Harrod Domar model

The Harrod-Domar model is an early, simple post-Keynesian growth theory that puts the dual character of investments at the center of considerations.

On the one hand, the demand for capital goods is part of the aggregate demand (the other part is demand for consumer goods).

On the other hand, the capital stock is increased by the investments and thus the overall economic supply of goods.

Roy F. Harrod and Evsey D. Domar investigated (Harrod: 1939 and Domar: 1946) independently of one another the conditions under which an economy can grow in such a way that demand and supply coincide with one another, taking into account that demand and supply differ in different ways the investments are influenced.

Domar assumed a technically given connection between capital stock and the production volume that can be achieved with it (which in turn should be equal to total demand), Harrod assumed an investment function according to which investors try to adapt their capital stock to changes in total demand (which are satisfied by the production volume should) adapt. In terms of content, there is a difference between the two economists, but formally or mathematically it amounts to the same equations.

These equilibrium conditions can also be found generally in growth models such as the Solow model . As Keynesians , Harrod and Domar believed that an economy that is not on this path of equilibrium can only be brought back there through economic policy. Neoclassical economists, on the other hand, rely on the market forces that lead back to the equilibrium path. An interim solution consists in making it dependent on the values of certain parameters whether the equilibrium path is stable or unstable.

Assumptions

Like most other growth models, the model is based on certain assumptions that are occasionally called into question. It is a one-good parabola , that is, for the sake of simplicity, it is assumed that only one good is produced in the economy, which can then be used as a consumer good or as an investment good . The capital controversy is also answered in the sense that capital is regarded as a production factor whose input quantity can be measured in terms of material. Although the capital stock K is measured in euros, this is understood as a measure of the material amount in which capital is available ( fixed assets measured at constant prices). Capital is then simply the accumulated , heaped-up amount of capital goods. Income or production Y and consumption C are also measured in euros, but this is interpreted as the physical or material quantity of a certain good ("real", "in constant prices").

Domar model

The supply side

There is a definitional relationship between capital stock K and investments I.

The capital stock K increases by the investments I of a year. With I lest the gross investment is meant but the net investment, ie gross investment minus depreciation on the capital stock. The capital stock is on the one hand larger in the amount of the gross investment and on the other hand smaller in the amount of the depreciation. On balance, it changes in line with the net investment. The net investments can also assume values less than zero if the gross investments are less than the depreciation.

${\ displaystyle K_ {t} = K_ {t-1} + I}$

K : capital stock
I : net investment

If one moves from the discrete difference equation to the continuous consideration by considering an infinitesimally small period t , t -1, then the following applies:

${\ displaystyle {\ dot {K}} = I}$

whereby . ${\ displaystyle {\ dot {K}} = \ lim _ {\ delta \ to 0} {\ frac {K_ {t} -K_ {t- \ delta}} {\ delta}}}$

There is a technical connection between the capital stock K and the production Y.

With a certain capital stock K , a certain production amount Y can be created according to the assumed constant capital productivity 1 / v :

${\ displaystyle Y = {1 \ over v} \ cdot K}$

With a larger capital stock, more can be produced, the increase in production is (with full utilization of production capacity):

${\ displaystyle {\ dot {Y}} = {1 \ over v} \ cdot {\ dot {K}}}$

or ( capacity effect of investments ):

(1) ${\ displaystyle {\ dot {Y}} = {1 \ over v} \ cdot I}$

v : capital coefficient
1 / v : capital productivity

The investments generate production capacities on the supply side and, on the other hand, also represent part of the demand (the other part of the demand is the demand for consumer goods). In equilibrium, supply should be equal to demand.

From these equations it follows immediately:

${\ displaystyle {{\ dot {Y}} \ over Y} = {\ hat {Y}} = {{\ dot {K}} \ over K} = {\ hat {K}}}$

If there is a constant ratio between K and Y, both quantities must grow with the same growth rates. Now the growth of the capital stock is defined as investments of a period, i.e. the capital growth of this period, related to the capital stock at the beginning of this period. The greater the growth rate, the more must be invested in a period, the greater must be the share of investment in total production, the investment rate or, from the financing side, the savings rate s.

