Local and global bifurcations in an economic growth model with endogenous labour supply and multiplicative external habits

This paper proposes a one-sector multigroup growth model with endogenous labor supply in discrete time. Proposing an alternative approach to behavior of households, we examine the dynamics of wealth and income distribution in a competitive economy with capital accumulation as the main engine of economic growth. We show how human capital levels, preferences, and labor force of heterogeneous households determine the national economic growth, wealth, and income distribution and time allocation of the groups. By simulation we demonstrate, for instance, that in the three-group economy when the rich group's human capital is improved, all the groups will economically benefit, and the leisure times of all the groups are reduced but when any other group's human capital is improved, the group will economically benefit, the other two groups economically lose, and the leisure times of all the groups are increased.

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The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model

Abstract and Applied Analysis ◽

10.1155/2013/901014 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 12

Author(s):

Carlo Bianca ◽

Massimiliano Ferrara ◽

Luca Guerrini

Keyword(s):

Economic Growth ◽

Growth Model ◽

Time Delays ◽

Sufficient Conditions ◽

Qualitative Behavior ◽

Solow Model ◽

Normal Form Theory ◽

Economic Growth Model ◽

Form Theory ◽

The Stability

A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results.

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Generalizations of the Lagrange mean value theorem and applications

Filomat ◽

10.2298/fil1304515m ◽

2013 ◽

Vol 27 (4) ◽

pp. 515-528 ◽

Cited By ~ 2

Author(s):

Miodrag Mateljevic ◽

Marek Svetlik ◽

Miloljub Albijanic ◽

Nebojsa Savic

Keyword(s):

Economic Growth ◽

Growth Model ◽

Arbitrary Function ◽

Mean Value ◽

Point Of View ◽

Neoclassical Economic ◽

Mean Value Theorem ◽

Mathematical Point ◽

Economic Growth Model

In this paper we give a generalization of the Lagrange mean value theorem via lower and upper derivative, as well as appropriate criteria of monotonicity and convexity for arbitrary function f : (a, b) ( R. Some applications to the neoclassical economic growth model are given (from mathematical point of view).

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The Dynamics of a Spatial Economic Model with Bounded Population Growth

Discrete Dynamics in Nature and Society ◽

10.1155/2021/9963437 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Yue Zhong

Keyword(s):

Economic Growth ◽

Population Growth ◽

Growth Model ◽

Explicit Solution ◽

Capital Accumulation ◽

Initial Distribution ◽

Time Behavior ◽

Continuous Space ◽

Infinite Dimensional ◽

Economic Growth Model

We investigate a spatial economic growth model with bounded population growth to obtain the asymptotic behavior of detrended capital in a continuous space. The formation of capital accumulation is expressed by a partial differential equation with corresponding boundary conditions. The capital accumulation interacts with the morphology to affect the optimal dynamics of economic growth. After redrafting the spatial growth model in the infinite dimensional Hilbert space, we identify the unique optimal control and value function when the bounded population growth is considered. With nonnegative initial distribution of capital, the explicit solution of the model is obtained. The time behavior of the explicit solution guarantees the convergence issue of the detrended capital level across space and time.

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