Bjarne S. Jensen

General equilibrium dynamics of multi-sector growth models

This paper analyzes Walrasian general equilibrium systems and calculates the static and dynamic solutions for competitive market equilibria. The Walrasian framework encompasses the basic multi-sector growth (MSG) models with neoclassical production technologies inN sectors (industries). The endogenous behavior of all the relative prices are analyzed in detail, as are sectorial allocations of the primary factors, labor and capital. Dynamic systems of Walrasian multi-sector economies and the family of solutions (time paths) for steady-state and persistent growth per capita are parametrically characterized. The technology parameters of the capital good industry are decisive for obtaining long-run per capita growth in closed (global) economies. Brief comments are offered on the MSG literature, together with apects on the studies of industrial (structural) evolution and economic history.

Walrasian General Equilibrium Allocations and Dynamics in Two‐Sector Growth Models

Abstract This paper analyzes and solves miniature Walrasian general equilibrium systems of momentary and moving equilibria. The Walrasian framework encompasses the fundamental neoclassical and classical two-sector growth models; the families of solutions of steady-state and persistent growth per capita in various competitive two-sector economies are parametrically characterized. Moreover, the endogenous behavior of relative prices and the sectoral allocation of primary factors are analyzed in detail. The technology parameters of the capital good industry are decisive for obtaining long-run per capita growth in closed (global) economies. A review of the literature complements the theorems on the general equilibrium allocations, dynamic systems, and the time paths of Walrasian two-sector economies.

The dynamic systems of basic economic growth models

Preface. Introduction and Overview. Book I: Basic Economic Growth Models -- An Axiomatic Approach. 1. Basic laws of production. Part 1: Basic One-Sector Growth Models. 2. Classical growth models and homogeneity. 3. Classical growth models and minimal factor rewards. 4. Aggregate endogenous growth models. Synopsis of endogenous growth models. 5. Neoclassical growth models. 6. Keynesian growth models. Part 2: Basic Two-sector Growth Models. 7. Leontief technology and efficient factor utilization. 8. Flexible technologies and proportional saving. 9. Flexible technologies and classical saving. Synopsis of two-sector growth models. Final comments. Book II: Basic Dynamic Systems. 10. Homogeneous dynamics in the plane. 11. Linear and affine dynamics in the plane. 12. Quasi-homogeneous dynamics in the plane. 13. Discrete linear dynamics in the plane. Addendum: Growth and long-run stability. Bibliography: Book I. Bibliography: Book II. Index.

Basic Stochastic Dynamic Systems of Growth and Trade

Uncertainties are intrinsic features of dynamic economic systems, and this paper considers the dynamic implications of factor endowment (labor, capital) uncertainties for a small growing trading economy. The stochastic growth models presented extend the open neoclassical two-sector growth model (Deardorff) to a stochastic environment in continuous time, and extend the diffusion dynamics of one-sector growth models (Merton; Bourguignon) to a trading two-sector economy. It is demonstrated that the basic propositions of deterministic steady-state growth and endogenous growth theory, under some specifications and certain parametric restrictions, are preserved within a stochastic framework. Copyright 1999 by Blackwell Publishing Ltd.

Saving Rates, Trade, Technology, and Stochastic Dynamics

This paper develops a framework for analyzing the stochastic dynamics of small growing trading economies with CES sector technologies. The open neoclassical two-sector growth model with a diffusion process (uncertainty) for the aggregate saving/investment ratio is demonstrated with sample paths and long-run probability distributions of the overall factor endowment ratio. Stochastic endogenous growth and cycles require a combination of fundamental growth parameter values: saving rates, terms of trade, and sectoral substitution elasticities. Copyright 2001 by Blackwell Publishing Ltd

Growth and long-run stability

This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.

Non‐Homothetic Multisector Growth Models

Multisector growth (MSG) models are dynamic versions of computable general equilibrium (CGE) models. Non-homothetic preference (utility) functions are required for the evolution of factor allocations and industrial structures in accordance with consumption expenditure patterns implied by the non-unitary income elasticities observed in all budget data since Engel in the 1850s. But comparative static general equilibrium solutions and particularly solving the dynamics of MSG models require explicit specifications of all demand and cost (price) functions. On the demand side, the constant differences of elasticity of substitution (CDES) non-homothetic indirect utility functions and Roys identity provide the explicit Marshallian demand functions and budget shares. Sectorial constant elasticity of substitution (CES) cost functions and Shephards lemma provide the explicit relative commodity price functions and the sectorial cost shares and capital–labor ratios. Walrasian equilibria are given by one equation and the multisector dynamics by three differential equations. Benchmark solutions are given for three cost regimes of a 10-sector MSG model. History patterns of industrial/allocational evolutions are recognized.

Comparative Cost and Factor Endowments: Ricardo and Ohlin

The concept (law, principle) of comparative advantage is due to Ricardo (1817, Ch. 7) — the term is also found in Ricardo (1817, Ch. 19, p. 175), cf. Ruffin (2002, p. 743). The expression ‘what a country can do most cheaply’ needed careful examination, and it was in analysing this idea more sharply that Ricardo enunciated the principle (term) of comparative advantage. The Ricardian term means the ability to produce a good at lower cost (relative to other goods), compared with another country. With perfect market competition relative costs are also relative autarchy prices, and the law of comparative advantage (cost) says that a country exports (imports) the good with the low (high) relative autarchy price. This Law of Comparative Costs will always remain a fundamental principle of economics and international trade.

Dynamic Extensions of the Solow Growth Model (1956): Editorial

The origin of the wealth of nations and the determinants of the long-term prospects of economic evolution were central topics in the classical economics of A. Smith, D. Ricardo, T. R. Malthus and J. S. Mill. Their discussions of the propagation of population, laws of returns (production), capital accumulation and income distributions were concerned with understanding processes for economic progress (development, growth). Although theories of economic growth thus go far back to the beginning of our discipline, growth models as quantitative dynamics appeared late, in the middle of the last century. Since systems of nonlinear differential equations are the dynamic fundamentals of economic growth models with continuous factor (labor and capital) accumulation, it is in retrospect not surprising that the solutions (evolutions) for labor, capital stock, wage and profit rates, and income distributions, were for many years controversial without clear, definite conclusions being established. This state of affairs for growth models and economic dynamics was changed with the breakthrough by Solow (1956): ‘A Contribution to the Theory of Economic Growth’. The effects in economic science were dramatic. The crucial innovation was the introduction of smooth production functions (linking factor inputs and output) that together with various saving functions provided the differential equations of capital accumulation. Explicit benchmark solutions of the basic dynamic model were rigorously established for CES technology parameter values of the factor substitution elasticity: s5 0, 1, 2 – allowing for steady-state growth or persistent (endogenous) growth per capita. To underline the character of the seminal Solow (1956) article for general readers of economic literature, it may be helpful on this matter here to quote Lucas (1988, p. 5): ‘I prefer to use the term ‘‘theory’’ in a very narrow sense, to refer to an explicit dynamic system, something that can be put on a computer and run. This is what I mean by the ‘‘mechanics’’ of economic development’. Indeed, Solow (1956) presented the ‘mechanics’ (explicit dynamic system) of

Neoclassical growth models

From an economic and mathematical point of view, neoclassical growth models [161,166,115] may be considered a special case (a dynamic simplification) of the aggregate endogenous (“classical”) growth models in chapter 4.