Economic Growth: Solow-Swan Model Overview
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Economic Growth: Solow-Swan Model Overview

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What does k* represent in the context of the model?

  • The optimal capital needed for growth
  • The level of output in the economy
  • The initial level of capital
  • The steady state capital (correct)

    • What determines the long-run growth rate of Y/L in this model?

  • Investment rates in the economy
  • The level of capital accumulation
  • Technological progress g (correct)
  • The rate of population growth n

    • If k is greater than k*, what will happen to the economy over time?

  • The economy will stabilize at k
  • The economy will grow indefinitely
  • The economy will converge to k* (correct)
  • The economy will experience a decline

    • What is the implication of diminishing marginal productivity of capital according to the model?

    <p>Eventually, capital accumulation results in smaller increases in output</p> Signup and view all the answers

    What condition is represented when sf(k) is greater than (n + g + δ)k?

    <p>The economy is accumulating capital</p> Signup and view all the answers

    What condition is necessary for attaining the maximum level of steady-state consumption according to the golden rule?

    <p>f'(kGR) = (n + g + δ)</p> Signup and view all the answers

    What is indicated by a saving rate greater than sGR?

    <p>Dynamic inefficiency</p> Signup and view all the answers

    If s < sGR, what does this imply about future consumption?

    <p>It requires a trade-off between current and future consumption.</p> Signup and view all the answers

    In the context of the golden rule, how is the desirability of certain outcomes assessed?

    <p>Based on specific assumptions about future discounting by households.</p> Signup and view all the answers

    What does the equation c* = f(k*) - (n + g + δ)k* represent?

    <p>Consumption at the steady state.</p> Signup and view all the answers

    What does the vertical logarithmic scale in the GDP per capita graph facilitate?

    <p>Easier reading of growth rates</p> Signup and view all the answers

    Which growth rate is indicated in the GDP per capita graph for the United States?

    <p>2.0% per year</p> Signup and view all the answers

    In the context of the data, what is the significance of the year 1929?

    <p>It is where modern data starts in this context.</p> Signup and view all the answers

    What is represented by the formula $y(t) = e^{gt} y(0)$ in the graph's context?

    <p>GDP growth over time</p> Signup and view all the answers

    What does 'spliced' data refer to in the context of the GDP statistics?

    <p>Data combined from different sources</p> Signup and view all the answers

    Which of the following years does not appear in the GDP per person graph?

    <p>2005</p> Signup and view all the answers

    What aspect of economic growth is noted to vary among different countries according to the data?

    <p>Growth patterns</p> Signup and view all the answers

    What does the term 'frontier' refer to in relation to economic growth?

    <p>Global economic leaders</p> Signup and view all the answers

    What does the equation $L· /L = n$ represent?

    <p>The constant growth rate of population</p> Signup and view all the answers

    In the equation $K· = I − δK$, what does the term $I$ represent?

    <p>Investment</p> Signup and view all the answers

    What happens to the investment per unit of effective labor if $s$ increases?

    <p>It increases</p> Signup and view all the answers

    Under what condition does the steady state exist?

    <p>When $n + g + δ &gt; 0$</p> Signup and view all the answers

    What does the term $c*$ represent in the equation $c* = f(k*) - (n + g + δ)k*$?

    <p>Consumption per unit of effective labor</p> Signup and view all the answers

    What does $sf(k*)$ denote in the steady state equation?

    <p>Gross investment per unit of effective labor</p> Signup and view all the answers

    Which of the following statements is true regarding steady state in this model?

    <p>The unique steady state is characterized by $k* &gt; 0$.</p> Signup and view all the answers

    What is implied if $k$ is differentiated with respect to $t$?

    <p>It shows the rate of change of capital per unit of effective labor.</p> Signup and view all the answers

    What is the relationship represented by Y = C + S in a closed economy with no government?

    <p>National income equals consumption plus savings.</p> Signup and view all the answers

    What do the Inada conditions indicate about the marginal products of capital and labor?

