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Consider the Solow model of economic growth with human capital. Using
the prope...
May 1, 2024
Consider the Solow model of economic growth with human capital. Using
the proper diagram, explain the effects of higher investment rate in human
capital on the steady-state levels of physical capital per efficient labour, human
capital per efficient labour and output per worker, holding other factors constant.
Answer
An increase in the investment rate in human capital leads to higher steady-state levels of physical capital per efficient labor, human capital per efficient labor, and output per worker.
Solution
a
The Solow Model with Human Capital: The Solow growth model extended to include human capital assumes that output per worker depends on both physical capital per efficient worker (k) and human capital per efficient worker (h), with the production function given by Y=F(K,H,L)=Kα(HL)1−α, where 0 < \alpha < 1
b
Steady-State Impact of Higher Investment in Human Capital: An increase in the investment rate in human capital (i^h) leads to a higher accumulation of human capital. This shifts the economy's steady-state to a new level where both physical capital per efficient worker (k∗) and human capital per efficient worker (h∗) are higher. This is because the increased human capital enhances the productivity of workers, which in turn raises the return on physical capital, encouraging more investment in physical capital as well
c
Output per Worker: With higher levels of both types of capital, the output per worker (y∗=f(k∗,h∗)) in the steady-state also increases. This is due to the fact that both physical and human capital are complementary in the production process, and an increase in one enhances the productivity of the other
Key Concept
Human Capital Investment and Economic Growth
Explanation
Investing in human capital increases the steady-state levels of physical capital, human capital, and output per worker in the Solow model of economic growth, reflecting the importance of human capital in enhancing overall economic productivity.
Consider the AK model of economic growth.
(i) How is the assumption of diminishing marginal productivity of capital
overcome in this model?
(ii) Demonstrate that lower savings rate in the AK model can lead to the permanent
deceleration of growth in output per worker. Compare this result to the
Solow model.
Answer
(i) In the AK model, the assumption of diminishing marginal productivity of capital is overcome by positing a constant marginal product of capital. (ii) A lower savings rate in the AK model can lead to a permanent deceleration of growth in output per worker, unlike in the Solow model where growth eventually returns to a steady state driven by exogenous factors.
Solution
a
AK Model Assumption: The AK model assumes a production function where output Y is a linear function of capital K, such that Y=AK, where A is a positive constant
b
Constant Marginal Product: This implies that the marginal product of capital (MPK) is constant and equal to A, which means there is no diminishing marginal productivity of capital
c
Savings and Growth: In the AK model, the growth rate of output per worker is directly proportional to the savings rate s, as given by the equation gY=sA
d
Effect of Lower Savings Rate: A lower savings rate reduces the growth rate of output per worker permanently, as the equation shows a direct relationship between s and gY
e
Comparison with Solow Model: In contrast, the Solow model predicts that a decrease in the savings rate affects the level of steady-state capital and output per worker but not the long-term growth rate, which is determined by exogenous technological progress
Key Concept
Marginal Productivity in Growth Models
Explanation
The AK model maintains constant marginal productivity of capital, which allows for endogenous growth without diminishing returns, contrasting with the Solow model's assumption of diminishing marginal productivity.
Key Concept
Savings Rate and Growth
Explanation
In the AK model, the savings rate directly influences the growth rate of output per worker, leading to permanent changes in growth rates with changes in savings, unlike the Solow model where the long-term growth rate is unaffected by savings.
3. Consider the Romer model of economic growth.
(i) What are key properties of ideas, which differ them from human capital?
(ii) Discuss the contemporary evidence on dynamics of research productivity
at the industry level, and its macroeconomic implications.
Answer
In the Romer model, ideas are non-rival and partially excludable, differing from human capital. Contemporary evidence suggests that research productivity at the industry level has been declining, which has significant macroeconomic implications for long-term economic growth.
