Sunday, March 27, 2011

How Do You Turn Yourself Into A Wolf

Solow model - steady state balance equations

The steady model is the condition of the completion of capital increase reflected in the equation of motion for capital per capita, which ends with a fixed capital without additional changes.

\begin{cases} \dot{k} =0 \ sy = (n+g+\delta)k \ y=f(k) \end{cases}


As it is assumed that the previous system will feature a unique solution and the per capita income levels effective, capital per capita cash, savings rate, rate of technological change and the same depreciation rate determine the called state of equilibrium or steady state of the Solow model.


Diagram Solow growth model
Equilibrium in the Solow model is the path to convergence of the countries: an economy through the ownership of diminishing marginal returns, production tends to decrease marginally, or, in other words, the total production grows increasingly less. It also tends to grow less, which eventually makes them equals. This condition keeps the per capita capital stock steady cash, unchanged. However, in steady state, it can be said that output per capita grows at the rate of growth of technology and total output grow at the rate of population growth and technology. The contribution of these exogenous variables fail to explain the growth in the long term, ie, when the economy reaches its steady capital.
This is the main chart of the Solow model and shows that in the long run equilibrium. The reason for convergence is that and is equal to the function of per capita GDP has diminishing returns, so the investment function effectively. Thus, diminishing returns to capital per capita mean that there is a convergence between replacement investment and actual investment. In the graph, k "EST" represents the steady state capital and, therefore, the state stationary product.

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