The demand side

There is no explicitly formulated consumption function (consumption as a function of income); instead, savings are directly considered which are assumed to act fully as a demand for capital goods. The part that is saved, resulting from the multiplication of the savings rate s with income Y . The savings rate s is assumed to be constant regardless of the size of the income:

Savings function , savings depending on income:

${\ displaystyle S = s \ cdot Y}$

The savings S are used to finance investments, so the following applies:

${\ displaystyle S = I}$

and thus:

${\ displaystyle I = s \ cdot Y}$

This is the demand for capital goods depending on the level of income Y.

Solved for Y ( income effect of investments ):

(2) ${\ displaystyle {\ dot {Y}} = {1 \ over s} \ cdot dI}$

If a certain income Y leads to a certain consumer demand C = c Y = (1-s) Y, then a certain investment volume (= saving volume) I gives a certain equilibrium income Y according to equation (2) on the demand side. This is the multiplier effect .

Merging of supply and demand side

Under all these assumptions one arrives at the equation of the (Harrod-) Domar model, which says that the growth of production or income Y , so that investment I must be equal to the ratio of the savings rate s to the capital coefficient v , because then and there the income effect on the demand side is equal to the capacity effect on the supply side:

By dividing equation (1) (capacity effect) by equation (2) (income effect) we get:

${\ displaystyle {{\ dot {Y}} \ over Y} = {s \ over v} = g}$

The growth rate is defined as the change in a variable in relation to its starting level, i.e. in continuous representation:

${\ displaystyle {\ hat {Y}} = {{\ dot {Y}} \ over Y} = g}$

g is the growth rate given by the economy. The formula says that the higher the investment rate (which is equal to the savings rate s), the greater the growth that can be achieved, i.e. the greater the part of production that is used to build up the capital stock. The larger the capital coefficient, the lower the growth, the more capital is required to produce a unit of production (K / Y). The growth rate s / v is also referred to as the "warranted rate of growth" because it represents the growth at which supply and demand are balanced.

Interim economic policy consideration

However, this growth does not have to coincide with the population growth, that is to say, in simplified terms, the growth in the supply of labor, which is also referred to as the "natural growth rate". If s / v is less than the growth rate of the labor supply n, then unemployment arises in the long term. If s / v is greater, then there is a shortage of labor, which can turn into an economic crisis . In the first case, the savings rate s would have to be increased in order to adapt economic growth to the growth of the workforce, in the second case s would have to be decreased. Usually it is assumed, for example according to a savings function according to Nicholas Kaldor , that the savings come primarily from capital income and less from wages. So if growth is to be increased, the profit ratio , the share of capital income in total income , must be strengthened, and vice versa, if growth is to be reduced, because the number of workers is not growing so rapidly.

If s / v = n, n is the population growth, so if the "desirable" growth given from the economic side has adapted exactly to the "natural" population growth, one speaks of the golden age following the economist Joan Robinson .

Double character of the investments

The investments have a dual character. On the one hand, the capital stock increases in the amount of the investment and thus, in accordance with the capital coefficient v, the possible production quantity, the possible supply. The so-called capacity effect is the first part of the double character.

The second part of the character is what is known as the income effect. Investments at a constant level lead to a certain constant overall economic demand Y via the multiplier effect .

In the equilibrium supply equals demand, the growth rate of national income Y according to Domar, the higher the higher the savings rate and the smaller the capital coefficient v . This contradicts Keynes, who blames a high savings rate for weak growth. The reason for this is that, according to Keynes, saving and (desired) investing do not necessarily have to match, while Domar assumes that the savings all lead to investments.

If a certain growth rate is given, for example by an exogenously assumed population growth n, then a problem arises. It would be a coincidence if s and v had exactly the values that lead to the desired growth. Further explanations are needed that indicate how s / v can be adjusted to the value n . In these explanations, the various theories differ (e.g. Keynesian versus neoclassical approaches). State economic policy is necessary for Keynesians ; from the neoclassical point of view, the market itself generates forces that lead to an adjustment.

Harrod model

In the Domar model, v is a technical parameter. There are no assumptions about the behavior of companies. Harrod now shows the conditions that lead to growth without underutilized (or overused) capacities ( warranted rate of growth , desirable growth rate) by introducing an investment function as a behavioral equation . The companies make their decisions about the investment volume dependent on the change in demand ( accelerator function ):

${\ displaystyle I = v \ cdot {\ dot {Y}}}$ ( represents the expected change in demand per unit of time. Simplified, it is assumed that the expected change in demand is equal to the last observed change in demand.) ${\ displaystyle {\ dot {Y}}}$

