Multi-sector Growth Model Research Articles

The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth

It is shown that under very general circumstances, the standard optimal growth model with two or more capital goods can give rise to optimal trajectories that are limit cycles. An example with a nonjoint production Cobb-Douglass technology giving rise to closed cycles around a unique steady state is constructed. The stability of orbits is also studied.

On the Uniqueness of Steady States in an Economy with Heterogeneous Capital Goods

It well known that in multisector models of optimal growth, optimal paths converge to a unique steady state when future utilities are not discounted. Sutherland [1970], Kurz [1968], and Liviatan and Samuelson [1969] gave examples of multiple steady states when future utilities are discounted. Beals and Koopmans [1969] and Iwai [1972] used intertemporal utility functions, which also yield multiple steady states. The uniqueness of steady states with multiple consumption goods when future utility discounted has been studied by Brock [1973]. He showed tlhat if we assume that none of the goods are inferior in consumption (he calls this the normality condition for the utility function) the uniqueness of the steady state assured. Brock did not allow for pure consumption goods. Later Brock and Burmeister [1976] generalized Brock's result to allow pure consumption goods as well (Morishima [1974] type). Brock also formulated an alternative approach where uniqueness assured under the of a non-vanishing Jacobian for every non-negative discount rate. He writes however that the non-singularity of the Jacobian is an obscure assumption and that it would be worthwhile to relate it to the normality condition of the utility function. We first propose to weaken Brock's of non-vanishing Jacobian for every discount rate. Then in Section 3, Theorem 2, we show that the normality condition on the utility function implies a non-vanishing Jacobian. In Theorem 3 we weaken the normality condition for the uniqueness of the steady state by investigating the conditions for a non-vanishing Jacobian. We then clarify the economic content of our weaker conditions. In the final section we observe that the normality theorem can be proved for the joint production case (Mirrlees [1969] type) using a technique due to McKenzie [1963, 1973].

Global asymptotic stability results for multisector models of optimal growth under uncertainty when future utilities are discounted

Global asymptotic stability results for multisector models of optimal growth under uncertainty when future utilities are discounted

Planning capital-labor substitution and intertemporal equilibrium with a non-linear multi-sector growth model

A non-linear multi-sector model, postulating sectoral production functions and price-responsive demand functions linked around an input-output matrix in a general equilibrium framework, is used to simulate capital-labor substitution on a growth path characterized by intertemporal equilibrium. It demonstrates how the ‘temporary equilibrium’ or ‘sequential temporary equilibrium’ form of models that allow substitution can be extended into an intertemporally indecomposable equilibrium model without abandoning interaction between prices and quantities in the determination of technology and demand. The model is applied to the analysis of the impact of changes in real-wage growth on the characteristics of the equilibrium growth path of the Turkish economy with special attention given to the employment problem.

Mathematical Theories of Economic Growth

One-sector growth models technological change in the one-sector model money and economic growth a preview of multisector growth models Leontief models and alternative techniques neoclassical multisector models without joint production turnpike theorems and efficient economic growth optimal economic growth.

WAGES, EMPLOYMENT AND GROWTH

SUMMARY The paper presents a multisectoral growth model which is readily computable with non-linear production functions and is descriptive of economic conditions prevailing in over-populated countries. The purpose is to show the optimal allocation of resources over time in a labor surplus economy if the dominant social consideration is to increase the rate of employment as fast as possible. Given an institutionally stipulated minimum wage rate and certain other assumptions, the path that maximizes the rate of economic growth also approximates the path that minimizes the time needed to attein full employment as long as the rate of increase of the capital stock exceeds the rate of growth of the potential labor force. A rigorous proof of the proposition is presented with the help of the calculus of variations and the numerically computable solution of the growth model is derived from the conditions underlying the optimum at any moment of time. The model is an analogue of competitive markets under appropriate demand conditions. In addition, since it is computable, the model can be used by economic planners in countries where large scale unemploffment or under-employ-ment exists.