The core problem in focus of this paper is studying how modern economy can keep sustained growth in terms of increasing reliance on both knowledge and human capitals and dependence on continuously depleting non-renewable natural resources. The aim of this paper is to bridge in some way the gap between macroeconomic growth models and models of technological evolution. The ultimate goal of this work is to determine the optimal rate of savings and the optimal, i.e. delivering maximum cumulative consumption during given period , total investment allocation among physical capital, human capital, natural capital and knowledge capital, all subject of endogenous growth, for the modern knowledge based economy where savings are the unique source of investments. The neo-classical CES production function extended to four factors including physical capital K, human capital L, raw materials (natural capital) R and knowledge capital A in three different forms: for perfect substitution, for the case of no substitution and for the case of unit elasticity of substitution, is accepted as the basic growth model.

There are four most important features which distinguish our all-factors endogenous growth model from basic endogenous growth model: 1.The total national capital stock which reflects the growth potential of economy is considered consisting of four parts: physical capital, human capital, natural capital and knowledge capital. Therefore our model embeds all four factors of production (physical capital, human capital, natural capital and knowledge capital) as opposed to three factors (physical capital, labour and knowledge) included in Romer model. 2. The labour, represented by Human capital, is not assumed equal to population and is measured in money units (total earnings of qualified labour which is considered equal to total household income). Investments in Education system transform Population in Human capital. Therefore in our model labour supply grows proportionally investments in human capital, whine the path of population growth is given exogenously according to exponential or logistics curves. 3. Marginal rate of consumption and consequently marginal rate of savings are assumed constant during exploring period; they are not given as initial conditions but are subject of optimisation inside the model. 4. Growth of every of four employed factors is considered depending on investments in corresponding sector of economy only. It is assumed that investments, measured in money units, absorb and exhaustively represent all underlying resources (physical capital, labour, raw materials).

A three steps algorithm for finding the optimum solution is created. The first step defines in general an optimum structure of investment allocation among K, L and R. The second step defines optimum investment allocation between A from one hand and all other factors from the other hand. The third step applies defined optimum value on optimum structure.

Source:http://mpra.ub.uni-muenchen.de/19932/