    <p>They will both approach zero as capital and labor approach infinity.</p> Signup and view all the answers

    Under constant returns to scale, how can the production function be expressed in intensive form?

    <p>F(K, AL) = f(K/AL, 1)</p> Signup and view all the answers

    What does the assumption of diminishing marginal productivity imply about the relationship between k and f(k)?

    <p>As k increases, f(k) increases, but at a decreasing rate.</p> Signup and view all the answers

    According to the neoclassical production function, what does the parameter α represent?

    <p>The constant capital share in income.</p> Signup and view all the answers

    How does the production function f(k) behave as k approaches zero?

    <p>f(k) approaches zero.</p> Signup and view all the answers

    What does it mean if f''(k) < 0 for the production function?

    <p>Increases in k lead to smaller increases in f(k).</p> Signup and view all the answers

    What implication does constant returns to scale (CRS) have for the scaling of inputs?

    <p>Doubling inputs leads to exactly double the output.</p> Signup and view all the answers

    What is a crucial assumption according to Solow's definition of economic theory?

    <p>An assumption on which conclusions depend sensitively.</p> Signup and view all the answers

    In the neoclassical production function, what does the term 'AL' represent?

    <p>Aggregate labor input adjusted for technology.</p> Signup and view all the answers

    What does the equation wL + rK = Y represent in the context of competitive markets?

    <p>The distribution of income between labor and capital.</p> Signup and view all the answers

    According to the neoclassical production function, what indicates diminishing returns to capital?

    <p>FKK(K, AL) &lt; 0</p> Signup and view all the answers

    What does the term 'conditional convergence' refer to in economic theory?

    <p>The phenomenon where poorer economies grow faster than richer ones under specific conditions.</p> Signup and view all the answers

    Which component is part of the equation Y = K^α(AL)^(1−α)?

    <p>Proportion of capital in total output.</p> Signup and view all the answers

    What does the symbol 'f''(k)' signify in economic production functions?

    <p>Marginal product of capital.</p> Signup and view all the answers

    In the neoclassical production function, what does the variable 'K' represent?

    <p>Total capital stock.</p> Signup and view all the answers

    What implication does it have when inputs are paid their marginal products under competitive markets?

    <p>It ensures efficient allocation of resources.</p> Signup and view all the answers

    Which factor is NOT included in the equation wL + rK = Y?

    <p>Total revenue from sales.</p> Signup and view all the answers

    Study Notes

    References

    • Solow-Swan Model notes are based on various resources: Economic Growth (2nd edition), MIT Press (Barro & Sala i Martin, 2004)
    • The Facts of Economic Growth (Jones, 2016), Handbook of Macroeconomics, 2A
    • Advanced Macroeconomics (5th edition), McGraw Hill (Romer, 2018)

    Outline

    • Introduction
    • Solow-Swan model assumptions
    • Dynamics of k
    • Steady state
    • Level effects
    • Golden rule
    • Convergence
    • Micro-foundations
    • Appendix

    Introduction

    • Figure 26 displays the lack of worldwide convergence in GDP per capita between 1960-2011

    The Solow-Swan Model

    • Very influential theory of economic growth, simple dynamic model.
    • Current income equals current production, based on current capital and labour endowments, and technology.
    • Part of current income is saved and invested into additional capital
    • Tomorrow's income results from tomorrow's capital and labour, and state of technology.
    • Explains how saving, investment, technology, and technical progress affect economic growth.
    • Provides empirical predictions to compare with data.

    Assumptions

    • Agents sell 1 unit of labour services, own and rent capital.
    • Income used for consumption and saving (investment in additional capital).
    • One final good, output Y, with constant price P = 1.
    • Firms hire labor and rent capital using a production function Y = F(K, AL) (AL is "effective" labor, A is labour-augmenting productivity).
    • Markets are perfectly competitive.
    • Constant returns to scale (CRS).

