Abstract
We consider the neoclassical one-sector growth model in continuous time with elastic labor supply and a learning-by-doing externality. It is shown that this model can have a continuum of balanced growth paths. Some of these balanced growth paths can be locally unique (determinate) whereas others can be indeterminate.
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Notes
- 1.
In growth theory, however, the labor-leisure trade-off is surprisingly often disregarded. Eriksson (1996) writes that “The choice between work and leisure has been remarkably neglected in the theory of economic growth” (Eriksson 1996, p. 533) and even the very comprehensive and more recent survey of economic growth theory provided by Acemoglu (2009) does not discuss the case of elastic labor supply except for briefly mentioning real business cycle models in Section 17.3.
- 2.
It follows from Walras’ law that the output market clears as well.
- 3.
The growth rate of a function \(z: \mathbb{R}_{+}\mapsto \mathbb{R}_{++}\) at time t is given by \(\dot{z}(t)/z(t)\).
- 4.
Partial derivatives are denoted by subscripts. For example, u 1 (c, 1 − ℓ) denotes the partial derivative of the function u with respect to its first argument evaluated at the point (c, 1 − ℓ).
- 5.
See Feichtinger and Hartl (1986).
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Sorger, G. (2016). Multiplicity of Balanced Growth Paths in an Endogenous Growth Model with Elastic Labor Supply. In: Dawid, H., Doerner, K., Feichtinger, G., Kort, P., Seidl, A. (eds) Dynamic Perspectives on Managerial Decision Making. Dynamic Modeling and Econometrics in Economics and Finance, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-39120-5_11
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DOI: https://doi.org/10.1007/978-3-319-39120-5_11
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