After resolved: ${\ displaystyle {\ dot {Y}}}$

(1) ${\ displaystyle {\ dot {Y}} = {1 \ over v} \ cdot I}$

With the condition that I must be equal to S , we also arrive at the desired growth rate in this model. The savings S are in turn used to finance investments, so that: ${\ displaystyle S = s \ cdot Y}$

${\ displaystyle S = I}$

and thus:

${\ displaystyle I = s \ cdot Y}$

Solved for Y :

(2) ${\ displaystyle Y = {1 \ over s} \ cdot I}$

Again equation (1) divided by equation (2):

${\ displaystyle {{\ dot {Y}} \ over Y} = {\ hat {Y}} = {s \ over v} = g}$

Mathematically or formally, this corresponds to the Domar result with the difference in content that this time it represents a behavioral parameter of the companies. ${\ displaystyle v}$

Economic fluctuations in the Harrod model

The Harrod model contains an investment function, the level of investment is proportional to the change in national income:

${\ displaystyle I = v \ cdot {\ dot {Y}}}$ ( represents the change in demand) ${\ displaystyle {\ dot {Y}}}$

Consumption C is proportional to national income Y :

${\ displaystyle C = (1-s) \ cdot Y}$

In addition, national income Y is the sum of consumption C and investments I :

${\ displaystyle Y = C + I}$

If the investments I and the consumption C react according to these equations, but with a time lag (so-called time lags), then different cases can arise depending on the size of s and v :

growth implodes
growth explodes
dampened growth vibrations
exploding growth vibrations
as a borderline case constant growth oscillations

By introducing time lags, the Harrod-Domar model can be further developed into a business cycle model (Samuelson-Hicks model or multiplier-accelerator model ).

"Growth on the knife edge"

As a rule, the economy will not be exactly at a point of “desirable growth”, but rather far away from it. Additional assumptions then have to be made about how economic operators react to an imbalance between supply and demand.

For example, if the production potential is greater than the demand, companies will want to invest less because they have underutilized capacities. However, this reduces the demand even further, so that the problem repeats itself in the next period. A worsening downturn is conceivable. At least that was the rather pessimistic opinion of the Keynesians. However, a lack of investment also means that the capital stock is shrinking, including production potential. Finally, the shrinking production potential could fall below the also falling overall demand, so that investments are now in demand again. This would be the lower turning point of an economic fluctuation.

In any case, the companies' reaction functions can also be formulated so that the equilibrium tendency prevails, that is, under certain conditions the economy tends to return to the equilibrium growth path of its own accord. The Harrod-Domar model is an equilibrium model in the sense that it examines the conditions under which equilibrium growth could take place. How the economy reacts when it is not in equilibrium must be examined in its own imbalance models. The difference between Keynesianism and Neoclassicism is not based on the actually tautological equilibrium conditions of the model, which are also found in other schools of economics - for example in the Solow model - but on the question of how this equilibrium path can be turned: through state intervention or through the free play of market forces.

Comparison of Domar and Harrod

The equilibrium solutions of Harrod and Domar agree mathematically and formally . The difference is the use of the technical capital coefficient v by Domar and the behavioral accelerator v by Harrod. Therefore, the two models are often combined. Other economists emphasized the differences more.

In your opinion, the fact that the capital coefficient and accelerator are quite different in terms of content is neglected .

Harrod's accelerator v is a behavioral parameter. The change in demand is the independent variable, investment and the associated change in the capital stock or production capacity is the dependent one.

Domar assumes the technically given capital productivity 1 / v. The capital stock and related production are the independent variable. Demand is the dependent variable. It is to be determined in such a way that it takes place in step with the growth of the capital stock and thus of the potential supply.

In the case of the capital coefficient v, nothing is said about the trigger of investments; autonomous (not explained in detail) as well as induced (depending on other variables) components can be included in the investments. The capital coefficient is a production-related quantity that does not make any statements about the behavior of entrepreneurs. The accelerator, on the other hand, contains the investments induced by the change in demand, but no autonomous components and thus describes entrepreneurial behavior.

Harrod's model is demand-driven and seeks to infer the conditions under which demand will cause the capital stock to grow necessary to meet that demand. Domar's model, on the other hand, is supply-oriented and formulates the need for demand that is constantly growing at a certain rate, which also decreases the supply, which is constantly growing via capacity effects.

