Quantifying Optimal Growth Policy

The optimal mix of growth policies is derived within a comprehensive endogenous growth model. The analysis captures important elements of the tax-transfer system and takes into account transitional dynamics. Currently, for calculating corporate taxable income US firms are allowed to deduct approximately all of their capital and R&D costs from sales revenue. Our analysis suggests that this policy leads to severe underinvestment in both R&D and physical capital. We find that firms should be allowed to deduct between 2-2.5 times their R&D costs and about 1.5-1.7 times their capital costs. Implementing the optimal policy mix is likely to entail huge welfare gains.economic growth, endogenous technical change, optimal growth policy, tax-transfer system, transitional dynamics

The macroeconomics of TANSTAAFL

This paper shows that dynamic inefficiency can occur in dynamic general equilibrium models with fully optimizing, infinitely-lived households even in a situation with underinvestment. We identify necessary conditions for such a possibility and illustrate it in a standard R&D-based growth model. Calibrating the model to the US, we show that a moderate increase in the R&D subsidy indeed leads to an intertemporal free lunch (i.e., an increase in per capita consumption at all times). Hence, Milton Friedman's conjecture There ain't no such thing as a free lunch (TANSTAAFL) may not apply. --intertemporal free lunch,dynamic inefficiency,R&D-based growth,transitional dynamics

Dynamically optimal R&D subsidization

Previous research on optimal R&D subsidies has focussed on the long run. This paper characterizes the optimal time path of R&D subsidization in a semi-endogenous growth model, by exploiting a recently developed numerical method. Starting from the steady state under current R&D subsidization in the US, the R&D subsidy should significantly jump upwards and then slightly decrease over time. There is a negligible loss in welfare, however, from immediately setting the R&D subsidy to its optimal long run level, compared to the case where the dynamically optimal policy is implemented. --R&D subsidy,transitional dynamics,semi-endogenous growth,welfare

Multi-dimensional transitional dynamics : a simple numerical procedure

We propose the relaxation algorithm as a simple and powerful method for simulating the transition process in growth models. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including multi-dimensional systems with stable eigenvalues that di.er drastically in magnitude. (2) The application of the procedure is fairly user friendly. The only input required consists of the dynamic system. (3) The variant of the relaxation algorithm we propose exploits in a natural manner the in.nite time horizon, which usually underlies optimal control problems in economics. Overall, it seems that the relaxation procedure can easily cope with a large number of problems which arise frequently in the context of macroeconomic dynamic models. As an illustrative application, we simulate the transition process of the well-known Jones (1995) model.saddlepoint problems, transitional dynamics, economic growth, multidimensional stable manifolds

Isotopenhydrologische Untersuchungen der Schneedecke am Pico de Teide (Teneriffa)

Meteorologische Messungen am Pico de Teide (Teneriffa) ergaben für die Hochlagen (> 2800 m ü. d. M.) ein Dampfdruckgefälle von der Schneedeckenoberfläche zur Atmosphäre. Damit sind Voraussetzungen für den Abbau der Schneedecke auch durch Verdunstung und Sublimation gegeben. Isotopenhydrologische Untersuchungen der Schneedecke bestätigen diese Energie- und Massenumsätze. 2H und 180 zeigen eine deutliche Anreicherung an der Oberfläche während des gesamten Meßzeitraumes. In tiefen Lagen um 2400 m ü. d. M. alternieren Verdunstung, Kondensation und Schmelze, da sowohl in der Nacht als auch am Tage Phasen mit einem niedrigeren Dampfdruck über der Schneedeckenoberfläche als in der Atmosphäre auftreten. Die Bedeutung von Schmelzvorgängen beim Abbau der Schneedecke steigt mit abnehmender Höhenlage. Mit dem Schmelzwasser kommt es zur Verlagerung schwerer Isotope zur Basis der Schneedecke. Der Abfluß aus der Schneedecke ist isotopisch schwerer als die verbleibende Schneerücklage, da mit dem Schmelzwasser bevorzugt schwere Isotope, die durch Verdunstungsvorgänge an der Schneedeckenoberfläche zunächst angereichert werden, transportiert werden. Der Abbau der Schneedecke erfolgt von der Oberfläche

Desiccation stress in two intertidal beachrock biofilms

© Springer-Verlag Berlin Heidelberg 2014. Chlorophyll a fluorescence was used to look at the effect of desiccation on the photophysiology in two beachrock microbial biofilms from the intertidal rock platform of Heron Island, Australia. The photophysiological response to desiccation differed between the beachrock microbial communities. The black biofilm from the upper shoreline, dominated by Calothrix sp., showed a response typical of desiccation-tolerant cyanobacteria, where photosynthesis closed down during air exposure with a rapid and complete recovery upon rehydration. In contrast, the pink biofilm from the mid-intertidal zone, dominated by Blennothrix sp., showed no distinct response to desiccation stress and instead maintained reduced photosynthesis throughout drying and re-wetting cycles. Spatial differences in photosynthetic activity within the black biofilm were evident with a faster recovery rate of photosynthesis in the surface cyanobacteria than in the deeper layers of the biofilm. There was no variation with depth in the pink biofilm. The photophysiological differences in desiccation responses between the beachrock biofilms exemplify the ecological niche specialisation of these complex microbial communities, where the functional differences help to explain their vertical distribution on the intertidal shoreline

Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.Comment: 11 pages, Revtex

Continuous limits of residual neural networks in case of large input data

Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean-field limit and show well-posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings