scholarly journals Dynamic Free Riding with Irreversible Investments

2014 ◽  
Vol 104 (9) ◽  
pp. 2858-2871 ◽  
Author(s):  
Marco Battaglini ◽  
Salvatore Nunnari ◽  
Thomas R. Palfrey
Keyword(s):  
Steady State ◽  
Public Good ◽  
Private Consumption ◽  
Free Riding ◽  
Steady States ◽  
Discount Factor ◽  
Unique Point ◽  
Efficient Level ◽  
Markov Equilibria ◽  
Irreversible Investments

We study the Markov equilibria of a model of free riding in which n infinitely lived agents choose between private consumption and irreversible contributions to a durable public good. We show that the set of equilibrium steady states converges to a unique point as depreciation converges to zero. For any level of depreciation, moreover, the highest steady state converges to the efficient level as agents become increasingly patient. These results are in contrast to the case with reversible investments, where a continuum of inefficient equilibrium steady states exists for any level of depreciation, discount factor, and size of population. (JEL D11, H41)

POVERTY TRAPS AND INFERIOR GOODS IN A DYNAMIC HECKSCHER–OHLIN MODEL

2012 ◽  
Vol 17 (6) ◽  
pp. 1227-1251 ◽  
Author(s):  
Eric W. Bond ◽  
Kazumichi Iwasa ◽  
Kazuo Nishimura
Keyword(s):  
Economic Theory ◽  
Steady State ◽  
World Economy ◽  
Steady States ◽  
The Other ◽  
Poverty Traps ◽  
Poverty Trap ◽  
Multiple Steady States ◽  
The World ◽  
State Capital

We extend the dynamic Heckscher–Ohlin model in Bond et al. [Economic Theory(48, 171–204, 2011)] and show that if the labor-intensive good is inferior, then there may exist multiple steady states in autarky and poverty traps can arise. Poverty traps for the world economy, in the form of Pareto-dominated steady states, are also shown to exist. We show that the opening of trade can have the effect of pulling the initially poorer country out of a poverty trap, with both countries having steady state capital stocks exceeding the autarky level. However, trade can also pull an initially richer country into a poverty trap. These possibilities are a sharp contrast with dynamic Heckscher–Ohlin models with normality in consumption, where the country with the larger (smaller) capital stock than the other will reach a steady state where the level of welfare is higher (lower) than in the autarkic steady state.

scholarly journals Zero Eigenvalue Analysis for the Determination of Multiple Steady States in Reaction Networks

1998 ◽  
Vol 53 (3-4) ◽  
pp. 171-177
Author(s):  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Reaction Network ◽  
Steady States ◽  
Eigenvalue Analysis ◽  
Zero Eigenvalue ◽  
Positive Steady State ◽  
Positive Steady States ◽  
Positive Rate ◽  
System Of Inequalities

Abstract A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of inequalities and equations. If a set of solutions for the system is found, then the network under study is able to admit multiple positive steady states for some positive rate constants. Otherwise, the network can exhibit at most one steady state, no matter what positive rate constants the system might have. The construction of a zero-eigenvalue positive steady state and a set of positive rate constants is also presented. The analysis is demonstrated by two examples.

scholarly journals El monopolio de las ideas: Contra la Propiedad Intelectual

2021 ◽  
pp. 47-104
Author(s):  
Albert Esplugas
Keyword(s):  
Intellectual Property ◽  
Public Good ◽  
Key Words ◽  
Market Economy ◽  
Private Property ◽  
Free Riding ◽  
Point Of View ◽  
Private Property Rights ◽  
Original Meaning ◽  
Palabras Clave

This paper presents a critique of intellectual property from an ethical and economical point of view. Once patents and copyrights are characterized as a monopolies of ideas, it is argued that intellectual pro-perty violates private property rights in its original meaning and it is not based in real scarcity but creates artificial scarcity instead. In addition, the paper challenges intellectual property as an incentive to innovation and studies the several costs of this kind of regulation. Eventually, diffe-rent market alternatives to tackle the free-riding problem are explored. Key words: intelectual property, patents, copyrights, private property, scar-city, public good, innovation incentives, market economy. Clasificación JEL: O310, O320, O340, H410. Resumen: En este trabajo se presenta una crítica a la propiedad intelec-tual desde una perspectiva ética y económica. Tras caracterizar las paten-tes y los copyrights como monopolios sobre ideas, se arguye que la pro-piedad intelectual viola el derecho de propiedad privada en su sentido tradicional y crea una escasez artificial en lugar de fundarse sobre la esca-sez. Se cuestiona, asimismo, que la propiedad intelectual suponga un incen-tivo a la creación, estudiando los distintos costes de una regulación de este tipo. Por último se mencionan varias alternativas de mercado para hacer frente a los problemas de free-riding. Palabras clave: propiedad intelectual, patentes, copyrights, propiedad privada, escasez, bien público, incentivos a la innovación, mercado.