Critical appraisal

The models clearly influenced economic policy in the 1950s and 1960s. The World Bank, for example, used the models for calculating the capital requirements for foreign aid. In their general form with a tautological character, however, they are still of influence today. With their help, both a moderate (moderating) and an expansive wage policy can be established. The first case would apply if one assumes that rising unemployment is the result of weak growth, that therefore the savings rate must be increased, hence the profit rate as well , because the savings come primarily from profit income (e.g. according to the savings function by Nicholas Kaldor ). Seen in this way, the "Keynesian" model is not union friendly.

The second case could play a role in an imbalance situation with a worsening downturn. If companies cut investment, which in turn lowers demand, so that overcapacities persist, which leads to further investment cuts, etc., then the purchasing power argument of wages could be used to stabilize demand through rising wages, which would stop the downturn could.

In the Domar version, the model assumes a constant capital coefficient v. Empirically, however, it can be observed that the capital coefficient has gradually increased in the OECD, for example. Since economic growth is determined by s / v, increasing v means decreasing economic growth , which can also be observed worldwide in the long term. This could be remedied by increasing the savings rate s, so that the growth rate s / v is stabilized. Indeed, since the 1980s , neoliberalism has been about increasing the propensity to save by increasing the profit ratio in economies in the hope that this will also increase the investment ratio (according to the GIB formula ). According to a study by the IMF , however, this has not been the case worldwide since the 1970s , and the investment rate has decreased.

The growth policy comes after Domar and Harrod the task of long-term stabilization of the market economy by influencing the demand for. The countercyclical fiscal policy must be used according to the teachings of Keynesianism for the short-term maintenance of the balance.

It is unsatisfactory in both models that the growth and its causes are not explained in more detail. A natural growth rate is taken into account, but it is simply given by the exogenously considered population growth. Therefore, nowadays the theories are not viewed as theories of growth in the actual sense, but merely as an important building block for them, as a derivation of the conditions under which equilibrium growth is possible. The models are normative . The achievement of this norm must be effected either technocratically or by market forces themselves.

Technical progress

Mathematical formulation

Technological progress can be easily introduced into the Harrod-Domar model. The equation for the " golden age ", in which the growth rate determined from the economic side corresponds to population growth, the growth in labor supply, was:

${\ displaystyle {s \ over v} = n}$

n: exogenously given growth rate of the population, n stands for “natural”.

Growth rate of production or income:

${\ displaystyle {{\ dot {Y}} \ over Y} = {\ hat {Y}} = {s \ over v} = n}$

The growth rate of the capital stock is the same:

${\ displaystyle {{\ dot {K}} \ over K} = {\ hat {K}} = {s \ over v} = n}$

With technical progress it is now simply assumed that labor productivity , the amount Y that a worker produces, increases at a certain rate m. Because of technical progress, the number of workers required is now shrinking at the rate m. It is no longer sufficient if the economy, i.e. production Y and capital stock K, grows with the natural growth rate, the growth rate n of the population, it must also grow by the growth rate m of technical progress if unemployment is not to arise. The equation for the `` Golden Age '' is now:

${\ displaystyle {s \ over v} = m + n}$

${\ displaystyle {{\ dot {Y}} \ over Y} = {\ hat {Y}} = {s \ over v} = m + n}$

${\ displaystyle {{\ dot {K}} \ over K} = {\ hat {K}} = {s \ over v} = m + n}$

That is, both labor productivity (Y per worker) and capital intensity (K per worker) grow with the rate of technical progress m. Every worker produces more and more at the rate m, but also needs an ever larger capital stock, which per worker also grows at the rate m.

If the capital coefficient v is given technically, the savings rate s must be higher, the greater the rate of technical progress m, if a certain growth in labor supply n is to be absorbed by the economy in order to avoid unemployment. If the savings rate s is not large enough to achieve this growth, then the number of workers required does not increase at the required rate; it could even shrink if s / v is less than m. Technical progress can lead to the destruction of jobs.

Numerical example

No technical progress

Labor A, capital K and production Y all grow at a certain rate, here 5% is assumed.

A number of workers
C number of consumer goods
C / A real wages : consumer goods per worker
K capital stock
N / A capital intensity
Y production
Y / A labor productivity per capita
K / Y capital coefficient

The production of one period is used to supply the workers with consumer goods (C) and means of production (K) in the next period. Then the production repeats itself on an ever larger scale from period to period. The division of production between K and C or A is based on the technically given capital intensity K / A, which is assumed to be a technically given constant.

