Chapter 7 The theoretical foundations of the growth policy part II






01st Growth theory, a sufficient foundation?

02nd The main determinants of growth

03rd The importance of natural resources

04th The quantitative increase of the quantity of labour

05th The improvement of the quality of labour

06th Intensive growth and labour input

07th Capital and post-Keynesian growth theory

08th Capital and neoclassical growth theory

09th Savings promotion versus investment promotion

10th Economic growth and capital structure

11th The role of technical progress

12th Stagnation on account of a too low demand?




07th Capital and post-Keynesian growth theory


The significance of the capital investment for the growth rate of the domestic product can be derived - based on the Keynesian theory - from the following equations: The starting point is the identity equation:


I = S,


whereat I corresponds to the investment amount and S to the savings amount.


 We now insert the determinants of S and I. Understood as a growth parameter, the investment volume (I) represents nothing else than the change in capital investment (dK).

I = dK


The capital investment (dK) may increase on one side because a larger capital investment (dK/dY) is required per domestic product unit, and on the other side because the domestic product (dY) has increased:


dK  = dK/dY * dY



Since in the framework of a Keynesian theory the savings amount (S) depends solely on the level of the national income (Y), we can replace the term (S) with the term: (s * Y):


S = s * Y


We now insert the values thus obtained for S and I into the identity equation:




Furthermore, we isolate (s) by dividing both sides of the equation by (Y):





dK/dY corresponds, however, to the capital output ratio (ß):


dK/dY = ß


 ß: capital output ratio



If we insert the value for (dK/dY) in our equation and put this term on the right side, we finally obtain the equilibrium condition of the Keynesian growth theory:


dY/Y = s/ß


Within the framework of the Keynesian theory, the growth rate of the domestic product thus depends solely on two factors. If the savings rate rises, equilibrium growth can only be achieved if the growth rate of the domestic product rises as well. If, however, the capital output ratio rises, the growth rate of the domestic product must decline if equilibrium growth shall be made possible.


In the framework of Keynesian theory, it is generally assumed that the capital output ratio is constant, at least in the short term. Under this assumption, the sole determinant of growth is therefore the saving.


However, this does not mean that thereby Keynes' basic statement, according to which saving was a burden on the economy, as saving led to unemployment, was turned into its opposite, the way that saving would now be regarded as growth-enhancing and thus as a virtue.


We remember: Keynes assumes that whenever the savings amount exceeds the investment amount, the savings amount is adjusted to the too low investment amount by decreasing the income until the savings amount corresponds to the investment amount. Thus, the growth rate of the domestic product is ultimately determined by the level of investment. And then it is the investment that forces an increase in savings.


The following policy conclusions were drawn from these considerations: growth of the domestic product can be achieved primarily by investment incentives. However, it should be noted critically that an increase in the investment itself can in turn lead to an increase in the capital output ratio and in this way the opportunities for economic growth can be reduced again. Thus, in this case it is doubted whether the capital output ratio can be regarded actually as constant.



08th Capital and neoclassical growth theory


By contrast, R. M. Solow and J. Meade take the following view to this:


Only the growth level, not the growth rate, depends on the level of capital investment. The starting point is a production function of the Cobb-Douglas type:


X = b*Aa *K1-a



        X :     real social product

        A :    labour input in hours

        K :    capital investment in quantity units

        b,α :  structural parameters.


The following assumptions are now made:


The domestic product is dependent on labour (A) and capital (K).


There is a neutral technical progress.


A partial differentiation of the production function:

X  =  b*Aa *K1-a







The total differential, on the contrary, results from the sum of the partial derivatives:



We shorten the equation by X and get:



If we now assume a neutral technical progress, the growth rates of the capital and the domestic prod-uct coincide, because K/X is only constant if dX/X = dK/K.    


The starting point of our analysis is the total differentiation of X:

dX/X= [a * dA /A] +[(1- a) * dK /K] + [ db/b].


