Equilibrium of Solow growth model with alternative trajectories of the number of workers
The aim of the study is to examine the long-run equilibrium of Solow growth model with a modified assumption for a rate of employment growth. In the first case, it is assumed that the number of workers changes in the trajectory defined by the logistic function. In the second case, it is assumed that...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Lodz University Press
2016-12-01
|
| Series: | Acta Universitatis Lodziensis. Folia Oeconomica |
| Subjects: | |
| Online Access: | https://czasopisma.uni.lodz.pl/foe/article/view/812 |
| _version_ | 1811200562845188096 |
|---|---|
| author | Katarzyna Filipowicz Maciej Grodzicki Tomasz Tokarski |
| author_facet | Katarzyna Filipowicz Maciej Grodzicki Tomasz Tokarski |
| author_sort | Katarzyna Filipowicz |
| collection | DOAJ |
| description | The aim of the study is to examine the long-run equilibrium of Solow growth model with a modified assumption for a rate of employment growth. In the first case, it is assumed that the number of workers changes in the trajectory defined by the logistic function. In the second case, it is assumed that the rate of growth of employment is a decreasing function of labor productivity (so called post-Malthusian growth path).
The capital labor ratio and labor productivity with logistic growth path of the number of workers are defined by certain functions composed of hypergeometric function of Gauss. When we consider post-Malthusian growth path of employment, solution of the Solow equation depends on the value of the parameter α (production elasticity with respect to capital) – it may have no, one or two non-trivial steady-states.
In performed numerical simulations, we calibrated elasticity of production with respect to capital at a level equal to 0.68216. In all variants of simulated investment rates, the standard, logistic and post-Malthusian trajectory of employment, labor productivity grows to a certain asymptote. Asymptotes of labor productivity for the logistic and post-Malthusian trajectory are located at a similar (slightly higher for logistic trajectory) level. Both are located far higher than the asymptotę of labor productivity function in the original Solow growth model. |
| first_indexed | 2024-04-12T02:05:34Z |
| format | Article |
| id | doaj.art-45322a9e4af74ee88161abdc9b4cf15c |
| institution | Directory Open Access Journal |
| issn | 0208-6018 2353-7663 |
| language | English |
| last_indexed | 2024-04-12T02:05:34Z |
| publishDate | 2016-12-01 |
| publisher | Lodz University Press |
| record_format | Article |
| series | Acta Universitatis Lodziensis. Folia Oeconomica |
| spelling | doaj.art-45322a9e4af74ee88161abdc9b4cf15c2022-12-22T03:52:33ZengLodz University PressActa Universitatis Lodziensis. Folia Oeconomica0208-60182353-76632016-12-01632610.18778/0208-6018.326.12515Equilibrium of Solow growth model with alternative trajectories of the number of workersKatarzyna Filipowicz0Maciej GrodzickiTomasz TokarskiUniwersytet Jagielloński, Katedra Ekonomii MatematycznejThe aim of the study is to examine the long-run equilibrium of Solow growth model with a modified assumption for a rate of employment growth. In the first case, it is assumed that the number of workers changes in the trajectory defined by the logistic function. In the second case, it is assumed that the rate of growth of employment is a decreasing function of labor productivity (so called post-Malthusian growth path). The capital labor ratio and labor productivity with logistic growth path of the number of workers are defined by certain functions composed of hypergeometric function of Gauss. When we consider post-Malthusian growth path of employment, solution of the Solow equation depends on the value of the parameter α (production elasticity with respect to capital) – it may have no, one or two non-trivial steady-states. In performed numerical simulations, we calibrated elasticity of production with respect to capital at a level equal to 0.68216. In all variants of simulated investment rates, the standard, logistic and post-Malthusian trajectory of employment, labor productivity grows to a certain asymptote. Asymptotes of labor productivity for the logistic and post-Malthusian trajectory are located at a similar (slightly higher for logistic trajectory) level. Both are located far higher than the asymptotę of labor productivity function in the original Solow growth model.https://czasopisma.uni.lodz.pl/foe/article/view/812stopa wzrostu liczby pracującychrównowaga modelu Solowa |
| spellingShingle | Katarzyna Filipowicz Maciej Grodzicki Tomasz Tokarski Equilibrium of Solow growth model with alternative trajectories of the number of workers Acta Universitatis Lodziensis. Folia Oeconomica stopa wzrostu liczby pracujących równowaga modelu Solowa |
| title | Equilibrium of Solow growth model with alternative trajectories of the number of workers |
| title_full | Equilibrium of Solow growth model with alternative trajectories of the number of workers |
| title_fullStr | Equilibrium of Solow growth model with alternative trajectories of the number of workers |
| title_full_unstemmed | Equilibrium of Solow growth model with alternative trajectories of the number of workers |
| title_short | Equilibrium of Solow growth model with alternative trajectories of the number of workers |
| title_sort | equilibrium of solow growth model with alternative trajectories of the number of workers |
| topic | stopa wzrostu liczby pracujących równowaga modelu Solowa |
| url | https://czasopisma.uni.lodz.pl/foe/article/view/812 |
| work_keys_str_mv | AT katarzynafilipowicz equilibriumofsolowgrowthmodelwithalternativetrajectoriesofthenumberofworkers AT maciejgrodzicki equilibriumofsolowgrowthmodelwithalternativetrajectoriesofthenumberofworkers AT tomasztokarski equilibriumofsolowgrowthmodelwithalternativetrajectoriesofthenumberofworkers |