In the following numerical example, the initial values of period 1 are assumed exogenously. For some quantities there are exogenous assumptions about how they change. These sizes are marked in blue in the second table. The capital intensity K / A remains unchanged and thus no change in labor productivity Y / A is triggered. In addition, the real wage C / A is kept constant. The remaining quantities are then calculated on the assumption that production is used in full for the next period as wages C and capital K.

period	A.	C.	C / A	K	N / A	Y	Y / A	K / Y
-	-	€	€	€	€	€	€	-
1	100.0	280.95	2.8095	100.0	1.00	400.0	4,000	0.25
2	105.0	295.0	2.8095	105.0	1.00	420.1	4,000	0.25
3	110.3	309.8	2.8095	110.3	1.00	441.0	4,000	0.25
4th	115.8	325.2	2.8095	115.8	1.00	463.1	4,000	0.25
5	121.6	341.5	2.8095	121.6	1.00	486.2	4,000	0.25
6th	127.6	358.6	2.8095	127.6	1.00	510.5	4,000	0.25

In period 2 the gross investments amount to K = € 105.0. Of this, € 100.0 is replacement or depreciation of the investments made in previous period 1 (€ 100.0). The net investments are therefore € 105.0 - € 100.0 = € 5.0. These net investments are to be related to the income of the previous period 1 Y = 400.0 €, as they are financed from this. The result is a savings rate of s = 5/400 = 1.25%. v is 0.25 or 25%. s / v gives 0.05 or 5%, the growth rate n of the economy and employment.

Production Y, number of workers required A, consumption of workers C and the capital stock K all grow annually by 5%, while real wages C / A, labor productivity Y / A and the capital coefficient v K / Y are constant.

W (...) growth rate in%

period	W (A)	WC)	W (C / A)	W (K)	W (K / A)	W (Y)	W (Y / A)	W (K / Y)
1	-	-	-	-	-	-	-	-
2	5	5	0	5	0	5	0	0
3	5	5	0	5	0	5	0	0
4th	5	5	0	5	0	5	0	0
5	5	5	0	5	0	5	0	0
6th	5	5	0	5	0	5	0	0

With technical progress

Labor productivity is now expected to increase by 5% annually. This is brought about by the assumption that an annual growth in capital intensity of 5% will do just that (cf. also technical progress function ). For the sake of simplicity, a productivity- oriented wage policy is assumed for wages , so that real wages grow at the same rate as labor productivity, i.e. at an annual rate of 5%. Because of the increasing capital intensity, the production surplus is no longer sufficient to create additional jobs; instead, employment A remains constant at 100. So there is “jobless growth”.

The table is now calculated in such a way that, due to technical progress, labor productivity Y / A grows annually by 5%, this is caused by a growth in capital intensity K / A of 5% annually. This also determines the real wage in accordance with productivity- oriented wage policy ; it grows just like labor productivity. The product Y of a period is now divided into C or A and K for the next period in accordance with the capital intensity K / A taking into account what A costs, i.e. taking into account the real wage C / A.

period	A.	C.	C / A	K	N / A	Y	Y / A	K / Y
-	-	€	€	€	€	€	€	-
1	100.0	280.95	2.8095	100.0	1.00	400.0	4,000	0.25
2	100.0	295.0	2.95	105.0	1.050	420.0	4,200	0.25
3	100.0	309.8	3.10	110.3	1.103	441.0	4,410	0.25
4th	100.0	325.2	3.25	115.8	1.158	463.1	4,631	0.25
5	100.0	341.5	3.41	121.6	1.216	486.2	4.862	0.25
6th	100.0	358.6	3.59	127.6	1.276	510.5	5.105	0.25

In period 2 the gross investments amount to K = € 105.0. Of this, € 100.0 is replacement or depreciation of the investments made in previous period 1 (€ 100.0). The net investments are therefore € 105.0 - € 100.0 = € 5.0. These net investments are to be related to the income of the previous period 1 Y = 400.0 €, as they are financed from this. The result is a savings rate of s = 5/400 = 1.25%. v is 0.25 or 25%. s / v gives 0.05 or 5%, the growth rate m of the economy. This growth is due to technical progress, which is growing at a rate m while employment remains constant.

