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.

"Credit Market Imperfections and Patterns of International Trade and Capital Flows"

In a world where credit relationships are subject to a variety of agency problems, corporate governance, contractual enforcement, and the balance sheet condition of the business sector are among many factors that can play an important role in the allocation of resources. This paper offers two simple models to illustrate how these factors can affect the patterns of international trade and capital flows in the presence of credit market imperfections.

"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.

"Financial Market Globalization, Symmetry-Breaking, and Endogenous Inequality of Nations"

This paper investigates the effects of financial market globalization on the inequality of nations. The world economy consists of inherently identical countries, which could differ only in their levels of capital stock. Each country is represented by the standard overlapping generations model, modified only to incorporate credit market imperfection. An integration of financial markets affects the set of stable steady states, as it changes the balance between the equalizing force of the diminishing returns technology and the unequalizing force of the wealth-dependent borrowing constraint. The model is simple and tractable enough to allow for a complete characterization of the stable steady states. In the absence of the international financial market, the world economy has a unique stable steady state, which is symmetric. When the international financial market is introduced, symmetry-breaking occurs under some conditions. That is to say, the symmetric steady state loses its stability and stable asymmetric steady states come to exist. In the stable asymmetric steady states, the world economy is endogenously divided into the rich and poor countries; the borrowing constraints are binding in the poor countries but not in the rich countries; the world output is smaller, the rich are richer and the poor are poorer in any of the stable asymmetric steady states than in the (unstable) symmetric steady state.

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