Study Notes on Endogenous Growth Theory

Lecture Objectives

The main objectives of this lecture are to understand the mechanics of endogenous growth, contrast neo-classical growth theory with endogenous growth theory, grasp the consequences of different returns to scale assumptions, and comprehend the concept of convergence.

Problems with Neoclassical Growth Theory

Neoclassical growth theory faces criticism due to its singular attribution of long-run economic growth solely to technological progress, failing to elaborate on the determinants that drive technological advancements. Additionally, the theory predicts no correlation between economic growth and savings at steady-state; however, empirical data reveals a positive correlation that the theory does not account for.

Endogenous Growth Theory: Contrast to Neoclassical Theory

In contrast to neoclassical theory, endogenous growth theory emphasizes the importance of both physical capital and knowledge capital as means for growth. While diminishing marginal returns to physical capital may exist, this does not necessarily apply to knowledge or human capital. In particular, increasing investments in human capital are crucial for linking higher savings rates with increased equilibrium growth rates.

Mechanics of Endogenous Growth

The production function within endogenous growth theory is modified to facilitate self-sustaining, endogenous growth, represented by a constant marginal product of capital (MPK). The foundational economy can be expressed through the formula $Y = aK$, where K is the sole factor of production and a indicates the MPK. The production and savings curves are characterized as straight lines situated above the required investment line. As the savings rate (s) escalates, the gap between savings (S) and required investment (I) widens, thereby accelerating growth.

Growth Rate of Capital Stock

For the growth analysis, we assume a constant savings rate (s), no population growth, and the absence of capital depreciation, disregarding trade and government factors; hence, all savings contribute to capital (K). The relationship can be defined as $S = sY$, with the change in capital stock (ΔK) articulated as $riangle K = sY = saK$. Consequently, the growth rate of capital stock can be represented as $rac{ riangle K}{K} = sa$.

Growth Rate of Output

Using the established output relationship, the change in output can be assessed via the foundational formula: $Y = aK$. This leads to the change in output expressed as $riangle Y = a riangle K$. By substituting ΔK with the savings formula, we derive $riangle Y = asY$ and, by dividing by Y, attain the growth rate of output as $rac{ riangle Y}{Y} = sa$. This implies that output positively correlates with capital stock; thus, a higher savings rate (s) results in increased growth rates for both capital and output.

Diminishing Returns and Microeconomic Principles

The elimination of diminishing returns to capital challenges fundamental microeconomic principles. If we assume constant returns to capital, it necessitates increasing returns to scale among all factors, which could lead to monopolization by a single firm — contradicting observed market behavior. Therefore, it is essential to introduce limits to increasing returns across all factors while maintaining constant returns for an individual factor. Moreover, it is acknowledged that a single firm may not capture all benefits from capital accumulation; for example, while it gains from its machinery investment, other firms may also benefit from this capital accumulation (known as social return).

Implications of Capital Investment

Investment yields dual benefits: private returns, where firms realize production advantages through new machinery, and social returns, where firms may not reap all technological benefits due to replicability. The concept of external returns is vital in endogenous growth theory and can be delineated: the creators of new knowledge capture only a fraction of its overall value, and new ideas foster further innovations, suggesting that knowledge can grow indefinitely.

Convergence of Economies

Endogenous growth theory raises questions regarding the potential for economies starting from different output levels to achieve similar living standards. According to neoclassical growth theory, absolute convergence can occur among economies with identical savings rates, population growth, and technologies, resulting in the same steady-state. In contrast, for economies with varying savings and population growth rates, while steady-state income levels might differ, growth rates can equalize assuming uniform population growth rate (n). The endogenous growth theory further posits that a higher savings rate is linked to a higher growth rate. Empirical findings, such as those by Barro, illustrate that the benefits of increased investment are temporary, facilitating movement toward higher steady-states but not ensuring sustained growth rate increases. Thus, conditional convergence is observed in practice, with endogenous growth theory providing insights into growth dynamics for technologically advanced nations, albeit offering limited insights into international growth disparities.