A necessary and sufficient condition on scattering for the regularly hyperbolic systems

The present paper is devoted to finding a necessary and sufficient condition on the occurence of scattering for the regularly hyperbolic systems with time-dependent coefficients whose time-derivatives are integrable over the real line. More precisely, it will be shown that the solutions are asymptotically free if the coefficients are stable in the sense of the Riemann integrability as time goes to infinity, while each nontrivial solution is never asymptotically free provided that the coefficients are not R-stable as times goes to infinity. As a by-product, the scattering operator can be constructed. It is expected that the results obtained in the present paper would be brought into the study of the asymptotic behaviour of Kirchhoff systems.Comment: 16 page

Binding Energy of Scalar Bound State by Topologically Massive Interaction: Fermion and Anti-fermion System with Heavy Mass

A bound state problem in a topologically massive quantum electrodynamics is investigated by using a non-perturbative method. We formulate the Bethe- Salpeter equation for scalar bound states composed of massive fermion and anti-fermion pair under the lowest ladder approximation. In a large mass expansion for the (anti-) fermion, we derive the Schr{\"o}dinger equation and solve it by a numerical method. The energy eigenvalues of bound states are evaluated for various values of a topological mass and also a fermion mass. Then we find a novel logarithmic scaling behaviour of the binding energy in varying the topological mass, fermion mass and also a quantum number. There exists a critical value of the topological mass, beyond which the bound states disappear. As the topological mass decreases, the energy eigenvalues of the bound states, which are negative, also decrease with a logarithmic dependence on the topological mass. A Chern-Simons term gives the bound system a repulsive effect.Comment: 14 pages, 3 figures, references added; version accepted for publication in Phys. Lett.

Why Are There Rich and Poor Countries? Symmetry-Breaking in the World Economy

To explain cross-country differences in economic performance, the economics of coordination failures typically portrays each country in a closed economy model with multiple equilibria and then argues that the poor countries are in an equilibrium inferior to those achieved by the rich. This approach cannot tell us anything about the degree of inequality in the world economy. A more satisfactory approach would be to build a world economy model and show why it has to be separated into the rich and the poor regions, i.e., to demonstrate the co-existence of the rich and poor as an inevitable aspect of the world trading system. In the present model, the symmetry-breaking of the world economy into the rich and the poor occurs because international trade causes agglomeration of different economic activities in different regions of the world. International trade thus creates a kind of pecking order among nations, and as in a game of musical chairs, some countries must be excluded from being rich.

The Good, The Bad, and The Ugly: An Inquiry into the Causes and Nature of Credit Cycles

This paper builds models of nonlinear dynamics in the aggregate investment and borrower net worth and uses them to study the causes and nature of endogenous credit cycles. The basic model has two types of projects: the Good and the Bad. The Bad is highly productive, but, unlike the Good, it generates less aggregate demand spillovers and contributes little to improve borrower net worth. Furthermore, it is relatively difficult to finance externally due to the agency problem. With a low net worth, the agents cannot finance the Bad, and much of the credit goes to finance the Good, even when the Bad projects are more profitable than the Good projects. This over-investment to the Good creates a boom and generates high aggregate demand spillovers. This leads to an improvement in borrower net worth, which makes it possible for the agents to finance the Bad. This shift in the composition of the credit from the Good to the Bad at the peak of the boom causes a deterioration of net worth. The whole process repeats itself. Endogenous fluctuations occur, as the Good breeds the Bad, and the Bad destroys the Good. The model is then extended to add a third type of the projects, the Ugly, which are unproductive but easy to finance. With a low net worth, the Good competes with the Ugly, creating the credit multiplier effect; with a high net worth, the Good competes with the Bad, creating the credit reversal effect. By combining these two effects, this model generates intermittency phenomena, i.e., relatively long periods of small and persistent movements punctuated intermittently by seemingly random-looking behaviors. Along these cycles, the economy exhibits asymmetric fluctuations; it experiences a long and slow process of recovery from a recession, followed by a rapid expansion, and possibly after a period of high volatility, plunges into a recession.wealth-dependent borrowing constraints, heterogeneity of projects, aggregate demand spillovers, credit multiplier effect, credit reversal effect, endogenous credit cycles, nonlinear dynamics, chaos, flip and tangent bifurcations, homoclinic orbits, intermittency, asymmetric fluctuations

"A One-Sector Neoclassical Growth Model with Endogenous Retirement"

This paper extends Diamond's OG model by allowing the agents to make the retirement decision. Earning a higher wage income when young not only enables the agents to save more. It also induces more agents to retire early and gives an additional incentive to save more for retirement. This leads to a higher capitallabor ratio in the following period, and hence the next generation of agents earns a higher wage income when young. Due to this positive feedback mechanism, endogenous retirement magnifies the persistence of growth dynamics and even generates multiple steady states for empirically plausible parameter values.

"Beyond Icebergs: Modeling Globalization as Biased Technical Change"

We propose a new approach to model costly international trade, which includes the standard approach, the "iceberg" transport cost, as a special case. The key idea is to make the technologies of supplying the good depend on the destination of the good. To demonstrate our approach, we extend the Ricardian model with a continuum of goods, due to Dornbusch, Fischer and Samuelson (1977), by introducing multiple factors of production and by making each industry consist of the domestic division, which supplies the good at home, and the export division, which supplies the good abroad. If the two divisions differ only in the total factor productivity, our model becomes isomorphic to the DFS model with the iceberg transport cost. When the two divisions differ also in the factor intensity, globalization changes the relative factor prices in the same direction across the countries, in sharp contrast to the usual Stolper-Samuelson effect, which suggests that the relative factor prices move in different irections in different countries.

Beyond Icebergs: Modeling Globalization as Biased Technical Change

We propose a new approach to model costly international trade, which includes the standard approach, the “iceberg” transport cost, as a special case. The key idea is to make the technologies of supplying the good depend on the destination of the good. To demonstrate our approach, we extend the Ricardian model with a continuum of goods, due to Dornbusch, Fischer and Samuelson (1977), by introducing multiple factors of production and by making each industry consist of the domestic division, which supplies the good at home, and the export division, which supplies the good abroad. If the two divisions differ only in the total factor productivity, our model becomes isomorphic to the DFS model with the iceberg transport cost. When the two divisions differ also in the factor intensity, globalization changes the relative factor prices in the same direction across the countries, in sharp contrast to the usual Stolper-Samuelson effect, which suggests that the relative factor prices move in different directions in different countries.

Endogenous Ranking and Equilibrium Lorenz Curve Across (ex-ante) Identical Countries

This paper considers a model of the world economy with a finite number of ex-ante identical countries and a continuum of tradeable goods. Productivity differences across countries arise endogenously through free entry to the local differentiated producer service sector in each country. It is shown that, in any stable equilibrium, the countries sort themselves into specializing in different sets of tradeable goods and that a strict ranking of countries in income, TFP, and the capital-labor ratio emerge endogenously. The equilibrium Lorenz curve is characterized by a second-order nonlinear difference equation with the two terminal conditions. As the number of countries increases, this equation converges to a differential equation whose unique solution can be solved analytically and depends on a few parameters in a tractable manner. This enables us to show when the equilibrium distribution obeys a power-law and how various forms of globalization affect inequality among countries and to study the welfare effects of trade.Endogenous Comparative Advantage, Endogenous Inequality, Globalization and Inequality, Dornbusch-Fischer-Samuelson model, Dixit-Stiglitz model of monopolistic competition, Symmetry-Breaking, Lorenz-dominant shifts, Log-submodularity, Power-law distributions