Podcast
Questions and Answers
What does k* represent in the context of the model?
What does k* represent in the context of the model?
What determines the long-run growth rate of Y/L in this model?
What determines the long-run growth rate of Y/L in this model?
If k is greater than k*, what will happen to the economy over time?
If k is greater than k*, what will happen to the economy over time?
What is the implication of diminishing marginal productivity of capital according to the model?
What is the implication of diminishing marginal productivity of capital according to the model?
Signup and view all the answers
What condition is represented when sf(k) is greater than (n + g + δ)k?
What condition is represented when sf(k) is greater than (n + g + δ)k?
Signup and view all the answers
What condition is necessary for attaining the maximum level of steady-state consumption according to the golden rule?
What condition is necessary for attaining the maximum level of steady-state consumption according to the golden rule?
Signup and view all the answers
What is indicated by a saving rate greater than sGR?
What is indicated by a saving rate greater than sGR?
Signup and view all the answers
If s < sGR, what does this imply about future consumption?
If s < sGR, what does this imply about future consumption?
Signup and view all the answers
In the context of the golden rule, how is the desirability of certain outcomes assessed?
In the context of the golden rule, how is the desirability of certain outcomes assessed?
Signup and view all the answers
What does the equation c* = f(k*) - (n + g + δ)k* represent?
What does the equation c* = f(k*) - (n + g + δ)k* represent?
Signup and view all the answers
What does the vertical logarithmic scale in the GDP per capita graph facilitate?
What does the vertical logarithmic scale in the GDP per capita graph facilitate?
Signup and view all the answers
Which growth rate is indicated in the GDP per capita graph for the United States?
Which growth rate is indicated in the GDP per capita graph for the United States?
Signup and view all the answers
In the context of the data, what is the significance of the year 1929?
In the context of the data, what is the significance of the year 1929?
Signup and view all the answers
What is represented by the formula $y(t) = e^{gt} y(0)$ in the graph's context?
What is represented by the formula $y(t) = e^{gt} y(0)$ in the graph's context?
Signup and view all the answers
What does 'spliced' data refer to in the context of the GDP statistics?
What does 'spliced' data refer to in the context of the GDP statistics?
Signup and view all the answers
Which of the following years does not appear in the GDP per person graph?
Which of the following years does not appear in the GDP per person graph?
Signup and view all the answers
What aspect of economic growth is noted to vary among different countries according to the data?
What aspect of economic growth is noted to vary among different countries according to the data?
Signup and view all the answers
What does the term 'frontier' refer to in relation to economic growth?
What does the term 'frontier' refer to in relation to economic growth?
Signup and view all the answers
What does the equation $L· /L = n$ represent?
What does the equation $L· /L = n$ represent?
Signup and view all the answers
In the equation $K· = I − δK$, what does the term $I$ represent?
In the equation $K· = I − δK$, what does the term $I$ represent?
Signup and view all the answers
What happens to the investment per unit of effective labor if $s$ increases?
What happens to the investment per unit of effective labor if $s$ increases?
Signup and view all the answers
Under what condition does the steady state exist?
Under what condition does the steady state exist?
Signup and view all the answers
What does the term $c*$ represent in the equation $c* = f(k*) - (n + g + δ)k*$?
What does the term $c*$ represent in the equation $c* = f(k*) - (n + g + δ)k*$?
Signup and view all the answers
What does $sf(k*)$ denote in the steady state equation?
What does $sf(k*)$ denote in the steady state equation?
Signup and view all the answers
Which of the following statements is true regarding steady state in this model?
Which of the following statements is true regarding steady state in this model?
Signup and view all the answers
What is implied if $k$ is differentiated with respect to $t$?
What is implied if $k$ is differentiated with respect to $t$?
Signup and view all the answers
What is the relationship represented by Y = C + S in a closed economy with no government?
What is the relationship represented by Y = C + S in a closed economy with no government?
Signup and view all the answers
What do the Inada conditions indicate about the marginal products of capital and labor?
What do the Inada conditions indicate about the marginal products of capital and labor?
Signup and view all the answers
Under constant returns to scale, how can the production function be expressed in intensive form?
Under constant returns to scale, how can the production function be expressed in intensive form?
Signup and view all the answers
What does the assumption of diminishing marginal productivity imply about the relationship between k and f(k)?
What does the assumption of diminishing marginal productivity imply about the relationship between k and f(k)?
Signup and view all the answers
According to the neoclassical production function, what does the parameter α represent?
According to the neoclassical production function, what does the parameter α represent?
Signup and view all the answers
How does the production function f(k) behave as k approaches zero?
How does the production function f(k) behave as k approaches zero?
Signup and view all the answers
What does it mean if f''(k) < 0 for the production function?
What does it mean if f''(k) < 0 for the production function?
Signup and view all the answers
What implication does constant returns to scale (CRS) have for the scaling of inputs?
What implication does constant returns to scale (CRS) have for the scaling of inputs?
Signup and view all the answers
What is a crucial assumption according to Solow's definition of economic theory?
What is a crucial assumption according to Solow's definition of economic theory?
Signup and view all the answers
In the neoclassical production function, what does the term 'AL' represent?
In the neoclassical production function, what does the term 'AL' represent?
Signup and view all the answers
What does the equation wL + rK = Y represent in the context of competitive markets?
What does the equation wL + rK = Y represent in the context of competitive markets?
Signup and view all the answers
According to the neoclassical production function, what indicates diminishing returns to capital?
According to the neoclassical production function, what indicates diminishing returns to capital?
Signup and view all the answers
What does the term 'conditional convergence' refer to in economic theory?
What does the term 'conditional convergence' refer to in economic theory?
Signup and view all the answers
Which component is part of the equation Y = K^α(AL)^(1−α)?
Which component is part of the equation Y = K^α(AL)^(1−α)?
Signup and view all the answers
What does the symbol 'f''(k)' signify in economic production functions?
What does the symbol 'f''(k)' signify in economic production functions?
Signup and view all the answers
In the neoclassical production function, what does the variable 'K' represent?
In the neoclassical production function, what does the variable 'K' represent?
Signup and view all the answers
What implication does it have when inputs are paid their marginal products under competitive markets?
What implication does it have when inputs are paid their marginal products under competitive markets?
Signup and view all the answers
Which factor is NOT included in the equation wL + rK = Y?
Which factor is NOT included in the equation wL + rK = Y?
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
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.
