Note on global dynamics and imbalance effects in the Lucas–Uzawa model

Boucekkine, Raouf; Martínez, Blanca; Ruiz-Tamarit, José Ramón

doi:10.1111/j.1742-7363.2008.00091.x

Cited by 21 publications

(9 citation statements)

References 13 publications

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“…Notice also the symmetry of optimal trajectories corresponding to initial relatively scarce capital and initial relatively abundant capital respectively. Symmetry here is granted because we have one production sector, the shape of imbalance effects are much less symmetric in two-sector modelsà la Lucas-Uzawa (see Boucekkine et al, 2008).…”

Section: Short Run Dynamicsmentioning

confidence: 99%

Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case

Boucekkine

Martínez

Ruiz-Tamarit

2018

Lecture Notes in Economics and Mathematical Systems

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This paper revisits the optimal population size problem in a continuous time Ramsey setting with costly child rearing and both intergenerational and intertemporal altruism. The social welfare functions considered range from the Millian to the Benthamite. When population growth is endogenized, the associated optimal control problem involves an endogenous effective discount rate depending on past and current population growth rates, which makes preferences intertemporally dependent. We tackle this problem by using an appropriate maximum principle. Then we study the stationary solutions (balanced growth paths) and show the existence of two admissible solutions except in the Millian case. We prove that only one is optimal. Comparative statics and transitional dynamics are numerically derived in the general case.

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Section: Short Run Dynamicsmentioning

confidence: 99%

Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case

Boucekkine

Martínez

Ruiz-Tamarit

2018

Lecture Notes in Economics and Mathematical Systems

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“…We have assumed that the depreciation rate of physical, human and technological capital is common and equal to zero 6 .…”

Section: The Modelmentioning

confidence: 99%

“…The opposite case, where δ < 0, corresponds to what the productivity literature defines as the fishing out effect, in which the rate of innovation decreases with the level of knowledge5 As Hiraguchi (2009) underlines, the Hamiltonian is nonconcave and thus the first order conditions (FOCs) and the transversality conditions does not imply the optimality 6. This is of course a simplifying assumption, but the outcome of the model would not change even if we introduce non zero depreciation rates.…”

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confidence: 99%

Endogenous technological progress in a multi-sector growth model

Torre

Marsiglio

2010

Economic Modelling

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This paper presents an endogenous growth model driven by human capital, where human capital can be allocated across three sectors: the production of the final consumption good, the educational sector and the production of technological capital (in the form of knowledge or ideas). In our model, which also includes public expenditure and population growth, labor augmenting technical progress is endogenous and this enriches the transitional dynamics of the economy. With respect to ideas-based growth models, we assume knowledge is produced according to a neoclassical technology, combining ideas and human capital. Such an assumption is motivated by empirical works showing the existence of significant decreasing returns in the creation of ideas at the aggregate level (as Kortum, 1993; and Pessoa, 2005) and of the weak relationship between some inputs of the knowledge production process (as the number of researchers) and the total factor productivity growth rate (as Jones, 2002). Under some general conditions, this economy exhibits the existence of a steady state equilibrium and an unstable multidimensional manifold. Numerical examples are provided to show the existence of stable arms.

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“…Bucci and Marsiglio (2018) and Bucci et al (2018) are significant contributions in theoretical literature on economic growth theory and have led a foundation of modeling of exogenous factors in theoretical models. Boucekkine and Ruiz-Tamarit (2008) established the closed-form solutions of the Lucas-Uzawa model under no parameter restrictions and expressed the closed-form solutions in terms of hypergeometric functions. This is a significant contribution to the economic growth theory in closed-form solutions perspective.…”

Section: Introductionmentioning

confidence: 99%

“…The results are opposite for the case of a negative relationship between finance and growth of the economy. Boucekkine et al (2008) studied the imbalance effects for the basic Lucas-Uzawa model under no parameter restrictions. The imbalance effects for the Lucas-Uzawa model with externalities were studied by Mulligan and Sala-i-Martin (1993), Barro and Sala-i-Martin (1995), and Boucekkine and Tamarit (2004).…”

Section: Introductionmentioning

confidence: 99%

The closed-form solutions for finance-extended Lucas–Uzawa model

Naz

2020

Comp. Appl. Math.

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In this paper, I establish the closed-form solutions for all the variables in the finance-extended Lucas-Uzawa model under no parameter restrictions by utilizing the partial Hamiltonian approach and second by direct utilization of the standard methods. I provide an overview of the model and properties of the balanced growth path (BGP) as discussed in Bucci and Marsiglio (Scot J Polit Econ 2018). I have provided sufficient conditions as well. First, the model is solved by utilizing the partial Hamiltonian approach and I obtain two first integrals. I utilize both first integrals to find the closed-form solutions for all variables of financeextended Lucas-Uzawa model. I also establish the growth rates of all the variables in the model to fully understand the dynamics of the model. The properties of BGP as described by Bucci and Marsiglio (2018) are analyzed and some additional properties are provided as well. Next, I establish a closed-form solution for all the variables of the model directly by utilizing the standard methods and these can be, alternatively, derived by utilizing only one first integral. This closed-form solution also satisfies all properties of the BGP. For the special case when inverse of intertemporal elasticity of substitution is equal to the share of physical capital, both approaches provide same closed-form solution for all the variables of the model which is presented in Bucci and Marsiglio (2018). The relationship between financial development and imbalance effects is analyzed in detail.

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Note on global dynamics and imbalance effects in the Lucas–Uzawa model

Cited by 21 publications

References 13 publications

Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case

Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case

Endogenous technological progress in a multi-sector growth model

The closed-form solutions for finance-extended Lucas–Uzawa model

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