Diagonalizing the Frobenius

Over a Noetherian, local ring R of prime characteristic p, the Frobenius functor F induces a diagonalizable map on certain quotients of rational Grothendieck groups. This leads to an explicit formula for the Dutta multiplicity, and it is shown that a weaker version of Serre's vanishing conjecture holds if only chi(F(X)) = p^{dim R}chi(X) for all bounded complexes X of finitely generated, projective modules with finite length homology.Comment: Revised (simplified) version. 12 page

Renormalization-Group Flows and Fixed Points in Yukawa Theories

We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling $y$ and quartic scalar coupling $\lambda$ by comparing the properties of flows obtained with the beta functions of these couplings calculated to different orders in the loop expansion. The results provide a determination of the region in $y$ and $\lambda$ where calculations up to two loops can yield reasonably reliable results.Comment: 15 pages, 7 figure

Asymptotically safe and free chiral theories with and without scalars

We unveil the dynamics of four dimensional chiral gauge-Yukawa theories featuring several scalar degrees of freedom transforming according to distinct representations of the underlying gauge group. We consider generalized Georgi-Glashow and Bars-Yankielowicz theories. We determine, to the maximum known order in perturbation theory, the phase diagram of these theories and further disentangle their ultraviolet asymptotic nature according to whether they are asymptotically free or safe. We therefore extend the number of theories that are known to be fundamental in the Wilsonian sense to the case of chiral gauge theories with scalars.Comment: ReVTeX, 28 pages, 14 figure

Appraising Schumpeter's 'Essence' after 100 Years: From Walrasian Economics to Evolutionary Economics

Schumpeter’s unique type of evolutionary analysis can hardly be understood unless we recognise that he developed it in relation to a study of the strength and weaknesses of the Walrasian form of Neoclassical Economics. This development was largely performed in his first book Wesen und Hauptinhalt der theoretischen Nationalökonomie. This German-language book - which in English might be called ‘Essence and Scope of Theoretical Economics’ - was published a century ago (in 1908). Different readings of Wesen provide many clues about the emergence and structure of Schumpeter’s programme for teaching and research. This programme included a modernisation of static economic analysis but he concentrated on the difficult extension of economic analysis to cover economic evolution. Schumpeter thought that this extension required a break with basic neoclassical assumptions, but he tried to avoid controversy by presenting it as only requiring the introduction of innovative entrepreneurs into the set-up of the Walrasian System. Actually, he could easily define the function of his type of entrepreneurs in this manner, but the analysis of the overall process of evolution required a radical reinterpretation of the system of general economic equilibrium. He thus made clear that he could not accept the standard interpretation of the quick Walrasian process of adaptation (tâtonnement). Instead, he saw the innovative transformation of routine behaviour as a relatively slow and conflict-ridden process. This reinterpretation helped him to sketch out his theory of economic business cycles as reflecting the waveform process of economic evolution under capitalism.Economic statics; evolutionary dynamics; business cycles; Joseph A. Schumpeter; Léon Walras

The Evolution of an Industrial Sector with a Varying Degree of Roundaboutness of Production

The evolutionary model presented in this paper depicts an industrial sector with a varying degree of economic roundaboutness, i.e. vertical division of labour between producers and users of different types of intermediate products that are ultimately used for the production of a single final product. To include this vertical aspect of industrial dynamics, the model adds the concept of production trees to the evolutionary models of Schumpeterian competition. The specification of this concept suggests the use of the notions of graph theory and the related algorithms of computer science in the treatment of industrial novelty, including structural innovations. Although the model is developed within the Nelson and Winter tradition, the introduction of the 'Austrian' issue of roundaboutness implies a major extension of the research agenda, including production- structure innovations, the emergence and functioning of markets for intermediate products, ways of coping with the instability of upstream markets, the spread of the effects of an upstream innovation, and the measurement of the degree of roundaboutness and of overall productivity. The model reflects a Schumpeterian version of the Böhm-Bawerkian vision of the emergence of increased long-term roundaboutness of production. The Schumpeterian approach implies an innovation- and entrepreneur-driven process of vertical disintegration and reintegration.Roundaboutness, production graphs, evolutionary economic modelling, Nelson and Winter

Escaping Satiation in an Evolutionary Model of Structural Economic Dynamics

This paper presents the problem of satiation in relation to a model of evolutionary endogenous growth. The model represents an attempt to provide an evolutionary economic micro foundation to Pasinetti's scheme of the structural economic dynamics of a labour economy. Like this scheme the model deals with an economic system with a varying number of sectors, each of which is producing a consumption good. The goods are produced within consumer-producer firms which organise both production and consumption for their workers. Through innovative activities firms increase their productivity with respect to individual goods. The long-run consequence of this is that labour becomes available for the production of new consumption goods. If such goods are not provided to a sufficient degree, "technological unemployment" will emerge. If there is slow productivity development in the production of new goods, the overall rate of growth will slow down irrespectively of productivity growth in old sectors. Thus, to enhance long-term growth there is a need of "anticipatory R&D", i.e. R&D which produces designs for novel consumption goods and increases productivity in the production of these goods.Evolutionary modelling, endogenous growth and development, structural economic dynamics, satiation of demand, Robinson Crusoe.

The Dynamics of the Organisation of Industry

The paper presents and formalises an approach to the evolution of the organisation of industry which starts from multi-activity firms, and which relates to economists like Young, Stigler, and Richardson. To capture the open-ended process of disintegration of industry, the paper operates with decomposable tasks and gives an account of the vertical and horizontal structure of production by means of weighted trees — in the graphtheoretical sense. Based on this addition to the analytical toolbox, the paper gives an account of the decomposition of industry as driven by the structural innovations and process innovations of firms that specialise and exchange in an open-ended evolutionary process.Vertical disintegration, horizontal disintegration, production trees, specialisation of production, specialisation of R&D, George B. Richardson

Fundamental Fields of: Post-Schumpeterian Evolutionary Economics

Although the branch of economics that deals with economic evolution has become established during the last couple of decades, its aims and potentials can most easily be understood on the background of the work of early pioneers. Joseph A. Schumpeter’s contribution not only analysed capitalist economic evolution as a process of the innovative renewal of business routines. He also explored the idea that the development of economics requires coordinated efforts within the “fundamental fields” of theory, history, statistics, and economic sociology. The paper applies this idea in an analysis of the development of modern evolutionary economics. The focus is on the characteristics and interdependencies of evolutionary history, evolutionary theory, and evolutionary statistics.Evolutionary economics; fundamental fields; Joseph A. Schumpeter