Asymptotic Behavior of Traveling Wave Solutions to Reaction-Diffusion Equations

We will discuss travelling wave solutions to reaction-diffusion equations of the form: ut=uxx+ up (1-uq) which can be used as a mathematical model for various biological phenomena, as well as to model problems in combustion theory. We identify conditions on the wave speed so that travelling wave solutions exist for the case p ≥1 and q ≥1. Moreover, we estimate the rate of decay of the travelling wave solutions. When p \u3e 1 and q ≥1, this estimate requires center manifold theory because the typical linear methods fail to work. Through the mathematical analysis of reaction diffusion equations, the results of this research create further studies and application in physical and industrial chemistry

Dundee Discussion Papers in Economics 126:Efficiency wages, unemployment and macroeconomic policy

We provide empirical evidence from a number of European countries, which shows that unemployment and output are positively related when unemployment is low and inversely related when unemployment is high. We then construct a stylised macro-model with goods and labour market imperfections to show that the economy can rationally operate at an inefficient equilibrium in the neighbourhood of which the relationship between output and unemployment is positive. Our results suggest that circumstances exist in which market imperfections pose serious obstacles to the smooth working of expansionary and/or stabilization policies whose final aim is to improve welfare. KEYWORDS: Efficiency wages; effort supply; monopolistic competition; multiple equilibria; stability; fiscal multiplie

Measuring quality in social care services: theory and practice

Measuring and assessing service quality in the social care sector presents distinct challenges. The 'experience' good properties of social care, for instance, and the large influence played by subjective judgements about the quality of personal relationships between carer and user and of process-related service characteristics make it difficult to develop indicators of service quality, including those of service impact on final outcomes. Using some of the key features of the 'Production of Welfare' approach, the paper discusses recent developments in the UK of the theoretical and practical frameworks used for assessing quality in social care and for understanding the final impact of services on the wellbeing of their recipients. Key current and future challenges to the development of such frameworks include difficulties in disentangling the impact of social care services on final outcomes from the often dominating effects of other, non-service related factors, and the generalization of consumer-directed care models and of the 'personalization' of care services. These challenges are discussed in the context of the different possible applications of quality indicators, including their role as supporting the service commissioning process and their use for assessing the performance of service providers

Productivity shocks and aggregate fluctuations in an estimated endogenous growth model with human capital

Employing an endogenous growth model with human capital, this paper explores how productivity shocks in the goods and human capital producing sectors contribute to explaining aggregate fluctuations in output, consumption, investment and hours. Given the importance of accounting for both the dynamics and the trends in the data not captured by the theoretical growth model, we introduce a vector error correction model (VECM) of the measurement errors and estimate the model’s posterior density function using Bayesian methods. To contextualize our findings with those in the literature, we also assess whether the endogenous growth model or the standard real business cycle model better explains the observed variation in these aggregates. In addressing these issues we contribute to both the methods of analysis and the ongoing debate regarding the effects of innovations to productivity on macroeconomic activity.Endogenous growth, human capital, real business cycles, VEC Mmeasurement errors, Bayesian estimation