We now replace dK/K with dX/X:

dX/X= [a * dA /A] +[(1- a) * dX/X] + [ db/b]



We take the X-terms to the left:

dX/X  - [(1- a) * dX/X] = [a * dA /A] + [ db/b]



by division of the entire equation by α finally results:

dX/X  = dA /A + (db/b)/ a


As a result, we obtain: The growth rate of the do-mestic product is independent of the amount of capital investment, since in our equation the growth rate of the domestic product (dX/X) is determined only by the growth rate of the employees (dA/A) as well as by the change in the growth factor (db/b) in relation to the elasticity of the labour input with regard to the domestic product (a).


A further consequence of this approach is further-more that intensive growth depends only on technical progress. The intensive growth relates indeed to labour productivity, and we achieve the growth rate of labour productivity by referring the domestic product to the labour input. Thus, if in the equation above we divide both sides by the growth rate of the factor labour (dA/A), it becomes apparent that the intensive growth (dXint/X) depends only on technical progress ((db/b)/ a):

dXint/X  = (db/b)/ a


These conclusions can, however, be criticised in several ways:


1st It is true that, under the assumptions of the neoclassical growth theory, the general growth rate is not directly dependent on capital input. Nevertheless, there is an indirect dependence. A capital input that is twice as high leads ceteris paribus to a domestic product that is twice as high, too.


2nd These conclusions of the neoclassical theory presuppose a Cobb-Douglas production function. Certainly, empirical studies have shown that conditions are present in industry very often that allow a Cobb-Douglas production function to describe the production conditions quite well. However, this does not prove that only such production functions exist in reality.


We had already pointed out that the classics of economic theory were assuming a somewhat different production function. They assumed that average and marginal costs would initially decrease with increasing production and increase as well only from a critical production volume onwards. This assumption was based on the quite plausible explanation that, depending on the technology, there was a very specific, optimum input ratio of the production factors with the result that unit costs increase both on this side and beyond this critical production quantity.


However, if one could now assume that entrepreneurs generally produce in the ascending branch of the cost function, one could still assume the assumptions of the Cobb-Douglas production function.


However, stagflation processes have been observed in reality in recent decades which are characterised by a rise in prices in the event of a decrease in out-put, that means that stagnation and inflation can be observed at the same time. This phenomenon can be explained by the fact that the share of fixed costs is extremely high.


Fixed costs are characterised by the fact that fixed unit costs always decline at increasing production. Thus, if the share of fixed costs is high, it can be expected that the total average costs will also decrease as production increases and that therefore, if production decreases, unit costs will indeed increase and with them the prices. And this in turn means that there can be no Cobb-Douglas production function, as this always leads to an increase in unit costs as production increases.


At other production functions, however, the growth rate may very well depend on the capital investment. The proof that the capital input does not play a role in determining the growth rate when assuming a Cobb-Douglas production function could indeed be provided only based on very specific assumptions due to witch the potentials of the labour input and the capital input just add up to one. With production functions of a different kind, the sum of these potentials can very well differ from one and in this case the capital input in the equilibrium formula can no longer be cancelled out.


3rd A dependence of the growth rate of the domestic product on the capital input arises additionally also in the case of so-called embodied technical progress. It is spoken of an embodied technical progress whenever the technical progress results automatically based on the production. In the course of production, the deficiencies of the previous process become evident and efforts are being made to eliminate or at least reduce these deficiencies by changing the technique. In this way it can be said that in the course of the production the desirability of technical improvements results automatically.


And it can be assumed that the sum of these possible automatically arising inventions also increases with the capital investment. This means, however, that increased capital investment leads to higher production and that in this way technical progress is stimulated. A higher capital investment can thus very well lead to an increase in the growth rate due to embodied technical progress.



09th Savings promotion versus investment promotion


The starting point of our considerations shall be the conclusion of the Keynesian growth theory: growth is dependent on the capital input:


               dY/Y = s/ß     


We have already noted above that this thesis does not permit the conclusion that saving must now also be considered a virtue in Keynesian theory and thus must be regarded as desirable. The formula: dY/Y = s/ß does not mean: the larger the savings ratio, the larger the growth rate, but: the larger the savings ratio, the higher the growth rate of the investment and thus also the equally large growth rate of the domestic product must be, in order that a dynamic equilibrium can be achieved. Whether this prerequisite for equilibrated growth is fulfilled in practice cannot be ascertained from this formula.


