Rethinking the Concept of Long-Run Economic Growth

This paper argues that growth theory needs a more general “regularity” concept than that of exponential growth. This offers the possibility of considering a richer set of parameter combinations than in standard growth models. Allowing zero population growth in the Jones (1995) model serves as our illustration of the usefulness of a general concept of “regular growth”.exponential growth, arithmetic growth, regular growth, semi-endogenous growth, knife-edge restrictions

Rethinking the Concept of Long-Run Economic Growth

This paper argues that growth theory needs a more general “regularity” concept than that of exponential growth. This opens up for considering a richer set of parameter combinations than in standard growth models. Allowing zero population growth in the Jones (1995) model serves as our illustration of the usefulness of a general concept of “regular growth”.exponential growth; arithmetic growth; regular growth; semi-endogenous growth; knife-edge restrictions

Knife-edge conditions in the modeling of long-run growth regularities

Balanced (exponential) growth cannot be generalized to a concept which would not require knife-edge conditions to be imposed on dynamic models. Already the assumption that a solution to a dynamical system (i.e. time path of an economy) satisfies a given functional regularity (e.g. quasi-arithmetic, logistic, etc.) imposes at least one knife-edge assumption on the considered model. Furthermore, it is always possible to find divergent and qualitative changes in dynamic behavior of the model – strong enough to invalidate its long-run predictions – if a certain parameter is infinitesimally manipulated. In this sense, dynamics of all growth models are fragile and "unstable".knife-edge condition, balanced growth, regular growth, bifurcation, growth model, long run, long-run dynamics

Knife-Edge Conditions in the Modeling of Long-Run Growth Regularities

Balanced (exponential) growth cannot be generalized to a concept which would not require knife-edge conditions to be imposed on dynamic models. Already the assumption that a solution to a dynamical system (i.e. time path of an economy) satisfies a given functional regularity (e.g. quasi-arithmetic, logistic, etc.) imposes at least one knife-edge assumption on the considered model. Furthermore, it is always possible to find divergent and qualitative changes in dynamic behavior of the model – strong enough to invalidate its long-run predictions – if a certain parameter is infinitesimally manipulated.knife-edge condition, balanced growth, regular growth, bifurcation, growth model, long-run dynamics

When Economic Growth is Less than Exponential

This paper argues that growth theory needs a more general notion of “regularity” than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set of parameter combinations than in standard growth models. And it avoids the usual oversimplistic dichotomy of either exponential growth or stagnation. Allowing zero population growth in three different growth models (the Jones R&D-based model, a learning-by-doing model, and an embodied technical change model) serve as illustrations that a continuum of “regular” growth processes fill the whole range between exponential growth and complete stagnation.quasi-arithmetic growth; regular growth; semi-endogenous growth; knife-edge restrictions; learning by doing; embodied technical change

What is good mathematics?

Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer\'edi's theorem is presented.Comment: 12 pages, no figures. To appear, Bull. Amer. Math. So