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Population growth and the depreciation rate

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Population growth and the depreciation rate

In this figure, the steady-state can then be explained. Y =f(k) is the production function, which depicts that the output per worker increases at a diminishing rate as k increases as per the law of diminishing returns. The sf (k) curve shows the savings per worker while the (n + d) k is the investment requirement line, which has a positive slope equal to (n + d). In this diagram, the steady-state is achieved at point E, where the sf (k) curve intersects the (n+d)k, showing that the savings per worker and investment per worker are equal.

In the question, we are assuming that the sum of the population growth and the depreciation rate, (n + d) k, is less than the savings rate expressed as sf (k). With this, we can conclude that such an economy does not converge at a steady state. This situation is explained by an economy that starts the capital-labor ration at k1. At this point, savings per worker k1B are more than the investment necessary to maintain the capital-labor ratio constant, hence convergence is not at a steady state.

 

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