An exactly solvable inflationary model

We discuss a model of gravity coupled to a scalar field that admits exact cosmological solutions displaying an inflationary behavior at early times and a power-law expansion at late times.Comment: 7 pages; several typos correcte

Collateral constraints and the amplification-persistence trade-off

Kiyotaki and Moore (1997) have stressed that an amplification-persistence trade-off arises when collateral constraints on borrowing interact with lumpy investment. In this paper, I confirm by way of example that collateral constraints are not by themselves responsible for such a deceptive trade-off. More precisely, I show in a standard general-equilibrium two-agent model that the amplification and persistence of the impact of temporary shocks go hand in hand. Unlike Kiyotaki-Moore's, the economy features concave utility and production functions, an endogenous interest rate and neo-classical input accumulationcollateral constraints; amplification and persistence of aggregate shocks

Laffer traps and monetary policy

This article focuses on the interaction, in a stylized economy with flexible prices, of monetary and fiscal policy when both are active-active in the sense that how the policy instrument is set depends on the state of the economy. Fiscal policy finances a given stream of government expenditures through distortionary labor taxes, and it operates under a strict balanced-budget rule. If monetary policy is passive, the economy may occasionally switch, because of self-fulfilling expectations, from the neighborhood of a "Laffer trap" equilibrium to the saddle-path leading to the high-welfare steady state. In the low-welfare stationary state, output, investment, and consumption are low while the tax rate is correspondingly high. However, active monetary policy may, by following a rule such that the nominal interest rate responds positively to the state of the economy, push the economy toward the high-welfare equilibrium and rule out expectation-driven business cycles.Monetary policy ; Fiscal policy

Endogenous Business Cycles and Dynamic Inefficiency

This paper explores how the occurrence of local indeterminacy and endogenous business cycles relates to dynamic inefficiency, as defined by Malinvaud (1953), Phelps (1965) and Cass (1972). We follow Reichlin (1986) and Grandmont (1993) by considering a two-period OLG model of capital accumulation with labor-leisure choice into the first-period of agents’ life and consumption in both periods. We first show that local indeterminacy and Hopf bifurcation are necessarily associated with a capital-labor ratio that is, at steady state, larger than the Golden Rule level. Consequently, paths converging asymptotically towards the steady state are shown to be dynamically inefficient, as there always exists another trajectory that starts with the same initial conditions and produces more aggregate consumption at all future dates. More surprising, however, is our main result showing that stable orbits, generated around a dynamically inefficient steady state through a supercritical Hopf bifurcation, may, in contrast, be dynamically efficient.Overlapping generations, endogenous labor supply, multiple equilibria, endogenous fluctuations, dynamic inefficiency

On the lifespan of classical solutions to a non-local porous medium problem with nonlinear boundary conditions

In this paper we analyze the porous medium equation \begin{equation}\label{ProblemAbstract} \tag{$\Diamond$} %\begin{cases} u_t=\Delta u^m + a\io u^p-b u^q -c\lvert\nabla\sqrt{u}\rvert^2 \quad \textrm{in}\quad \Omega \times I,%\\ %u_\nu-g(u)=0 & \textrm{on}\; \partial \Omega, t>0,\\ %u({\bf x},0)=u_0({\bf x})&{\bf x} \in \Omega,\\ %\end{cases} \end{equation} where $\Omega$ is a bounded and smooth domain of $\R^N$, with $N\geq 1$, and $I= [0,t^*)$ is the maximal interval of existence for $u$. The constants $a,b,c$ are positive, $m,p,q$ proper real numbers larger than 1 and the equation is complemented with nonlinear boundary conditions involving the outward normal derivative of $u$. Under some hypothesis on the data, including intrinsic relations between $m,p$ and $q$, and assuming that for some positive and sufficiently regular function u_0(\nx) the Initial Boundary Value Problem (IBVP) associated to \eqref{ProblemAbstract} possesses a positive classical solution u=u(\nx,t) on $\Omega \times I$: \begin{itemize} \item [$\triangleright$] when $p>q$ and in 2- and 3-dimensional domains, we determine a \textit{lower bound of} $t^*$ for those $u$ becoming unbounded in $L^{m(p-1)}(\Omega)$ at such $t^*$; \item [$\triangleright$] when $p<q$ and in $N$-dimensional settings, we establish a \textit{global existence criterion} for $u$. \end{itemize

Resuscitating the credit cycle

This paper resuscitates the credit-cycle theory of Kiyotaki and Moore (1997) in a two-agent RBC model with conventional preferences and standard neoclassical technologies. It is shown that small transitory shocks to credit demand (or supply) can generate large, highly persistent, dampened cycles in aggregate output. Key to our results is the interaction between credit constraints and habit formation. Credit constraints based on collateralized assets mainly amplify the impact of shocks while habit formation in consumption demand mainly propagates it. Hump-shaped boom-bust cycles do not arise in the model under standard parameter values if either one of the two elements is missing.Credit

Modeling of strain-induced Pockels effect in Silicon

We propose a theoretical model to describe the strain-induced linear electro-optic (Pockels) effect in centro-symmetric crystals. The general formulation is presented and the specific case of the strained silicon is investigated in detail because of its attractive properties for integrated optics. The outcome of this analysis is a linear relation between the second order susceptibility tensor and the strain gradient tensor, depending generically on fifteen coefficients. The proposed model greatly simplifies the description of the electro-optic effect in strained silicon waveguides, providing a powerful and effective tool for design and optimization of optical devices.Comment: typos corrected in eq. 29 with respect to the published versio

Leveraged borrowing and boom-bust cycles

Investment booms and asset "bubbles" are often the consequence of heavily leveraged borrowing and speculations of persistent growth in asset demand. We show theoretically that dynamic interactions between leveraged borrowing and persistent asset demand can generate a multiplier-accelerator mechanism that transforms a one-time technological innovation into large and long-lasting boom-bust cycles. The predictions are consistent with the basic features of investment booms and the consequent asset-market crashes led by excessive credit expansion.Asset pricing ; Credit

Is History a Blessing or a Curse? International Borrowing without Commitment, Leapfrogging and Growth Reversals

We develop a simple open-economy AK model with collateral constraints that accounts for growth-reversal episodes, during which countries face abrupt changes in their growth rate that lead to either growth miracles or growth disasters. Absent commitment to investment by the borrowing country, imperfect contract enforcement leads to an informational lag such that the debt contracted upon today depends upon the past stock of capital. The no-commitment delay originates a history effect by which the richer a country has been in the past, the more it can borrow today. For (arbitrarily) small deviations from perfect contract enforcement, the history effect offsets the growth benefits from international borrowing and dampens growth, and it leads to leapfrogging in long-run levels. When large enough, the history effect originates growth reversals and we connect the latter to leapfrogging. Finally, we argue that the model accords with the reported evidence on growth disasters and growth accelerations. We also provide examples showing that leapfrogging and growth reversals may coexist, so that currently poor but fast-growing countries experiencing sharp growth reversals may end up, in the long-run, significantly richer than currently rich but declining countries.Growth Reversals; Leapfrogging; International Borrowing; Open Economies