TOPIC 5: Growth and Classic Models
Economic Growth and Classic Models
Review of the Production Function
- Economic growth is defined as the change in the total value of production between time periods. It is fundamentally tied to the underlying production processes within an economy.
- At both macro and micro levels, the production process is described using production functions:
- Key components of economic growth and their representation in the production function:
- Capital Accumulation (K): Represents the level of capital.
- This includes all new investments in land, physical equipment, and human resources.
- It results from diverting present income into savings, which are then invested to augment future output.
- Comprises capital stock, economic infrastructure, and human capital.
- Population Growth (L): Represents the level of labor supplied.
- Population growth determines the size of the labor force.
- While at the micro level, additional labor generally increases total production, at the macro level, very large increases in population can sometimes reverse this relationship.
- Technological Progress (f()): Represents the technological capabilities.
- Currently considered the most important factor in long-term economic growth.
- Definition: Increased application of new scientific knowledge in the form of inventions and innovations concerning both human and physical capital.
- Results in new and improved ways of accomplishing existing tasks (e.g., growing crops, making clothes).
- Examples:
- IR-8 Miracle Rice (1960s): A new strain of rice developed to be much more productive in the climates of Southern and Southeastern Asia.
- Transistor Radios: Transistors replaced vacuum tubes, making radios more reliable and significantly less fragile.
Types of Technological Progress
- Neutral Technological Progress:
- Occurs when higher output levels are achieved with the same quantity and combinations of factor inputs.
- Does not affect the relative marginal productivity of either capital or labor.
- Example: The introduction of the division of labor, which changed the organization of capital and labor but not what each could achieve individually.
- Factor-Saving Technological Progress:
- Allows either capital or labor to substitute for the other.
- Labor-Saving Technology: Achieves a given output level using less labor in exchange for more capital.
- This is typically what people in developed countries associate with technological progress, as labor is more expensive than capital in these regions.
- Capital-Saving Technology: Achieves a given output level using less capital in exchange for more labor.
- This type of technology is particularly useful in developing countries where labor is often cheaper than capital.
- Generally results in lower demand for one input and increased demand for the other.
- Factor-Augmenting Technological Progress:
- Increases the marginal product of a given factor of production.
- Can change the ratio of inputs in equilibrium if factor prices are different.
- Labor-Augmenting: Improvements in human capital, such as education or health.
- Capital-Augmenting: The development of iron to substitute for bronze in metal products, increasing the productivity of capital.
- The ultimate effect on demand for the augmented factor depends on market equilibrium, considering both relative prices and the marginal products of other factors.
Introduction to Growth Models
- Detailed coverage of all growth models requires a graduate-level course.
- Reasons for covering growth models in this course:
- History of Thought: Illustrate how thinking about developing countries' growth has evolved.
- Overview of Methodology: Provide insight into how academic economists theoretically discuss these ideas.
- Illustrate Diversity of Perspectives: Offer different lenses for interpreting the development process.
- Show Limitations: Provide an understanding of the limits of these analytical techniques.
Categories of Growth Models
- Classic Growth Models:
- Focused on achieving higher levels of production through capital deepening (increasing the capital-to-labor ratio).
- Neoclassical Growth Models:
- Focused on developing efficient markets.
- Driven by the fundamental theorems of market equilibrium.
- Modern Growth Models:
- Focus on the functioning of markets in more detail.
- Special emphasis on situations where the necessary conditions for the Efficient Market Hypothesis are violated.
Classic Growth Models
- Two primary types:
- Linear-in-Stages Models
- Rostow's Stages of Growth
- Harrod-Domar Growth Model
- Structural Change Models
- Common Characteristics of Classic Growth Models:
- Output is used as a proxy for development.
- Development is assumed to be a uniform process across countries.
- Savings and capital deepening are considered the main mechanisms for generating greater output.
Linear-in-Stages Models
- Characteristics:
- Development is seen as a progression through a series of universal, necessary stages of progress.
- Universal: All countries follow the same path.
- Necessary: There is only one path to development.
- Historical Context: Popular in the 1950s and 1960s, strongly influenced by the Marshall Plan, and emphasized capital accumulation.
Rostow's Stages of Growth
- Developed by Walter Whitman Rostow, a UT Professor and Special Assistant for National Security Affairs to LBJ.
- Five stages of development universally applicable to all countries:
- Traditional Society: Characterized by subsistence agriculture, limited technology, and static social structures.
- Pre-conditions Stage: Building infrastructure, emergence of entrepreneurship, and increasing investment in education and technology.
- Take-off: Rapid economic growth, industrialization, and self-sustaining growth fueled by rising investment.
- Drive to Maturity: Diversification of industries, innovation, and decreasing reliance on imports.
- Age of High Mass Consumption: High income levels, widespread consumption of durable goods, and expansion of the service sector.
- Core Mechanism: The process involves mustering savings for capital accumulation.
Harrod-Domar Growth Model
- Explains how a country can generate economic growth primarily through capital accumulation.
- Key Mechanism: Capital accumulation via investments generated by saving.
- While not the direct basis for Rostow's model, it shares strong similarities in its emphasis on capital accumulation.
- Structure of the Model (Simple Version):
- Multi-Period Model: Actions in a given time period (e.g., t) depend on actions taken in previous periods (t-1). The next period is t+1.
- Simple Production Function: Assumes capital is the only input.
- Capital stock in period t is denoted as K_t.
- National income (output) in period t is denoted as Y_t.
- Output is related to its input by a constant ratio, c, which represents the amount of capital necessary to create a given level of output (income). Therefore, Kt = cYt.
- Savings and Investment:
- Income in any given period (Y_t) is either consumed or saved.
- The amount of income saved in period t is S_t.
- The fraction of income that is saved is denoted by s (the marginal propensity to save), so St = sYt.
- The amount of savings invested in period t is I_t.
- Derivation of the Model (Fundamental Equation of Growth):
- Investment as Change in Capital Stock: Investment in a period equals the change in the capital stock between periods.
- Investment Equals Savings: In a closed economy, investment is equal to savings.
- Savings Function: Savings are a proportion of national income.
- Production Function (Capital-Output Ratio): Capital stock is proportional to output.
- Kt = cYt and K{t+1} = cY{t+1}
- Substituting (2) and (3) into (1):
- Substituting (4) into the equation from step 5:
- Rearranging to find the growth rate of national income:
- sYt = c(Y{t+1} - Y_t)
- Divide both sides by cY_t:
- \frac{s}{c} = \frac{Y{t+1} - Yt}{Y_t}
- Let g be the rate of economic growth (the percentage change in national income).
- g = \frac{\Delta Y}{Y} = \frac{s}{c}
- Conclusion: The Harrod-Domar model suggests that the rate of economic growth (g) is directly proportional to the savings rate (s) and inversely proportional to the capital-output ratio (c).