Growth Dynamics and Returns to Scale: Bifurcation Analysis |
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| Affiliation: | 1. Research Unit of Psychiatry, Odense University Hospital/Department of Clinical Research, University of Southern Denmark, Odense, Denmark;2. Institute of Clinical Research and OPEN [Odense Patient data Explorative Network], Odense University Hospital/Department of Clinical Research, University of Southern Denmark, Odense, Denmark;3. Mental Health Services in the Region of Southern Denmark, Odense, Denmark;4. Department of Psychiatry, Schizophrenia Treatment Research Laboratory, University of Rochester Medical Center, Rochester, NY;5. Office for Aging Research and Health Services and Department of Psychiatry, University of Rochester Medical Center, Rochester, NY;1. Institut Universitari de Matemàtiques i Aplicacions de Castelló, Universitat Jaume I, Castelló, Spain;2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Vallès 08193, Barcelona, Spain;3. Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra. Cerdanyola del Vallès 08193, Barcelona, Spain;4. Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain;5. Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra. Cerdanyola del Vallès 08193, Barcelona, Spain |
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| Abstract: | We investigate the dependence of the dynamic behavior of an endogenous growth model on the degree of returns to scale. We focus on a simple (but representative) growth model with publicly funded inventive activity. We show that constant returns to reproducible factors (the leading case in the endogenous growth literature) is a bifurcation point, and that it has the characteristics of a transcritical bifurcation. The bifurcation involves the boundary of the state space, making it difficult to formally verify this classification. For a special case, we provide a transformation that allows formal classification by existing methods. We discuss the new methods that would be needed for formal verification of transcriticality in a broader class of models. Journal of Economic Literature Classification Numbers: O41, O30. |
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