    Assumptions: Neoclassical Production Function

    • Constant returns to scale (CRS).
    • Positive, diminishing marginal products.
    • Inada conditions: lim Fk = ∞ as K approaches 0, lim Fk = 0 as K approaches ∞. Same for FL.
    • Production function in intensive form: f(k) = F(K, AL)/AL = F(K/AL, 1). k = K/AL (capital per effective labor), y = Y/AL = f(k) (output per effective labor).

    Assumptions: Diminishing Marginal Productivity

    • f'(k) > 0: an increase in k leads to an increase in f(k).
    • f"(k) < 0: the higher k, the smaller the increases in f(k) when k rises, leading to decreasing returns to capital.

    Assumptions: Dynamic Behavior

    • Variables are functions of time (t). Dynamic behavior of variables like labor (L), productivity (A), and capital (K) is assumed, accounting for factors like population growth (n), technological progress (g), and depreciation (δ).

    Dynamics of k

    • k̇ = sf(k) - (n + g + δ)k.
    • sf(k) = gross investment per unit of effective labor
    • (n + g + δ)k = break-even investment per unit of effective labor

    Steady State

    • sf(k*) = (n + g + δ)k*. Unique steady state with k* > 0.
    • y* = f(k*). Steady state where all variables grow at constant rates.
    • k = 0 is ignored.
    • K/L and Y/L grow at constant rate g+n.

    Steady State & Phase Diagram

    • k < k* --> sf(k) > (n+g+δ)k (investment more than break-even).
    • k > k* --> sf(k) < (n+g+δ)k (investment less than break-even).

    Steady State

    • The economy converges to a unique steady state from any starting point k(0) > 0

    Golden Rule

    • sf(kGR) = (n+g+δ)kGR
    • CGR= max{f(k) - (n+g+δ)k} where CGR is maximum consumption.
    • This represents the optimal capital stock for maximum long-run consumption.

    Golden Rule

    • c* = f(k*) - (n+g+δ)k* The optimal saving rate leads to max consumption.
    • If S is below SGR, the economy tends to have dynamic inefficiency or over-saving.
    • If S is above SGR, it leads to higher initial consumption and lower future consumption.

    Absolute Convergence

    • identical parameter values lead to the same k*.
    • Countries with lower initial capital stocks grow faster toward the common steady state.

    Conditional Convergence

    • Differences in parameter values lead to different k*.
    • Lower initial capital stocks don't necessarily grow faster.

    Convergence

    • Absolute convergence: converging to same steady state.
    • Conditional convergence: differing parameter values could prevent convergence.

    Micro-foundations

    • Production with side effects (pollution). Is this relevant in the Solow model? What should the government do?
    • Model predicts the effects of (1) Income tax reduction on saving rates and (2) News on future productivity levels on today's economic variables.
    • Limitations: lacks welfare evaluation and behavioral responses to environment, policies, etc.
    • Models like Overlapping Generations and Ramsey address these challenges.

    Appendix: Do Differences in Growth Rates Matter?

    • Examples showing that even small differences in growth rates lead to large differences in income after years.

    Appendix: Lucas on Growth

    • Discusses the importance of considering factors like actions governments can take to grow countries like India and Indonesia. The welfare implications are also noted.

    Appendix: Solow on Economic Theory

    • Theory depends on assumptions that are not always true.
    • The art of theorizing is making assumptions that make final results not strongly dependent on the assumptions.
    • Crucial assumptions should be realistic.

    Appendix: Neoclassical Production Function

    • From definitions: Y = F(K, AL), AL = f(k), KF(K, AL) = f'(k) > 0, K^2F(K, AL) = f"(k) < 0.
    • Under CRS and competitive markets, inputs are paid marginal products and factor payments exhaust output (wL + rK = Y).

    Appendix: Conditional Convergence

    • Shows graph of convergence of personal income across Japanese prefectures against the log of 1930 per capita income for growth rates from 1930-1990.

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    Description

    Explore the Solow-Swan model, a foundational theory of economic growth that explains the relationship between capital, labor, and technology in production. This quiz delves into its assumptions, dynamics, steady state, golden rule, and convergence concepts, providing a comprehensive understanding of its implications for economic growth.

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