However, the saving still plays a decisive role in Kaldor's Keynesian distribution theory: increases in demand can fizzle out into price increases if the saving is small.


The Kaldorian theory thus leads to the following conclusion: An increase in the use of capital triggered from the capital demand side will lead to price increases and thus to a deterioration in the wage ratio. In order to prevent this, it is also necessary to increase voluntary saving. These considerations lead for a Keynesian savings policy to the conclusion that also the promotion of savings and not only of investment is necessary for the success of the growth policy.


It is still true that growth is only possible if entrepreneurs are willing to invest. There can be no growth without willingness to invest. Nevertheless, voluntary saving by private households is also needed, as investments without the willingness to save by households lead to price increases, profits are increased at the expense of employees and incomes are redistributed to the disadvantage of employees.


This market process does indeed force the savings sum to adjust ex post to the investment sum by in fact increasing the incomes of the self-employed, who have a higher propensity to save than the not self-employed. However, since this process is unde-sirable primarily for distribution policy reasons, the policy must work towards ensuring that employee households save more on their own initiative and thus create the prerequisites that the saving necessary for growth is possible without price and profit increases.


There are now different types of savings promotion:


        financial incentives (savings premiums and tax rebates)

        investment pay and investment profit sharing and

        Investment fund plans.


A detailed analysis of these savings promotion plans will be given in the lecture: Social and Distribution Policy.




10th Economic growth and capital structure


Thus, if it is necessary for the state, from a Keynesian perspective, to create investment incentives in order to stimulate economic growth in this way, the further question arises as to whether the state should give a slice of the budget to all investment projects of private entrepreneurs or whether only those investment projects should be specifically supported by the state which give reason to expect the highest capital productivity.


In fact, the investment projects of private entrepreneurs even differ greatly in the capital productivity to be expected and therefore it appears that the support of investments with the in each case highest capital productivity is desired, so that the state should limit itself specifically to the support of the most productive investment projects.


But it is necessary to critically object firstly, that the level of productivity of investments only emerges afterwards and secondly, that the significance of externalities is neglected in this analysis. An investment with above-average capital productivity can also be undesirable, since external effects can cause macroeconomic losses elsewhere in production.


A not-targeted investment support may well be superior to a targeted support for regulatory reasons, because with a not-targeted support the market forces decide about the selection, and market forces are generally better able than politicians to head for an optimal allocation.


The current principle of liability in the private economy ensures that the person who has made a profitable investment is also entitled to the profits arising from it, but that the person who has caused losses must also bear these losses himself. This presupposes, however, that the entrepreneurs do not have the possibility of having losses compensated by the state. If the entrepreneurs have a monopolistic structure, they can very well pass these losses on to the state, since without state support the entire financial market can collapse in the event of a financial crisis.


An official acting on behalf of the state does not receive any profits nor will any losses be personally imputed to him. It is precisely for these reasons that a government investment decision bears the risk of promoting unprofitable projects and, at the same time, very risky projects are approached that would never have been approached at private initiative.



11th The role of technical progress


The quantitative significance of technical progress for growth is undisputed. Technical progress manifests itself in changes in the structure parameters of the production function:


X = b * A α * K 1- α    b, α: structure parameters


Difficulties arise in the practical attribution of the share of technical progress in growth: technical progress can depend for one thing on the capital investment. Moreover, a higher level of technology usually requires also a higher quality of work. Here, it is no longer possible to determine to what extent the realised growth is attributable to increased capital investment, higher training of the labour force or technical progress.


But on what does it depend to what extent technical progress can spread? The classics of economic theory make competition primarily responsible for technical progress. The classics assume that entrepreneurs only have sufficient incentives for rationalisation if they are in competition.


By contrast, J. A. Schumpeter assumes that only large enterprises and corporate groups have the ability to innovate.


