Stability properties of a growth model (original) (raw)

Stability Properties in an Endogenous Growth Model With Elastic Labour Supply

The inclusion of a labour#leisure choice in endogenous growth models has interesting and somewhat counter-intuitive e#ects. In existing one sector models a condition for indeterminacy is that labour demand is upwardsloping, which is di#cult to reconcile with evidence. In this paper we give conditions for indeterminacy in a one sector model with decreasing returns to labour. We show that this requires that consumption and leisure are both highly intertemporally substitutable while the factors of production are highly complementary. # We wish to thank G. Cazzavillan, R. Farmer, M. Salmon and participants in seminars in Florence, Istanbul and Warwick for helpful comments. All remaining errors are our own. 1 Introduction In this paper we study whether the market outcome can be indeterminate in a one sector model of endogenous growth, where agents elastically supply labour and there are decreasing returns to labour. Recently there has been a renewed interest in the problem of ind...

A two-sector model of endogenous growth with leisure externalities

Journal of Economic Theory, 2013

This paper considers leisure externalities in a Lucas (1988) type model in which physical and human capital are necessary inputs in both sectors. In spite of a non-concave utility, the balanced growth path is always unique in our model which guarantees global stability for comparative-static exercises. We analyze and quantify the effects of preferences toward leisure on labor supply and welfare. We find that small differences in preferences toward leisure can explain a substantial fraction of differences in hours worked between Americans and Europeans. Quantitative results indicate that these differences also explain why Europeans grow less and consume less, but still prefer their lifestyle to that of the United States.

General existence of competitive equilibrium in the growth model with an endogenous labor–leisure choice

Journal of Mathematical Economics, 2020

We prove the existence of competitive equilibrium in the canonical optimal growth model with elastic labor supply under general conditions. In this model, strong conditions to rule out corner solutions are often not well justified. We show using a separation argument that there exist Lagrange multipliers that can be viewed as a system of competitive prices. Neither Inada conditions, nor strict concavity, nor homogeneity, nor differentiability are required for existence of a competitive equilibrium. Thus, we cover important specifications used in the macroeconomics literature for which existence of a competitive equilibrium is not well understood. We give examples to illustrate the violation of the conditions used in earlier existence results but where a competitive equilibrium can be shown to exist following the approach in this paper.

Consumption and Leisure Externalities, Economic Growth and Equilibrium Efficiency

Scottish Journal of Political Economy, 2008

This paper analyzes the effects of consumption and leisure externalities on growth and welfare in a two-sector endogenous growth model with human capital accumulation. Both types of externalities are shown to affect the long-run equilibrium and optimal growth rates in a rather different way. The relationship between the steady state of the market and the centrally planned economy is also analyzed. The optimal growth path can be decentralized by resorting to consumption or labor income taxation, whereas capital income should be untaxed. Numerical simulations suggest that growth and welfare effects of mild consumption and leisure externalities may be quantitatively important.

Indeterminacy and Welfare Increasing Taxes in a Growth Model with Elastic Labour Supply

1995

The inclusion of a labour/leisure choice in endogenous growth models has interesting and somewhat counter-intuitive effects. For some pa rameter values the economy is a stable dynamical system so the market equilibrium is indeterminate. Odd effects of policy appear. The long-run growth rate is increased by lump sum taxes used to fund wasteful gov ernment spending. Again for parameter values, such policy can increase the representative consumer's welfare. *We would like to thank Michele Boldrin, Roger Farmer, Akos Valentinyi and the par ticipants in the 1995 Annual Meeting of the Society for Economic Dynamics and Control in Barcelona for helpful suggestions. The usual disclaimer applies. This work was partly financed by the

Welfare Implications and Equilibrium Indeterminacy in a Two-Sector Growth Model with Consumption Externalities

Macroeconomic Dynamics, 2014

In one-sector neoclassical growth models, consumption externalities lead to an inefficient allocation in a steady state and indeterminate equilibrium toward a steady state only if there is a labor–leisure trade-off. This paper shows that in a two-sector neoclassical growth model, even without a labor–leisure trade-off, consumption spillovers easily lead to an inefficient allocation in a steady state and indeterminate equilibrium toward a steady state. Negative consumption spillovers that yield ove-accumulation of capital in a one-sector model may lead to underaccumulation or overaccumulation of capital in two-sector models, depending on the relative capital intensity between sectors. Moreover, a two-sector model economy with consumption externalities is less stabilized than an otherwise identical one-sector model economy.

An aggregative model of capital accumulation with leisure-dependent utility

Journal of Economic Dynamics and Control, 1998

This paper analyzes an aggregative optimal-growth model where both consumption and leisure enter as arguments in the utility function. If consumption and leisure are substitutes, the model can generate multiple steady states. If consumption and leisure are complements, the optimal path may turn out to be cyclical. Preferences play an important role in determining the steady state to which the economy converges.

Utility and production externalities, equilibrium efficiency and leisure specification

Journal of Macroeconomics, 2008

This paper analyzes the implications that the specification of the leisure activity has on the equilibrium efficiency in a two-sector endogenous growth model with human capital accumulation. We consider external effects of consumption and leisure in utility, and sector-specific externalities associated to physical and human capital in production. The optimal tax policy to correct for the distortions caused by the externalities is characterized under all the typical leisure specifications considered in the literature: home production, quality time and raw time. We show that the optimal policy depends markedly on the leisure specification.

Indeterminacy in a two-sector endogenous growth model with productive government spending

Journal of Macroeconomics, 2008

We extend the Barro (1990) model of endogenous growth to a two-sector one which consists of pure consumption and investment goods. It is possible that the extended version has a unique balanced growth rate such that for given initial values of state variables, (i) the extended model economy grows at the unique rate right from the beginning or (ii) it has a continuum of equilibrium paths whose growth rates commonly converge to the balanced growth rate. That is, unlike the original one-sector model, it has transitional dynamics in case (ii). We also show that the effects of small changes in some parameters on the balanced growth rate and the price of the consumption good in terms of the investment good are opposite between (i) and (ii).