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Population growth and the Solow-Swan model
One of the key elements in any standard economic growth theory is that population growth is exponential with a constant rate n > 0. This simple model can provide an adequate approximation to such growth only for the initial period because, growing exponentially, population approaches infinity when t goes to infinity, which is clearly unrealistic. The exponential model does not accommodate growth reductions due to competition for environmental resources such as food and habitat. In this paper we reformulate the neoclassical Solow model of economic growth by assuming that the law describing population growth verifies two stylized facts: 1) population is strictly increasing and bounded and 2) the rate of growth of population is strictly decreasing to zero. The main result of the paper is the proof of the convergence of capital per worker to a constant value independently of the initial condition. This constant value coincides with the steady state of the original Solow model with zero population growth rate.
Solow-Swan model; population models
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