Competitive equilibrium cycles with endogenous labor (original) (raw)
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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.
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.
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.
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.
Equilibrium dynamics in two-sector models of endogenous growth
Journal of Economic Dynamics & Control, 1997
_ This paper presents an account of the dynamics of endogenous growth models with physical capital and human capital. We consider some important extensions of the basic framework of and Uzawa (1964), including physical capital in the human capital technology and leisure activities as an additional argument of agents' welfare.
On competitive cycles in productive economies
Journal of Economic Theory, 1988
In a model of overlapping generations with production, money, and an endogenous labor supply, general conditions are given for the existence of two different types of cyclical equilibria. The conditions are given in terms of the elasticities of demand for savings and for capital with respect to the interest rate and of the capital-consumption ratio at the golden rule steady state. Examples using CES technologies are also studied.
A two-sector economic growth model with optimal labor and capital allocation
In this paper, a two-sector growth model with optimal labor force and capital allocation is given. By treating the quantities of the labor force and capital in the consumption production sector as the control variables in the model, we obtain a two-dimension dynamical system from solving the household utility maximum problem. It is proved that the system has a unique nonzero equilibrium which is a saddle, so there exists an optimal labor force and capital allocation process in the economic growth. The capital accumulation and consumption production strictly increase along the growth path. At the end of this paper, a numerical computation is given to present the allocation process of capital and labor.