Computational Economics: A concise introduction (Routledge Advanced Texts in Economics and Finance) by Afonso Oscar & Vasconcelos Paulo B

Author:Afonso, Oscar & Vasconcelos, Paulo B. [Afonso, Oscar]
Language: eng
Format: epub
ISBN: 9781317508656
Publisher: Taylor and Francis
Published: 2015-08-26T21:00:00+00:00

Transitional dynamics: the Solow diagram

From (9.2) and (9.4) the denominated Solow diagram can be depicted (Figure 9.1). This diagram can be used to understand how per capita output evolves over time, taking into account an economy that starts out with a given stock of capital per worker, k0, and a given population growth rate, depreciation rate and investment. The Solow diagram consists of two curves, plotted as functions of k(t).

The first curve, y(t) = f(k(t)) = k(t)α, is the production function. The second curve is the amount of per capita investment, sy(t) = sk(t)α, which has the same shape as the production function, but is shifted down by the factor s. The third curve is the line (δ+n)k(t), which represents the amount of new per capita investment required to keep the amount of per capita capital constant. Indeed, both depreciation and the growing labour force tend to reduce the amount of per capita capital. The difference between these two curves is the change in the amount of per capita capital. When this change is positive and the economy is increasing its per capita capital, it is said that capital deepening is occurring. When the difference is zero, the per capita change is zero, but the capital stock, K, is growing (due to population growth), and it is said that only capital widening is occurring.

Figure 9.1 Solow diagram.

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