The document provides an overview of the Solow growth model, which models economic growth through capital accumulation over time. It describes the key components of the model, including the production function, capital accumulation equation, investment determination, and steady state. The model predicts that economies will eventually stop growing as they approach the steady state, due to diminishing returns to capital. However, it does not fully explain long-run economic growth. The document also discusses how the model can be used to analyze the effects of changes to parameters like the investment and depreciation rates.
This document provides an overview of a macroeconomic model of production. It introduces a Cobb-Douglas production function to model how output is determined by capital and labor inputs. The model assumes constant returns to scale and is solved to find the equilibrium levels of output, capital, labor, wage rates and rental rates. The model predicts that countries with more capital per person will have higher output per person. However, the model initially overpredicts output for many countries. Accounting for differences in total factor productivity across countries significantly improves the model's predictive power.
This document provides an overview of the IS curve model. It begins with an introduction that establishes the relationship between interest rates and output in the short run. The IS curve captures this relationship graphically.
It then goes on to describe how to set up the basic IS curve model, which involves deriving the IS curve equation from the national income identity and consumption, investment, government spending, export, and import functions. It also discusses how to use the IS curve to show the effects of interest rate changes and aggregate demand shocks.
Finally, it discusses the microeconomic foundations of consumption behavior, investment decisions, and multiplier effects that provide the underlying basis for the IS curve relationship.
This document discusses endogenous and exogenous growth theories. Endogenous growth theory views technological progress as endogenous to the economic system and driven by factors like investment in human capital and ideas. Exogenous growth theory sees technology as an external factor determined outside the economic system. The Harrod and Domar models emphasize the role of capital accumulation in driving growth, and define actual, warranted, and natural growth rates. Steady growth requires the actual and warranted rates to be equal, and the natural rate puts an upper limit on growth. Disequilibriums can cause inflation or overproduction.
The document summarizes key aspects of the Solow growth model. It explains that the Solow model replaced the fixed production function of the Harrod-Domar model with a neoclassical production function allowing for factor substitution. It presents the basic equations of the Solow model showing that changes in capital per worker are determined by savings, population growth, and depreciation. It illustrates the Solow diagram and how steady state equilibrium is reached. It analyzes how changes in the saving rate and population growth rate impact the model.
The Harrod-Domar growth model uses 3 key variables to determine the growth rate:
1. The saving rate, which determines how much can be invested.
2. Capital productivity, or how much output increases with each unit of new capital.
3. The depreciation rate, which accounts for aging of the existing capital stock.
The model's formula is: Growth Rate = Saving Rate x Capital Productivity - Depreciation Rate. It provides a simple framework for analyzing how changes to these variables impact long-term economic growth.
This document discusses the dual gap analysis model for analyzing savings-investment gaps and foreign exchange gaps that constrain economic growth in developing countries. It explains that if a country's targeted growth rate requires higher investment than can be supported by domestic savings, there will be an ex-ante savings gap that can be filled by foreign aid inflows. Similarly, if the foreign exchange required for imports to support the targeted growth rate exceeds potential foreign exchange earnings, there will be an ex-ante foreign exchange gap that can also be filled by foreign aid. The dual gap analysis is useful for developing countries to estimate capital requirements and calculate how much investment and savings can be generated domestically versus relying on foreign resources.
Econometrics is the application of statistical and mathematical methods to economic data in order to test economic theories and estimate relationships between economic variables. The methodology of econometrics involves stating an economic theory or hypothesis, specifying the theory mathematically and as an econometric model, obtaining data, estimating the model, testing hypotheses, making forecasts, and using the model for policy purposes. Regression analysis is a key tool in econometrics that relates a dependent variable to one or more independent variables, with an error term included to account for the inexact nature of economic relationships.
The document summarizes key concepts from Chapter 6 of an economics textbook on long-run economic growth. It introduces the Romer model of economic growth, which distinguishes between ideas and objects. Ideas are nonrival and lead to increasing returns. The Romer model generates sustained long-run growth through expanding knowledge. The document also combines the Solow and Romer models to develop a full theory of long-run growth accounting for both physical capital and ideas. It shows how growth accounting can be used to analyze sources of economic growth.
