Model Answer
0 min readIntroduction
New Growth Theory, emerging in the 1980s as a response to the limitations of the Solow-Swan model, posits that sustained economic growth is primarily driven by endogenous factors, particularly technological progress resulting from investment in research and development (R&D) and human capital. Unlike the Solow model which treats technological progress as exogenous, New Growth Theory emphasizes the role of innovation and knowledge accumulation. This theory is particularly relevant in understanding the dynamics of modern economies where R&D plays a crucial role. This answer will demonstrate, within a two-sector economy comprising goods production and R&D, how capital and aggregate output grow at the same rate, and how per capita output growth is determined by the rate of technological advancement.
Theoretical Framework: New Growth Theory
The core of New Growth Theory lies in the idea of increasing returns to scale, driven by knowledge spillovers and non-rivalrous knowledge. Knowledge, once created, can be used by multiple agents without diminishing its value. This contrasts with physical capital, which is subject to diminishing returns. Romer (1986) highlighted the importance of R&D as a key engine of growth, while Lucas (1988) emphasized the role of human capital accumulation.
The Two-Sector Economy
Consider an economy with two sectors: a goods-producing sector (Y) and a Research & Development (R&D) sector (A). Let:
- Y = Aggregate output
- K = Total capital stock
- L = Labor force
- A = Level of technology (total factor productivity)
- gY = Growth rate of aggregate output
- gK = Growth rate of capital stock
- gA = Growth rate of technology
- gL = Growth rate of labor force
- y = Per capita output (Y/L)
(i) Capital and Aggregate Output Growth
In a simplified production function for the goods-producing sector, we can represent output as:
Y = A * Kα * L(1-α), where 0 < α < 1
Taking the growth rate of both sides:
gY = gA + αgK + (1-α)gL
Now, assume that the R&D sector’s output (A) is directly proportional to the capital invested in R&D (KR&D). This implies that investment in R&D leads to technological progress. Furthermore, assume that the total capital stock (K) is allocated between the goods-producing sector (KY) and the R&D sector (KR&D), so K = KY + KR&D.
If we assume that the growth rate of the labor force (gL) is zero (or constant and not influencing long-run growth), the equation simplifies to:
gY = gA + αgK
The key insight from New Growth Theory is that the growth rate of technology (gA) is itself dependent on the capital stock allocated to R&D (KR&D). If we assume a constant share of capital allocated to R&D, then gA is proportional to gK. Specifically, if gA = βgK (where β is a constant representing the effectiveness of R&D investment), then:
gY = βgK + αgK = (α + β)gK
This equation demonstrates that the growth rate of aggregate output (gY) is directly proportional to the growth rate of the total capital stock (gK). Therefore, both capital and aggregate output must grow at the same rate.
(ii) Per Capita Output Growth and Technological Progress
Per capita output (y) is defined as Y/L. Its growth rate (gy) is:
gy = gY - gL
Since we assumed gL = 0, then gy = gY.
From the previous section, we know that gY = gA + αgK. However, in the long run, capital accumulation is subject to diminishing returns. Therefore, the contribution of capital accumulation to growth (αgK) will eventually diminish. This means that sustained per capita output growth can only be achieved through continuous technological progress (gA).
Therefore, per capita output must grow at the rate of growth of technology (gy = gA). This is because, in the long run, the growth in capital stock becomes less significant, and technological progress becomes the primary driver of per capita output growth.
Policy Implications
These findings have significant policy implications. Governments should encourage investment in R&D through subsidies, tax incentives, and protection of intellectual property rights. Investing in education and human capital is also crucial, as a skilled workforce is essential for innovation and the adoption of new technologies. Furthermore, policies that promote competition and knowledge spillovers can accelerate technological progress.
Conclusion
In conclusion, New Growth Theory provides a compelling framework for understanding the drivers of sustained economic growth. The analysis of a two-sector economy demonstrates that capital and aggregate output grow at the same rate, and that per capita output growth is fundamentally determined by the rate of technological progress. This underscores the importance of policies that foster innovation, R&D, and human capital development to achieve long-term economic prosperity. The focus should shift from merely accumulating capital to creating an environment conducive to knowledge creation and dissemination.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.