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This book aims to include the effects of a progressive personal tax into the deterministic dynamic theory of the firm. To this end the author investigates the impact of a progressive personal tax on the optimal dividend, financing and investment policy of a shareholder-controlled, value-maximising firm. More specifically, the principal aim is the justification of the thesis that during each stage of their evolution, firms will be controlled by investors in different tax brackets. With this aim in mind, the author develops a dynamic equilibrium and portfolio theory under certainty, which considers: - the market value of an arbitrary firm such that no excess demand for or supply of shares exists, - the portfolio selection of differently taxed investors, - the succession of differently taxed investors, who possess the shares of any value-maximizing firm, in the course of time, - the optimal resulting policy string and corresponding evolution of a firm in the course of time.
1.1. Scope of the Book This book is a contribution to the area of "dynamic models of the firm". The motivation for this kind of research is the following: Empirical studies (e.g. Albach (1976)) have shown that the development of the firm over time can be divided into different stages. such as growth. stationarity and contraction. In order to understand and evaluate these stages in a proper way. it is important to develop a suitable theoretical framework. To that end. economists have applied dynamic mathematical techniques. such as optimal control theory. calculus of variations and dynamic programming to design and analyse dynamic models of the firm. In this way. the economic theory of the firm is extended to a dynamic context. Within the field of the dynamics of the firm this book - develops a general investment decision rule. based on the concept "net present value of marginal investment". which is applicable in deterministic dynamic models of the firm; - studies the influence of adjustment costs of investment on optimal dynamic firm behavior; - extends the stochastic dynamic theory of the firm by connecting it with a dynamic version of the Capital Asset Pricing Model. Before elaborating on "the dynamics of the firm". we first review the subject of net present value in the classical analysis.
In this book we open our insights in the Theory of the Firm, obtained through the application of Optimal Control Theory, to a public of scholars and advanced students in economics and applied mathematics. We walk on the micro economic side of the street that is bordered by Theory of the Firm on one side and by Optimal Control Theory on the other, keeping the reader away from all the dead end roads we turned down during our 10 years lasting research. We focus attention on the expressiveness and variety of insights that are obtained through studying only simple models of the firm. In this book mathematics is our tool, insight in optimal corporate policy our goal. Therefore most of the mathematics and calculations is put into appendices and in the main text all attention is on modelling corporate behaviour and on analysing the results of the calculations. So, the main text focusses on micro economics, even more specific: on Theory of the Firm. In that way this book is contrasted from such famous text books in applied Optimal Control with a much broader portfolio of applications, like Feichtinger & Hartl (1986) or with a more rigorous introduction into theory, like Seierstad & Sydsaeter (1987).
This book contributes to the scientific field of optimal control theory applied to dynamic models of the firm. It discusses optimal investment, financing and production policies of the firm, that have to deal with a variety of aspects, such as financial constraints, start-up costs, business cycles, increasing returns to scale, production life cycles and experience curves. In contrast to many other publications on this subject, here, in combination with an analytical approach, the dynamic optimization problems are solved numerically with the aid of a powerful computer and specific programs for optimizing non-linear functions of a finite number of variables and non-linear constraints.
This thesis is a theoretical study of the optimal dynamic policies of a, to some extent, slowly adjusting firm that faces an exogeneously given technological progress and an exogeneously given business cycle. It belongs to the area of mathematical economics. It is intended to appeal to mathematical economists in the first place, economists in the second place and mathematicians in the third place. It entails an attempt to stretch the limits of the application of deterministic dynamic optimisation to economics, in particular to firm behaviour. A well-known· Dutch economist (and trained mathematician) recently stated in 1 a local university newspaper that mathematical economists give economics a bad reputation, since they formulate their problems from a mathematical point of view and they are only interested in technical, mathematical problems. At the same time, however, "profound as economists may be, when it comes to extending or modifying the existing theory to make it applicable to a certain economic problem, an understanding of optimal control theory (which is the mathematical theory used in this thesis, ovh) based solely on heuristic arguments will often turn out to be inadequate" (SydS
In this book interrelated factor demand models are surveyed. New methods are developed and are analysed empirically using Dutch and U.K. time series data. New methods are discussed for obtaining closed form solutions of linear ratinal expectations models, providing deeper insights into the identification of structural parameters of underlying theoretical models; recently developed time series techniques are applied in order to estimate structural parameters and test for model specification, stationarity and stability through time; new models are developed in which the rather stringent and questionable restrictions of symmetry generally imposed upon stochastic adjustment models of labour demand are relaxed, the models are analysed empirically using time series data of Dutch and U.K. manufacturing production and nonproduction workers.
Elements of a Nonlinear Theory of Economic Dynamics provides both a framework and a survey of its needs. First, principle results and techniques of the theory relevant to applications in dynamic economics are discussed, then their application in view of older endogenous cycle theories are considered in a unified mathematical framework. Models incorporating the government budget constraint and the Goodwin model are analysed using the method of averaging and the centre manifold theory. The dynamic instability problem is solved by placing models in a nonlinear framework.
The present study is a preliminary draft on nonlinear economic dynamics, with which the author has been concerned the last years. It grew out from the joint work by Professor Martin Beckmann and the present author on nonlinear statics in spatial economics, Beckmann and Puu, "Spatial Economics" (North-Holland 1985). The monograph mentioned contains sections on price waves and business cycles, but in a linear format. The rest is static theory. The author has finally come to the conviction that linear dynamic modelling has very little to yield. This is due to the poor set of alternatives -decay or explosion of motion -pertinent to linear models. Therefore, the pr~sent work centres on non-linearity. Another distinction is that only purely causal models are dealt with, as those formatted as inter-temporal equilibria hardly belong to the more restricted field of dynamics. The spatial origin is visible in the choice of models. Chapter 2 summarizes the work by the author on the stmctural stability of continuous spatial market equilibrium models. Chapter 3 deals with a re-formulation of the ingenious population growth and diffusion model invented by the young Hotelling in 1921. Chapter 4 is a detailed digression on business cycle models in a continuous spatial format with interregional trade.
In this book a rigorous, systematic, mathematical analysis is presented for oligopoly with multi-product firms in static as well as dynamic frameworks in the light of recent developments in theories of games, oligopoly and industrial organization. The general results derived in this book on oligopoly with multi-product firms contain, as special cases, all previous results on oligopoly with single product as well as oligopoly with product differentiation and single product firms. A constructive nu- merical method is given for finding the Cournot-Nash equilibrium, which may be extremely valuable to those who are interested in numerical analysis of the effects of various industrial policies. A sequential adjustment process is also formulated for finding the equilibrium. Dynamic adjustment processes have two versions, one with a discrete time scale and the other with a continuous time scale. The stability of the equilibrium is thoroughly investigated utilizing powerful mathematical results from the stability and linear algebra literature. The methodology developed for analyzing stability proves to be useful for dynamic analysis of economic models.
The history of many sciences is characterized by an almost continuous emer gence of new theories. From a normative point of view, the survival of a new theory should mainly be determined by its ability to explain a new body of facts which the existing theories are unable to explain. If in addition the new theory is able to explain all the results obtained by the existing theories and if it can point out why these theories fail to explain certain facts, it should become the dominant theory. Otherwise, it might coexist with other theories for some time. Hence, a new theory ought to be judged not only by confronting it with existing facts, but also by confronting it with existing theories. The idea that a theory should be able to account for the results ob tained by other theories, although implicitly adhered to by many scientists, has rarely been formalized. The statistics literature on parametric hypoth esis testing, though, might be seen as an instance of such a formalization.