. A unique global solution is constructed and a homogeneous stationary solution with evenly distributed population is shown to be unstable. Furthermore, it is shown numerically that the destabilized homogeneous stationary solution eventually forms spiky spatial distributions. The number of the spikes decreases as the preference for variety increases or the transport cost decreases.

econ.TH↗