The difference between the two positions is there-fore that the classics aim at the incentives, while Schumpeter emphasises more the possibilities.


But competition itself also depends on a number of factors. These include the following factors in particular:


• the economic situation. In times of excess demands, the competitive forces are failing.


• free market access. Competition can be prevented by a prohibitive customs policy.


• the possibility of entrepreneurial mergers (groups, cartels). Entrepreneurs can deliberately eliminate competition by forming cartels or merging individual enterprises to form a group.


• The structuring of the patent legislation. The purpose of patent protection legislation is to prevent dirty competition. Such dirty competition would be present if individual enterprises initially try out new technical processes at high cost expenditure. Once it has been established that an invention can be successfully applied, there is a risk without patent legislation that other enterprises will adopt these technical processes. Since these enterprises did not have to incur any testing costs, they are in the position to offer the products more cheaply than the enterprise which introduced this innovation, and thus are able to drive them out of the market.


In order to prevent this dirty competition, the patent protection was introduced. Whoever patents an invention enjoys the protection of being the only one allowed to offer this product for an extended time. Without this protection, there would be a risk that the willingness to introduce new products or processes would dwindle. Despite this positive effect, however, there is a danger that competition will be prevented for a long time. The idea that competition will become possible after the patent period has expired is often illusory, because demanders and suppliers have already turned to other products and processes due to the very long duration of the patent.


These disadvantages could be avoided by granting licences for innovations, each of which can be acquired by more than one enterprise, instead of one patent, which is entitled only one enterprise. In this case it would be ensured that each licensee would share proportionately in the invention costs, so that there would be no unjustified advantage for the imitators, but nevertheless competition would always be allowed. Under current law such a regulation is legally possible, but generally it is not exercised.



12th Stagnation on account of a too low demand?


In the course of the history of economics teaching, the thesis was repeatedly put forward that sooner or later stagnation would occur, because the demand for goods would lag behind the possible supply and one day be saturated. Schumpeter pointed out that these theses of stagnation have always been disproved by reality.


Nevertheless, stagnation theses were also formulated within the framework of Keynesian theory. In contrast to John Maynard Keynes, especially Alvin Hansen opined that the demand for goods was not only too low in times of depression, but also too low in the long term to employ all workers. To conclude this chapter, let us consider these theses.


The starting point shall be the equilibrium condition of Keynesian growth theory:

dI/I = s/ß


        dI/I: annual growth rate of the investment volume

        s: macroeconomic saving rate

        ß: capital output ratio


If we assume a value of 0.2 for the savings ratio and a value of 1 for the capital output ratio, then according to the abovementioned output equation, the growth rate of the domestic product being necessary for equilibrium growth amounts to dI/I = 0.2 = 20%.


Alvin Hansen tried to prove that the actual growth rate was significantly below 20%. The volume of investment depended mainly on population growth. Although population growth was very high at the beginning of industrialisation, but stagnation in population growth was observed in all saturated national economies.


This demographic decline is leading to economic stagnation, as demand for new housing and jobs was decreasing. Only in the case of strong population growth will new housing and jobs be needed to an extent that leads to a sufficient investment volume for full employment.


This theory, like the Keynesian theory in general, ignores the fact that there is not only expansion investment, but also rationalisation investment. It may be that, with a shrinking population, the level of necessary expansion investment is too low to en-sure full employment.


But in general, the willingness of enterprises to invest in rationalisation is great just at times when demand is decreasing and competition between entrepreneurs is increasing. In times of strong competition, only those entrepreneurs can survive in the market who always try to reduce costs and improve the quality of goods by means of rationalisation investments.


Quite apart from that, worldwide we are not faced with the problem of stagnation in the world population, but on the contrary with the problem that natural resources do no longer suffice to feed such a rapidly growing world population. The so-called emerging countries (especially India and China) today must contend with overpopulation that is growing too rapidly and the countries, in economic terms as developing countries, that have not yet reached the stage of industrialisation will face the danger of overemployment in the future. For decades to come, there will be a worldwide danger of overpopulation and not of population stagnation.