scholarly journals Thermal Robustness of Entanglement in a Dissipative Two-Dimensional Spin System in an Inhomogeneous Magnetic Field

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1066
Author(s):  
Gehad Sadiek ◽  
Samaher Almalki
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Nearest Neighbor ◽  
Quantum Phase Transitions ◽  
Inhomogeneous Magnetic Field ◽  
Steady States ◽  
Inhomogeneous Field ◽  
Spin States ◽  
Two Dimensional ◽  
Spin Lattice

Recently new novel magnetic phases were shown to exist in the asymptotic steady states of spin systems coupled to dissipative environments at zero temperature. Tuning the different system parameters led to quantum phase transitions among those states. We study, here, a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian Lindblad environment at finite temperature. We show how applying an inhomogeneous magnetic field to the system at different degrees of anisotropy may significantly affect the spin states, and the entanglement properties and distribution among the spins in the asymptotic steady state of the system. In particular, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness against the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas the beyond nearest neighbor ones vanish entirely. The spins of the system in this case reach different steady states depending on their positions in the lattice. However, the inhomogeneity of the field shows no effect on the entanglement in the completely isotropic (XXX) system, which vanishes asymptotically under any system configuration and the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state. Interestingly, applying the same field to a partially anisotropic (XYZ) system does not just enhance the nearest neighbor entanglements and their thermal robustness but all the long-range ones as well, while the spins relax asymptotically to very distinguished spin states, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.

scholarly journals The unraveling of balanced complexes in metabolic networks

2021 ◽  
Author(s):  
Damoun Langary ◽  
Anika Kueken ◽  
Zoran Nikoloski
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Metabolic Networks ◽  
Network Models ◽  
Steady States ◽  
Biochemical Networks ◽  
Computational Approaches ◽  
Metabolic Models ◽  
Large Scale Networks ◽  
General Conditions

Balanced complexes in biochemical networks are at core of several theoretical and computational approaches that make statements about the properties of the steady states supported by the network. Recent computational approaches have employed balanced complexes to reduce metabolic networks, while ensuring preservation of particular steady-state properties; however, the underlying factors leading to the formation of balanced complexes have not been studied, yet. Here, we present a number of factorizations providing insights in mechanisms that lead to the origins of the corresponding balanced complexes. The proposed factorizations enable us to categorize balanced complexes into four distinct classes, each with specific origins and characteristics. They also provide the means to efficiently determine if a balanced complex in large-scale networks belongs to a particular class from the categorization. The results are obtained under very general conditions and irrespective of the network kinetics, rendering them broadly applicable across variety of network models. Application of the categorization shows that all classes of balanced complexes are present in large-scale metabolic models across all kingdoms of life, therefore paving the way to study their relevance with respect to different properties of steady states supported by these networks.

scholarly journals Pattern Formation in Keller–Segel Chemotaxis Models with Logistic Growth

2016 ◽  
Vol 26 (02) ◽  
pp. 1650033 ◽  
Author(s):  
Ling Jin ◽  
Qi Wang ◽  
Zengyan Zhang
Keyword(s):  
Steady State ◽  
Pattern Formation ◽  
Neumann Boundary ◽  
Steady States ◽  
Local Theory ◽  
Logistic Growth ◽  
Homogeneous Steady State ◽  
Cellular Aggregation ◽  
Chemotaxis Models ◽  
Steady State Stability

In this paper, we investigate pattern formation in Keller–Segel chemotaxis models over a multidimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as chemoattraction rate [Formula: see text] increases. Then using Crandall–Rabinowitz local theory with [Formula: see text] being the bifurcation parameter, we obtain the existence of nonhomogeneous steady states of the system which bifurcate from this homogeneous steady state. Stability of the bifurcating solutions is also established through rigorous and detailed calculations. Our results provide a selection mechanism of stable wavemode which states that the only stable bifurcation branch must have a wavemode number that minimizes the bifurcation value. Finally, we perform extensive numerical simulations on the formation of stable steady states with striking structures such as boundary spikes, interior spikes, stripes, etc. These nontrivial patterns can model cellular aggregation that develop through chemotactic movements in biological systems.

