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See detailA Generalized Steady-State Growth Theorem
Irmen, Andreas UL

in Macroeconomic Dynamics (2018)

Uzawa’s steady-state growth theorem (Uzawa (1961)) is generalized to a neoclassical economy that uses current output, e.g., to create technical progress or to manufacture intermediates. The difference ... [more ▼]

Uzawa’s steady-state growth theorem (Uzawa (1961)) is generalized to a neoclassical economy that uses current output, e.g., to create technical progress or to manufacture intermediates. The difference between aggregate final-good production and these resources is referred to as net output. The new generalized steady-state growth theorem holds since net output exhibits constant returns to scale in capital and labor. This insight provides an understanding for why technical change is labor-augmenting in steady state even if capital-augmenting technical change is feasible. By example, this point is made for four growth mod-els that allow for endogenous capital- and labor-augmenting technical change, namely, Irmen and Tabakovic (2015), Acemoglu (2003), Acemoglu (2009), Chapter 15, and for the typical model of the induced innovations literature of the 1960s.The reduced form of these models is shown to be consistent with the generalizedsteady-state growth theorem. [less ▲]

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See detailA Note on the Characterization of the Neoclassical Production Function
Irmen, Andreas UL

in Macroeconomic Dynamics (2017)

We study production functions with capital and labor as arguments that exhibit positive, yet diminishing marginal products and constant returns to scale. We show that such functions satisfy the Inada ... [more ▼]

We study production functions with capital and labor as arguments that exhibit positive, yet diminishing marginal products and constant returns to scale. We show that such functions satisfy the Inada conditions if (i) both inputs are essential and (ii) an unbounded quantity of either input leads to unbounded output. This allows for an alternative characterization of the neoclassical production function that altogether dispenses with the Inada conditions. Although this proposition generalizes to the case of n > 2 factors of production, its converse does not hold: 2n Inada conditions do not imply that each factor is essential. [less ▲]

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See detailA Generalized Steady-State Growth Theorem
Irmen, Andreas UL

in Macroeconomic Dynamics (2017)

Is there an economic justification for why technical change is by assumption labor-augmenting in Dynamic Macroeconomics? The literature on the endogenous choice of capital- and labor-augmenting technical ... [more ▼]

Is there an economic justification for why technical change is by assumption labor-augmenting in Dynamic Macroeconomics? The literature on the endogenous choice of capital- and labor-augmenting technical change finds that technical change is purely labor-augmenting in steady state. The present paper shows that this finding is mainly an artefact of the underlying mathematical models. To make this point Uzawa’s steady-state growth theorem (Uzawa (1961)) is generalized to a neoclassical economy that, besides consumption and capital accumulation, uses current output to create technical progress or to manufacture intermediates. The generalized steady-state growth theorem is shown to encompass four models of endogenous capital- and labor-augmenting technical change, namely, Irmen and Tabakovic (2015), Acemoglu (2003), Acemoglu (2009), Chapter 15, and the typical model of the induced innovations literature of the 1960s. [less ▲]

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See detailMonetary Policy, Factor Substitution, and Convergence
Klump, Rainer UL; Jurkat, Anne

in Macroeconomic Dynamics (2016)

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See detailA Note on the Characterization of the Neoclassical Production Function
Irmen, Andreas UL; Maussner, Alfred

in Macroeconomic Dynamics (2016)

We study production functions with capital and labor as arguments that exhibit positive, yet diminishing marginal products and constant returns to scale. We show that such functions satisfy the Inada ... [more ▼]

We study production functions with capital and labor as arguments that exhibit positive, yet diminishing marginal products and constant returns to scale. We show that such functions satisfy the Inada conditions if i) both inputs are essential and ii) an unbounded quantity of either input leads to unbounded output. This allows for an alternative characterization of the neoclassical production function that altogether dispenses with the Inada conditions. While this proposition generalizes to the case of n > 2 factors of production its converse does not hold: 2n Inada conditions do not imply that each factor is essential. [less ▲]

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See detailBridging the gap between growth theory and the new economic geo-graphy : The spatial Ramsey model
Boucckine, Raouf; Camacho, Carmen; Zou, Benteng UL

in Macroeconomic Dynamics (2009), 13(1), 20-45

We study a Ramsey problem in in¯nite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the ... [more ▼]

We study a Ramsey problem in in¯nite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature to derive the Pontryagin conditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic system gives rise to an ill-posed problem in the sense of Hadamard (1923). We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly different from those of the non-spatial linear Ramsey model due to the spatial dynamics induced by capital mobility. [less ▲]

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