Reexamination of the Serendipity Theorem from the stability viewpoint

2019 ◽  
Vol 85 (1) ◽  
pp. 43-70
Author(s):  
Akira Momota ◽  
Tomoya Sakagami ◽  
Akihisa Shibata
Keyword(s):  
Growth Rate ◽  
Steady State ◽  
Population Growth ◽  
Numerical Simulations ◽  
Policy Implication ◽  
Population Growth Rate ◽  
Golden Rule ◽  
The Social ◽  
The Stability ◽  
Parameter Values

AbstractThis paper reexamines the Serendipity Theorem of Samuelson (1975) from the stability viewpoint, and shows that, for the Cobb–Douglas preference and CES technology, the most-golden golden-rule lifetime state being stable depends on parameter values. In some situations, the Serendipity Theorem fails to hold despite the fact that steady-state welfare is maximized at the population growth rate, since the steady state is unstable. Through numerical simulations, a more general case of CES preference and CES technology is also examined, and we discuss the realistic relevance of our results. We present the policy implication of our result, that is, in some cases, the steady state with the highest utility is unstable, and thus a policy that aims to achieve the social optima by manipulating the population growth rate may lead to worse outcomes.

scholarly journals Hopf bifurcation in an overlapping generations resource economy with endogenous population growth rate

2016 ◽  
Vol 20 (5) ◽  
Author(s):  
Burcu Fazlıoğlu ◽  
Hüseyin Çağrı Sağlam ◽  
Mustafa Kerem Yüksel
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Population Growth ◽  
Resource Availability ◽  
Overlapping Generations ◽  
Population Growth Rate ◽  
Growth Dynamics ◽  
Feedback Mechanism ◽  
Parameter Values ◽  
Resource Economy

AbstractAs scarce environmental resources necessarily put a constraint on population growth, we use more realistic population growth dynamics which contemplates a feedback mechanism between population growth rate and resource availability. We examine the local stability properties in overlapping generations resource economies which takes this feedback mechanism into account. The results indicate that Hopf bifurcation may arise without requiring logistic regeneration or unconventional constraints on parameter values. In particular, Hopf bifurcation is encountered under convex-concave dependence of carrying capacity on the resource availability.

scholarly journals Biological scaling in green algae: the role of cell size and geometry

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Helena Bestová ◽  
Jules Segrestin ◽  
Klaus von Schwartzenberg ◽  
Pavel Škaloud ◽  
Thomas Lenormand ◽  
...  
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Population Growth Rate ◽  
Internal Diffusion ◽  
Scaling Exponent ◽  
Power Scaling ◽  
Nutrient Distribution ◽  
Metabolic Scaling ◽  
Key Factor ◽  
Size And Morphology

AbstractThe Metabolic Scaling Theory (MST), hypothesizes limitations of resource-transport networks in organisms and predicts their optimization into fractal-like structures. As a result, the relationship between population growth rate and body size should follow a cross-species universal quarter-power scaling. However, the universality of metabolic scaling has been challenged, particularly across transitions from bacteria to protists to multicellulars. The population growth rate of unicellulars should be constrained by external diffusion, ruling nutrient uptake, and internal diffusion, operating nutrient distribution. Both constraints intensify with increasing size possibly leading to shifting in the scaling exponent. We focused on unicellular algae Micrasterias. Large size and fractal-like morphology make this species a transitional group between unicellular and multicellular organisms in the evolution of allometry. We tested MST predictions using measurements of growth rate, size, and morphology-related traits. We showed that growth scaling of Micrasterias follows MST predictions, reflecting constraints by internal diffusion transport. Cell fractality and density decrease led to a proportional increase in surface area with body mass relaxing external constraints. Complex allometric optimization enables to maintain quarter-power scaling of population growth rate even with a large unicellular plan. Overall, our findings support fractality as a key factor in the evolution of biological scaling.

Sign in / Sign up

Export Citation Format

Share Document