On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 4. Generalized isovorticity principle for three-dimensional flows

1999 ◽  
Vol 390 ◽  
pp. 127-150 ◽  
Author(s):  
V. A. VLADIMIROV ◽  
H. K. MOFFATT ◽  
K. I. ILIN
Keyword(s):  
Steady State ◽  
Variational Principles ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Steady States ◽  
Mhd Equations ◽  
Quadratic Functional ◽  
The First Variation ◽  
The Stability ◽  
And Variational Principles

The equations of magnetohydrodynamics (MHD) of an ideal fluid have two families of topological invariants: the magnetic helicity invariants and the cross-helicity invariants. It is first shown that these invariants define a natural foliation (described as isomagnetovortical, or imv for short) in the function space in which solutions {u(x, t), h(x, t)} of the MHD equations reside. A relaxation process is constructed whereby total energy (magnetic plus kinetic) decreases on an imv folium (all magnetic and cross-helicity invariants being thus conserved). The energy has a positive lower bound determined by the global cross-helicity, and it is thus shown that a steady state exists having the (arbitrarily) prescribed families of magnetic and cross-helicity invariants.The stability of such steady states is considered by an appropriate generalization of (Arnold) energy techniques. The first variation of energy on the imv folium is shown to vanish, and the second variation δ2E is constructed. It is shown that δ2E is a quadratic functional of the first-order variations δ1u, δ1h of u and h (from a steady state U(x), H(x)), and that δ2E is an invariant of the linearized MHD equations. Linear stability is then assured provided δ2E is either positive-definite or negative-definite for all imv perturbations. It is shown that the results may be equivalently obtained through consideration of the frozen-in ‘modified’ vorticity field introduced in Part 1 of this series.Finally, the general stability criterion is applied to a variety of classes of steady states {U(x), H(x)}, and new sufficient conditions for stability to three-dimensional imv perturbations are obtained.

Swirling flow states in finite-length diverging or contracting circular pipes

2017 ◽  
Vol 819 ◽  
pp. 678-712 ◽  
Author(s):  
Zvi Rusak ◽  
Yuxin Zhang ◽  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Finite Length ◽  
Vortex Breakdown ◽  
Steady States ◽  
Inviscid Limit ◽  
Circular Pipes ◽  
Outlet Flow ◽  
Separation Zones ◽  
Steady State Solutions

The dynamics of inviscid-limit, incompressible and axisymmetric swirling flows in finite-length, diverging or contracting, long circular pipes is studied through global analysis techniques and numerical simulations. The inlet flow is described by the profiles of the circumferential and axial velocity together with a fixed azimuthal vorticity while the outlet flow is characterized by a state with zero radial velocity. A mathematical model that is based on the Squire–Long equation (SLE) is formulated to identify steady-state solutions of the problem with special conditions to describe states with separation zones. The problem is then reduced to the columnar (axially-independent) SLE, with centreline and wall conditions for the solution of the outlet flow streamfunction. The solution of the columnar SLE problem gives rise to the existence of four types of solutions. The SLE problem is then solved numerically using a special procedure to capture states with vortex-breakdown or wall-separation zones. Numerical simulations based on the unsteady vorticity circulation equations are also conducted and show correlation between time-asymptotic states and steady states according to the SLE and the columnar SLE problems. The simulations also shed light on the stability of the various steady states. The uniqueness of steady-state solutions in a certain range of swirl is proven analytically and demonstrated numerically. The computed results provide the bifurcation diagrams of steady states in terms of the incoming swirl ratio and size of pipe divergence or contraction. Critical swirls for the first appearance of the various types of states are identified. The results show that pipe divergence promotes the appearance of vortex-breakdown states at lower levels of the incoming swirl while pipe contraction delays the appearance of vortex breakdown to higher levels of swirl and promotes the formation of wall-separation states.

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