This document provides an overview of a macroeconomic model of production. It introduces a Cobb-Douglas production function to model how output is determined by capital and labor inputs. The model assumes constant returns to scale and is solved to find the equilibrium levels of output, capital, labor, wage rates and rental rates. The model predicts that countries with more capital per person will have higher output per person. However, the model initially overpredicts output for many countries. Accounting for differences in total factor productivity across countries significantly improves the model's predictive power.
This document provides an overview of the IS curve model. It begins with an introduction that establishes the relationship between interest rates and output in the short run. The IS curve captures this relationship graphically.
It then goes on to describe how to set up the basic IS curve model, which involves deriving the IS curve equation from the national income identity and consumption, investment, government spending, export, and import functions. It also discusses how to use the IS curve to show the effects of interest rate changes and aggregate demand shocks.
Finally, it discusses the microeconomic foundations of consumption behavior, investment decisions, and multiplier effects that provide the underlying basis for the IS curve relationship.
This document discusses endogenous and exogenous growth theories. Endogenous growth theory views technological progress as endogenous to the economic system and driven by factors like investment in human capital and ideas. Exogenous growth theory sees technology as an external factor determined outside the economic system. The Harrod and Domar models emphasize the role of capital accumulation in driving growth, and define actual, warranted, and natural growth rates. Steady growth requires the actual and warranted rates to be equal, and the natural rate puts an upper limit on growth. Disequilibriums can cause inflation or overproduction.
The document summarizes key aspects of the Solow growth model. It explains that the Solow model replaced the fixed production function of the Harrod-Domar model with a neoclassical production function allowing for factor substitution. It presents the basic equations of the Solow model showing that changes in capital per worker are determined by savings, population growth, and depreciation. It illustrates the Solow diagram and how steady state equilibrium is reached. It analyzes how changes in the saving rate and population growth rate impact the model.
The Harrod-Domar growth model uses 3 key variables to determine the growth rate:
1. The saving rate, which determines how much can be invested.
2. Capital productivity, or how much output increases with each unit of new capital.
3. The depreciation rate, which accounts for aging of the existing capital stock.
The model's formula is: Growth Rate = Saving Rate x Capital Productivity - Depreciation Rate. It provides a simple framework for analyzing how changes to these variables impact long-term economic growth.
This document discusses the dual gap analysis model for analyzing savings-investment gaps and foreign exchange gaps that constrain economic growth in developing countries. It explains that if a country's targeted growth rate requires higher investment than can be supported by domestic savings, there will be an ex-ante savings gap that can be filled by foreign aid inflows. Similarly, if the foreign exchange required for imports to support the targeted growth rate exceeds potential foreign exchange earnings, there will be an ex-ante foreign exchange gap that can also be filled by foreign aid. The dual gap analysis is useful for developing countries to estimate capital requirements and calculate how much investment and savings can be generated domestically versus relying on foreign resources.
Econometrics is the application of statistical and mathematical methods to economic data in order to test economic theories and estimate relationships between economic variables. The methodology of econometrics involves stating an economic theory or hypothesis, specifying the theory mathematically and as an econometric model, obtaining data, estimating the model, testing hypotheses, making forecasts, and using the model for policy purposes. Regression analysis is a key tool in econometrics that relates a dependent variable to one or more independent variables, with an error term included to account for the inexact nature of economic relationships.
The document summarizes key concepts from Chapter 6 of an economics textbook on long-run economic growth. It introduces the Romer model of economic growth, which distinguishes between ideas and objects. Ideas are nonrival and lead to increasing returns. The Romer model generates sustained long-run growth through expanding knowledge. The document also combines the Solow and Romer models to develop a full theory of long-run growth accounting for both physical capital and ideas. It shows how growth accounting can be used to analyze sources of economic growth.
Investment Multiplier and Super multiplierKhemraj Subedi
Investment Multiplier and Super Multiplier are very important concept of Macroeconomics to understand the effect of autonomous investment and induced investment in final increase in national income.
This document discusses heteroscedasticity, or non-constant error variance, in regression analysis. It begins by defining heteroscedasticity and explaining how it violates assumptions of the classical linear regression model. The nature and potential causes of heteroscedasticity are then explored through various examples. The document introduces the method of generalized least squares (GLS) as a way to produce best linear unbiased estimators when heteroscedasticity is present. GLS transforms the data so that error variances are constant, allowing standard least squares to be applied. The consequences of using ordinary least squares in the presence of heteroscedasticity are then discussed.
