On the Equilibrium in a Discrete-Time Lucas Model with Endogeneous Leisure (original) (raw)

On the equilibrium in a discrete-time Lucas Model with endogenous leisure

2006

In this paper I study a discrete-time version of the Lucas model with the endogenous leisure but without physical capital. Under standard conditions I prove that the optimal human capital sequence is increasing. If the instantaneous utility function and the production function are Cobb-Douglas, I prove that the human capital sequence grow at a constant rate. I finish by studying the existence and the unicity of the equilibrium in the sense of Lucas or Romer.

6 on the Equilibrium in a Discrete-Time Lucas Model

2014

In this paper I study a discrete-time version of the Lucas model with the endogenous leisure but without physical capital. Under standard conditions I prove that the optimal human capital sequence is increasing. If the instantaneous utility function and the production function are Cobb-Douglas, I prove that the human capital sequence grow at a constant rate. I finish by studying the existence and the unicity of the equilibrium in the sense of Lucas or Romer.

On the equilibrium in a discrete-time Lucas Model

RePEc: Research Papers in Economics, 2006

In this paper I study a discrete-time version of the Lucas model with the endogenous leisure but without physical capital. Under standard conditions I prove that the optimal human capital sequence is increasing. If the instantaneous utility function and the production function are Cobb-Douglas, I prove that the human capital sequence grow at a constant rate. I finish by studying the existence and the unicity of the equilibrium in the sense of Lucas or Romer.

A Note on the Inclusion of Human Capital in the Lucas Model

International Journal of Business and …, 2006

We include human capital in the utility function in an otherwise standard Lucas (1988) model of endogenous growth and show that there may be multiple steady-state equilibria. We also analyze the transitional dynamic properties of this model.

Existence of a competitive equilibrium in the Lucas (1988) model without physical capital

Journal of Mathematical Economics, 2006

This paper considers an endogenous growth model with human capital accumulation. It gives sufficient conditions and a necessary condition for the existence of a unique competitive equilibrium with externalities. These conditions are more stringent than those which prevail for the existence of an equilibrium defined as the solution to a fixed-point problem.

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.

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.

Uniqueness and Multiple Trajectories for the Case of Lucas Model

Computational Economics, 2018

The main aim of this paper is to prove that the model introduced by Lucas and further analyzed by Caballe and Santos, Mulligand and Sala-I-Martin, Benhabib and Perli and finally by Boucekkine and Ruiz-Tamarit, has two interesting properties. If the externality parameter in the production of human capital is greater than the elasticity of output with respect to physical capital, then the system is characterized by multiple transitional paths, indexed by the starting value of the fraction of labor allocated to the production of physical capital, leading to different steady-states equilibrium. Alternatively, if the externality parameter in the production of human capital is smaller than the elasticity of output with respect to physical capital, then the system is characterized by an unique transitional path, convergent to the unique steady-state equilibrium. For the special case where the inverse of the elasticity of intertemporal substitution equals the elasticity of output with respect to physical capital, we obtain closed-form solutions and thus, our approach contains as particular cases some other results, as those obtained by Boucekkine and Ruiz-Tamarit. More than this, differently to Boucekkine and Ruiz-Tamarit we obtain closed-form solutions for all variables of the model and thus we are able to verify the two transitional conditions.