The causality runs from increasing capital intensity to increasing labor productivity. It is assumed that if the technical equipment of a worker increases by 5%, i.e. the capital intensity increases by 5%, this also causes an increase in labor productivity of 5%. By providing the workforce with more means of production, they are also able to produce more.

period	W (A)	WC)	W (C / A)	W (K)	W (K / A)	W (Y)	W (Y / A)	W (K / Y)
1	-	-	-	-	-	-	-	-
2	0	5	5	5	5	5	5	0
3	0	5	5	5	5	5	5	0
4th	0	5	5	5	5	5	5	0
5	0	5	5	5	5	5	5	0
6th	0	5	5	5	5	5	5	0

If one further assumes that the natural growth rate, the growth rate of the population, is n.5%, then in this scenario unemployment would increase because an increasing supply of labor meets a constant demand from the economy for work. If one continues to assume that workers spend their income fully on consumer goods, but companies save their income fully and invest, then a one-off wage cut can help. The uniqueness consists in the fact that in one period the wage is reduced, but then a productivity-oriented wage policy is followed again. However, the one-time wage waiver will remain forever, the wage growth curve will never catch up with the old higher curve. In the following example it is assumed that the real wage of the workers in the first period is no longer 2.8095 C per worker, but only 2.63 C per worker. Since production in this period is still set at 400 Y, more can now be invested. With the increase in capital intensity of still 5% - so the assumption - there is still something left to create additional jobs to make expansion investments. The number of jobs required is now increasing by 5%, as is the demographically given job supply. The '' Golden Age '', i.e. growth with full employment, has been restored, since a growth in the labor supply of 5% was assumed exogenously given.

period	A.	C.	C / A	K	N / A	Y	Y / A	K / Y
-	-	€	€	€	€	€	€	-
1	100.0	262.8	2.63	100.0	1.00	400.0	4,000	0.25
2	105.0	289.7	2.76	110.25	1.050	441.0	4,200	0.25
3	110.3	319.5	2.90	121.6	1.103	486.2	4,410	0.25
4th	115.8	352.2	3.04	134.0	1.158	536.1	4,631	0.25
5	121.6	388.3	3.19	147.8	1.216	591.1	4.862	0.25
6th	127.6	428.1	3.35	162.9	1.276	651.7	5.105	0.25

In period 2 the gross investments are K = € 110.25. Of this, € 100.0 is replacement or depreciation of the investments made in previous period 1 (€ 100.0). The net investments are therefore € 110.25 - € 100.0 = € 10.25. These net investments are to be related to the income of the previous period 1 Y = 400.0 €, as they are financed from this. The result is a savings rate of s = 10.25 / 400 = 2.56%. v is 0.25 or 25%. s / v gives 0.1025 or 10.25%, the growth rate of the economy, which results from the growth of technical progress m and employment n.

Employment A grows by 5%, a growth of 5% was also assumed for technical progress, so that labor productivity and capital intensity also grow by 5%. According to the formula

${\ displaystyle {s \ over v} = m + n}$

Production Y, capital K and consumption of workers C now grow at the rate of 5% plus 5%, i.e. 10%. However, the formula was derived for the continuous case, here in the numerical example there are discrete periods, so that the formula only applies approximately. Y, K and C grow by 10.25% (1.05 times 1.05 = 1.1025).

period	W (A)	WC)	W (C / A)	W (K)	W (K / A)	W (Y)	W (Y / A)	W (K / Y)
1	-	-	-	-	-	-	-	-
2	5	10.25	5	10.25	5	10.25	5	0
3	5	10.25	5	10.25	5	10.25	5	0
4th	5	10.25	5	10.25	5	10.25	5	0
5	5	10.25	5	10.25	5	10.25	5	0
6th	5	10.25	5	10.25	5	10.25	5	0

literature

RGD Allen: Macro-Economic Theory : A Mathematical Treatment. Macmillan, London / Melbourne / Toronto 1968.

Lutz Arnold: Growth Theory . Vahlen Verlag, Munich 1997, ISBN 3-8006-2242-4 .

J. Kromphardt: Growth Theory III: postkeynesian . In: Willi Albers (Ed.): Concise Dictionary of Economics , Volume 8. Stuttgart, ISBN 3-525-03149-1

Michael Frenkel, Hans-Rimbert Hemmer : Foundations of the growth theory . Verlag Vahlen, Munich 1999, ISBN 3-8006-2396-X , pp. 9–25,

The original essays by Harrod and Domar as well as other interesting articles on this topic can be found as a German translation in:

H. König (Hrsg.): Growth and development of the economy . Cologne / Berlin 1968, p. 55 ff.

Web links

Analysis of the IMF on investment and saving behavior (PDF; 285 kB; English)