The document discusses technological progress in economic growth models. It introduces an endogenous growth model where the rate of technological progress is determined within the model rather than assumed constant. It also discusses policies that can promote economic growth, such as increasing the savings rate, allocating investment efficiently among different types of capital, and encouraging innovation. Empirical evidence generally confirms predictions of the Solow growth model.
This document discusses the relationship between investment, national income, and the stock of capital over multiple time periods. It presents a formula to calculate the present value of future returns from a capital asset. It also shows a table illustrating how output, income, capital stock, replacement costs, net investment, and gross investment change over 6 time periods. The capital output ratio and depreciation rate are assumed to remain constant.
This document discusses economic growth and technological progress. It begins by introducing the Solow growth model and its limitations in accounting for long-run growth. The chapter then incorporates technological progress into the Solow model by including labor-augmenting technological change. It discusses how this affects the model's predictions and steady states. Later sections examine empirical evidence on growth, including balanced growth, conditional convergence between countries, and the roles of capital accumulation and productivity in determining income differences. The chapter concludes by considering how policies like free trade may impact productivity and long-run growth.
The document discusses government debt and perspectives on it. It covers measurement problems with the deficit figure due to inflation, business cycles, and uncounted liabilities. It also summarizes the traditional view that debt lowers national saving versus the Ricardian view that it does not affect saving. Most economists oppose a balanced budget rule as it hinders fiscal policy goals like stabilization.
This document summarizes Harrod's growth model, which argues that steady economic growth is inherently unstable due to entrepreneurs' inability to accurately predict the warranted rate of growth. It outlines Harrod's key assumptions and shows how the actual growth rate diverging from the warranted rate leads to boom/bust cycles. The model concludes that full employment steady growth is impossible to achieve due to exogenous factors like savings, technology, and population growth being rigid over time.
Joan Robinson developed growth models that rejected many neoclassical assumptions. Her models considered capital as durable and heterogeneous, not easily substitutable for labor. She argued the value of capital depends on distribution and cannot be estimated without knowing interest rates. Robinson built multiple models to analyze growth under different economic conditions. Her key model showed the relationship between the actual and desired rates of accumulation and profit. Steady growth required these rates to be equal, but various factors could cause them to diverge, making sustained steady growth difficult to achieve.
This document provides an overview of investment. It discusses three types of investment: business fixed investment, residential investment, and inventory investment. It then explains the neoclassical model of business fixed investment, which shows how investment depends on the marginal product of capital, interest rate, and tax rules. It also discusses Tobin's q theory of investment and factors that can influence investment like the stock market, financing constraints, and the housing market.
(1) Saving is income not consumed or paid in taxes, and is channeled to firms through bonds/stocks or bank deposits for investment.
(2) Investment adds to physical capital stock or replaces old assets, including private and fixed investment like structures and machinery.
(3) The saving-investment theory explains how equality between saving and investment determines the price level, with disequilibrium causing price fluctuations through changes in income.
Permanent and Life Cycle Income HypothesisJosephAsafo1
The document discusses the Permanent Income Hypothesis (PIH) and Life Cycle Hypothesis (LCH). It explains that according to PIH, consumption is based on permanent income rather than current income. Current income has both permanent and transitory components. The LCH suggests that consumption varies over a person's life cycle as they save when young and spend when retired to maintain smooth consumption levels. The LCH consumption function shows consumption depends on both wealth and income levels over a person's lifetime.
1) Several economists have proposed theories to explain the relationship between consumption and income over time. Keynes proposed that current consumption depends on current income, while Fisher argued that consumption depends on lifetime income and consumers smooth consumption over periods.
2) Modigliani built on Fisher's model with the life-cycle hypothesis, arguing consumption depends on lifetime wealth and income that varies over one's career. Friedman's permanent income hypothesis claims consumption depends on permanent rather than transitory income, allowing consumers to smooth consumption.
3) Hall's random walk hypothesis adds that if consumers have rational expectations, then consumption changes should be unpredictable and only change with unanticipated income or wealth fluctuations. Laibson challenged the assumption of
In economics, the theory of the second best concerns the situation when one or more optimality conditions cannot be satisfied.
The economists Richard Lipsey and Kelvin Lancaster showed in 1956, that if one optimality condition in an economic model cannot be satisfied, it is possible that the next-best solution involves changing other variables away from the values that would otherwise be optimal.
