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» Economics » Economic theory » Topics begins with S » Solow model

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The Solow model is an economical model for the explanation of the long-term growth of a national economy. The central statement of the Solow model is that only the speed of the technical progress is long-term for durable economic growth of importance. Therefore growth politics can be only successful in the long term, if it favours the technical progress. The model became of Robert Merton Solow (1956) and Trevor Swan (1956) develops.

It is an important component of the neoclassical growth theory and developed from the criticism that the Determinaten of the economic growth was not regarded e.g. in the Harrod Domar model. With Harrod and Domar also the goods complementary needed for the capital are excluded like the worker and/or the "natural" growth of the work offer is exogenously accepted and the economic growth has itself e.g. over the rate of saving to adapt.

Derivation of the Solow model

The Solow model explains growth as consequence made of use of technology, work and principal in a national economy. The central acceptance is that growth converges on a long-term basis against an equilibrium, in which the investments into the capital stick equal to the writings-off from the capital stick is. That is a plausible acceptance, since in this equilibrium the cast-off machines straight are replaced by new. From it it results that the national economy grows, if the investments are larger than the writings-off and that them shrink, if the investments are smaller than the writings-off.

Further acceptance are met to that extent that the pro head capital stick sinks with a rising population growth, since the entire existing income must be distributed on more heads. In addition a rate of the technical progress is indicated in the national economy, which lets the existing capital stick become outdated.

The model comes to the result that the growth of each national economy converges against a point given on a long-term basis, that by the investments in the national economy, the constant writing-off rate, which is determined population growth and the rate of the technological progress. Thus the national economy grows on a long-term basis must technological progress be present.

Mathematical description of the Solow model

Mathematically for the computation of the Solow model a Cobb Douglas function is taken to the assistance, that describes the economical output as follows:

\ mathbf {Y = A * F (K, L) = K^ \ alpha * (aluminium) ^ {1 \ alpha}}

The equation for the Solow model is reached by a set of shapings and assumptions. Thus the output function is rewritten as Pro-Kopf-Einkommen:

\ mathbf {\ frac {Y} {L} = \ left (\ frac {K} {L} \ right) ^ \ alpha} \ Leftrightarrow y = k^ \ alpha = f (k)

It is accepted that there is a rate of saving s, which describes the portion pro head of the income (and thereby invested) becomes saved, a writing-off rate \ mathbf {\ delta}, which seizes the purge of the existing capital stick, the population growth n and the rate of the technological progress G.

In the long-term equilibrium (Steady state level of the national economy) it must apply that the investments equal to the writings-off plus the population growth and the rate of the technological progress is (a result, which corresponds also to the Harrod Domar model):

\ mathbf {s*f (k) = (\ delta + n + g) * k} \ mathbf {\ Leftrightarrow s*f (k) - (\ delta + n + g) * k = 0}

Golden rule of the capital accumulation

The golden rule of the accumulation describes that rate of saving in a national economy, by which the consumption is maximized. Mathematically the optimal rate of saving results as derivative of the motion equation of the Solow model after the variable k.

Development of the theory

Robert Solow could prove the empirical evidence of the Solow model to 1957 on the basis growth data of the USA. In addition it used methodically the so-called Solow residues, also as total factor productivity designation, in order to constitute the portion of the technological progress from the total growth of a yearly. It turned out that the largest portion of growth not on work or capital factors separate annual to the technological progress to due is.

Criticism at the theory and advancement

The Solow model is criticized for the 80's, before all of the advocates of endogenous growth. In the center of the criticism the convergence of the growth of a national economy in the Solow model was located. This means that poorer national economies unlock on a long-term basis to the wealthier, since they can grow without larger troubles faster. This convergence could not be proven however in all national economies. To the cases of converging growth belong above all the market managing made of Europe, North America and - up to the financial crises in the 90's - the so-called tiger states made of Southeast Asia. Besides the computed convergence speeds are too high and the model supply only useful results for 20. Century. One goes having far back the results no more significance.

A further point of criticism is the fact that in the Solow model the technological progress than only factor of long-term growth is called, the model however avowedly like these comes. Technological progress is regarded as exogenously given and is not explained therefore by the model.

The criticism to exogenous technological progress takes up the endogenous growth theory. Around the further mentioned above points of criticism at the Solow model to eliminate have Mankiw, Romer and because 1992 publish a revised version of the model, which includes the factor human capital and education also into the computation of growth. The problems of missing convergence and exaggerated convergence speeds are explained exactly thereby.

Finally the Solow model was criticized as in property parabola. Some results model leave itself not to generalize, if one of (unexpressed) the acceptance of a national economy, which only one property "Y" produced, which can be used then as consumer ("C") or Investitionsgut ("I"), to the realitynear acceptance of a national economy, in which "goods are manufactured by means of goods" (Piero Sraffa), turn into.


  • Robert Merton Solow: "A Contribution ton the Theory OF Economic Growth "in Quarterly journal OF Economics volume 70, 1956, P. 65-94
    • German translation: King, H. (Hrsg.): "A contribution for the theory of economic growth "in growth and development of the economy, Cologne, 1968, P. 67-96

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