Solution
a
Non-Rivalry and Partial Excludability: Ideas are non-rival, meaning one person's use of an idea does not diminish the ability of others to use it. They are also partially excludable, as intellectual property rights can prevent others from using them without permission, but these rights are not perfect
b
Declining Research Productivity: Empirical studies have shown that the number of researchers required to achieve a certain level of technological progress has increased over time, indicating a decline in research productivity
c
Macroeconomic Implications: This decline in research productivity can lead to a slowdown in economic growth, as more resources are required to generate new ideas, which are the engine of growth in the Romer model
Key Concept
Ideas vs. Human Capital in Romer Model
Explanation
Ideas are non-rival and partially excludable, which allows for sustained economic growth through innovation. However, declining research productivity poses a challenge to maintaining growth rates.
Key Concept
Declining Research Productivity
Explanation
The increasing number of researchers needed to maintain technological progress suggests that it is becoming harder to generate new ideas, which could slow down economic growth.
4. (i) Explain the difference between absolute and conditional convergence, using the diagram from the basic Solow model.
(ii) Is there currently a consensus about the existence
Answer
Absolute convergence suggests that poorer economies will grow faster than richer ones, leading to a reduction in income disparities over time, while conditional convergence recognizes that economies will only converge if they have similar savings rates, population growth rates, and human capital investment levels. There is no clear consensus on the existence of absolute convergence, but there is some support for conditional convergence when countries share similar characteristics.
Solution
a
Absolute Convergence in the Solow Model: In the basic Solow model, absolute convergence implies that all economies will eventually converge to the same steady-state level of per capita income, regardless of their initial levels of capital and income. This is depicted in the Solow diagram by different countries with different initial capital stocks moving along the same steady-state growth path
b
Conditional Convergence in the Solow Model: Conditional convergence, on the other hand, suggests that economies will only converge to their own country-specific steady-state levels of per capita income, which are determined by country-specific factors such as savings rates, population growth, and human capital investment. In the Solow diagram, this is shown by countries with different steady-state paths due to different savings rates or population growth rates
c
Current Consensus: While the concept of absolute convergence is debated, with evidence both supporting and refuting it, there is more empirical support for conditional convergence. Economists generally agree that countries with similar structural characteristics tend to converge in terms of income levels, but there is no consensus that all countries will converge regardless of their characteristics
Key Concept
Convergence in Economic Growth
Explanation
Absolute convergence suggests a universal catch-up in income levels, while conditional convergence recognizes the importance of structural similarities for economies to converge. The consensus leans towards conditional convergence, with absolute convergence remaining a contentious topic.
5. (i) What is the difference between growth accounting and development accounting?
(ii) Using the development accounting methodology, discuss the role of physical capital and TFP in explaning cross-country income differences.
Answer
The difference between growth accounting and development accounting lies in their focus: growth accounting analyzes the contribution of factor inputs and productivity to economic growth over time within a country, while development accounting seeks to explain income differences across countries at a point in time. Physical capital and TFP are crucial in development accounting for explaining cross-country income differences, with TFP often accounting for a larger share of these differences.
Solution
a
Growth Accounting vs. Development Accounting: Growth accounting is a method used to decompose the economic growth of a country over time into contributions from capital, labor, and TFP. Development accounting, on the other hand, is used to explain the differences in income levels across countries at a specific point in time by analyzing the role of physical capital, human capital, and TFP
b
Role of Physical Capital in Development Accounting: Physical capital accumulation can explain part of the income differences across countries. Countries with higher levels of capital per worker tend to have higher levels of output per worker, all else being equal. The production function, often assumed to be Cobb-Douglas, is given by Y=AKαL1−α, where Y is output, A is TFP, K is physical capital, L is labor, and α is the output elasticity of capital
c
Role of TFP in Development Accounting: TFP reflects the efficiency with which capital and labor are used in the production process and is often found to be the most significant contributor to cross-country income differences. It captures elements such as technological innovation, institutional quality, and economic policies that are not directly measured by the amount of capital or labor
Key Concept
Development Accounting
Explanation
Development accounting is a framework used to understand the sources of cross-country income differences by decomposing these differences into components attributable to physical capital, human capital, and TFP.
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