Sustainable Economic Development and Human Capital

In this theoretical paper the key role of human capital for a sustainable economic development is introduced into a simplified version of the green Solow model. The main result of this integration is the derivation of a kind of environmental Kuznets curve.


Introduction
Investments in human capital are recognised as a key factor of sustainable economic development (see the very recent papers by World Bank, 2019, andBuevich et al., 2020). Indeed, empirical evidences from the EU states (Diaconu and Popescu, 2016) show the existence of a strong positive correlation among Human Sustainable Development Index (HSDI), United Nations' Human Development Index (HDI) and Human Capital Index (HCI).
In this vein, the present paper offers a theoretical contribution and introduces human capital in a simplified version of the green Solow model (Brook and Taylor, 2004). The key assumption of the model is that the higher the level of human capital in the economy, the larger the sensitivity and concern for environmental issues. Thus, more economic resources (human and physical) will be devoted to the technological progress in the environmental sector. Technological progress in the environmental sector, therefore, increases with human capital. Precisely, in the initial phase, the contribution of human capital concerns exclusively production. Subsequently, if human capital continues to increase and reaches a high level in the economy, the main benefits of a greater human capital concern economic sustainability and environmental respect. As a result, a kind of environmental Kuznets curve can be derived from the model (Note 1).
The rest of this theoretical paper is organised as follows: the next Section presents a simple economic growth model with human capital; while, Section 3 introduces the main elements of the green Solow model and derives a kind of environmental Kuznets curve. Conclusions and policy implications are also provided.

A Simple Economic Growth Model with Human Capital
In presence of human capital (H) as a further input, the production function of final goods and services (Y) is the following (Note 2): like physical capital (K), the hypothesis of diminishing marginal returns (0 < α < 1) prevents the infinite accumulation of human capital. Taking the natural logarithm of (1) and deriving with respect to time, we get the growth rate of the economy: Of course, the way of capital accumulation is different. As regards physical capital, we have the key equation of the Solow model (without exogenous technological progress): where 0 < s < 1 is the marginal propensity of saving ad δ is the depreciation rate of physical capital. In a balanced growth path, the constancy of Y/K implies that Y and K must grow at the same rate: Instead, as regards human capital, a key role is played by the investment in education (t is the time reference): where u is the time devoted to the investment in education and φ is the (positive) percentage change in human capital associated to a unitary increase in the time devoted to education. Thus, the growth rate of human capital is given by: It follows that equation (2) becomes: Equation (2') accentuates a well-known result in growth theory: human capital is (one of) the main determinant(s) of economic growth (see, e.g., Savvides and Stengos, 2008).

Technology Production Function in the Environmental Sector
We start with a simple function of pollution emissions (E): Pollution emissions (E) increases with production and decreases with technological progress in the environmental sector (A). It follows that the growth rate of pollution emissions is equal to the difference between the growth rate of the economy and the growth rate of technological progress in the environmental sector, viz.: The key assumption of this model is that the higher the level of human capital in the economy, the larger the sensitivity and concern for environmental issues. Thus, more economic resources (human and physical) will be devoted to the technological progress in the environmental sector. We formalise these positive externalities of human capital on economic sustainability in a very simple way. First, we include human capital in the technology production function in the environmental sector: where A 0 is an exogenous starting value of A. Thus, the growth rate of A is given by: As a result, technological progress in the environmental sector increases with human capital at increasing rates.
Introducing (5) and (2') into (3) we get: Equation (3') depicts a kind of environmental Kuznets curve where the main determinant of the relation between economic growth and economic sustainability is human capital (see Figure 1). In the initial phase, the contribution of human capital concerns exclusively production; thus, the growth rate of pollution increases with human capital. nomy, the pos y and concern l concern econ Of course, thi the potential st to be addre me per capita ronmental Ku nt is introduced of human capi economic resou or. We find tha