The most economics students learn solow growth model.

Notebook for solow model

https://github.com/jonduan/Economics_note/blob/master/macroeconomics/ECON453-Solow.ipynb

Quick summary of Solow (1956)

The following summary of the Solow model of economic growth largely follows Romer (2011).

Romer (2011): http://highered.mheducation.com/sites/0073511374/index.html

Solow (1956): http://piketty.pse.ens.fr/files/Solow1956.pdf

The production function

The Solow model of economic growth focuses on the behavior of four variables: output, Y, capital, K, labor, L, and knowledge (or technology or the “effectiveness of labor”), A. At each point in time the economy has some amounts of capital, labor, and knowledge that can be combined to produce output according to some production function, F.

$$Y(t) = F(K(t), A(t)L(t))$$

where t denotes time.

The evolution of the inputs to production

The initial levels of capital, :math:$K_0$, labor, :math:$L_0$, and technology, $A_0$, are taken as given. Labor and technology are assumed to grow at constant rates:

$\dot{A}(t) = gA(t)$ $\dot{L}(t) = nL(t)$

where the rate of technological progrss, g, and the population growth rate, n, are exogenous parameters.

Output is divided between consumption and investment. The fraction of output devoted to investment, 0 < s < 1, is exogenous and constant. One unit of output devoted to investment yields one unit of new capital. Capital is assumed to decpreciate at a rate $0\le \delta$. Thus aggregate capital stock evolves according to

$$\dot{K}(t) = sY(t) - \delta K(t).$$

Although no restrictions are placed on the rates of technological progress and population growth, the sum of g, n, and :math: $\delta$ is assumed to be positive.

The dynamics of the model

Because the economy is growing over time (due to exogenous technological progress and population growth) it is useful to focus on the behavior of capital stock per unit of effective labor

$$k \equiv K/AL.$$

Applying the chain rule to the equation of motion for capital stock yields (after a bit of algebra!) an equation of motion for capital stock per unit of effective labor.

$$\dot{k}(t) = s f(k) - (g + n + \delta)k(t)$$

That’s it! The Solow model of economic growth reduced to a single non-linear ordinary differential equation.

Short version of Romer textbook

http://www.reed.edu/economics/parker/314/notes/314-notes-solow.pdf

http://www.reed.edu/economics/parker/314/Coursebook/ch02-2017.pdf

http://www.reed.edu/economics/parker/314/Coursebook/ch04-2017.pdf

http://www.reed.edu/economics/parker/s11/314/book/Ch03.pdf

http://www.reed.edu/economics/parker/s11/314/book/Ch04.pdf

https://github.com/solowPy/solowPy

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