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:
    • Q = f(K, L)
    • Y = f(K, L)
  • 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
      • Lewis Model
  • 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:
    1. Traditional Society: Characterized by subsistence agriculture, limited technology, and static social structures.
    2. Pre-conditions Stage: Building infrastructure, emergence of entrepreneurship, and increasing investment in education and technology.
    3. Take-off: Rapid economic growth, industrialization, and self-sustaining growth fueled by rising investment.
    4. Drive to Maturity: Diversification of industries, innovation, and decreasing reliance on imports.
    5. 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):
    1. Investment as Change in Capital Stock: Investment in a period equals the change in the capital stock between periods.
      • It = K{t+1} - K_t
    2. Investment Equals Savings: In a closed economy, investment is equal to savings.
      • It = St
    3. Savings Function: Savings are a proportion of national income.
      • St = sYt
    4. Production Function (Capital-Output Ratio): Capital stock is proportional to output.
      • Kt = cYt and K{t+1} = cY{t+1}
    5. Substituting (2) and (3) into (1):
      • sYt = K{t+1} - K_t
    6. Substituting (4) into the equation from step 5:
      • sYt = cY{t+1} - cY_t
    7. 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).