Politically, the theory implies that if it is infeasible to remove a particular market distortion, introducing a second (or more) market distortion may partially counteract the first, and lead to a more efficient outcome.
The Solow-Swan model assumes constant returns to scale in production using capital and labor. It predicts an economy will reach a steady state equilibrium where the savings rate equals the investment needed to maintain the capital-labor ratio. The key assumptions include diminishing returns to individual inputs, exogenous population growth and technological progress, and savings being a constant fraction of income. The model shows how an economy converges over time to this steady state level of capital per worker and output per worker, regardless of its starting point.
The document discusses the Keynesian multiplier theory and the concept of the multiplier. It explains that the multiplier captures the cumulative effect of a change in investment on national income through induced consumption. The value of the multiplier depends on the marginal propensity to consume (MPC) and is determined as 1/(1-MPC). The document provides an example of the multiplier process showing how an initial investment leads to increasing rounds of consumption and income. It also discusses some assumptions and limitations of the multiplier model.
This document provides an introduction to panel data analysis and regression models for panel data. It defines panel data as longitudinal data collected on the same units (like individuals, firms, countries) over multiple time periods. Panel data allow researchers to study changes over time and estimate causal effects. The document outlines common panel data structures, reasons for using panel data analysis, and basic estimation techniques like fixed effects and random effects models to account for unobserved heterogeneity across units. It also discusses assumptions and limitations of different panel data models.
Macro Economics -II Chapter Two AGGREGATE SUPPLYZegeye Paulos
1) The document discusses four models of short-run aggregate supply: the sticky-price model, imperfect information model, and sticky-wage model.
2) In the sticky-price model, some prices are fixed in the short-run due to contracts or costs of changing prices. This can cause output to deviate from natural levels when demand changes.
3) The imperfect information model assumes suppliers don't know the overall price level when making decisions. Output will rise if actual prices are above expected prices.
4) In the sticky-wage model, nominal wages are fixed by contracts in the short-run. A price rise will lower real wages and induce firms to hire more workers and produce more output
The document summarizes key growth models:
1) The Harrod-Domar model assumes fixed capital-output and capital-labor ratios and that the growth rate is determined by the savings ratio. However, it fails to account for substitutability between factors.
2) The Solow-Swan model introduces variable factor ratios and exogenous technological progress. It shows how capital accumulation, labor force growth, and technology affect output over time.
3) Endogenous growth models developed by Romer relax the assumption of diminishing returns to capital and allow technological progress to be endogenous.
The document summarizes key concepts from macroeconomic growth models including the Harrod-Domar, Solow-Swan, and endogenous growth models. It discusses the Harrod-Domar model which relates an economy's growth rate to its capital stock and savings ratio. It then summarizes the Solow-Swan model which incorporates technological progress and assumes diminishing returns to capital. The model predicts economies will eventually reach a steady state level of capital and output. Finally, it briefly mentions endogenous growth models which seek to explain technological progress.
Investment Multiplier and Super multiplierKhemraj Subedi
Investment Multiplier and Super Multiplier are very important concept of Macroeconomics to understand the effect of autonomous investment and induced investment in final increase in national income.
This document discusses heteroscedasticity, or non-constant error variance, in regression analysis. It begins by defining heteroscedasticity and explaining how it violates assumptions of the classical linear regression model. The nature and potential causes of heteroscedasticity are then explored through various examples. The document introduces the method of generalized least squares (GLS) as a way to produce best linear unbiased estimators when heteroscedasticity is present. GLS transforms the data so that error variances are constant, allowing standard least squares to be applied. The consequences of using ordinary least squares in the presence of heteroscedasticity are then discussed.
The document discusses technological progress in economic growth models. It introduces an endogenous growth model where the rate of technological progress is determined within the model rather than assumed constant. It also discusses policies that can promote economic growth, such as increasing the savings rate, allocating investment efficiently among different types of capital, and encouraging innovation. Empirical evidence generally confirms predictions of the Solow growth model.
This document discusses the relationship between investment, national income, and the stock of capital over multiple time periods. It presents a formula to calculate the present value of future returns from a capital asset. It also shows a table illustrating how output, income, capital stock, replacement costs, net investment, and gross investment change over 6 time periods. The capital output ratio and depreciation rate are assumed to remain constant.
This document discusses economic growth and technological progress. It begins by introducing the Solow growth model and its limitations in accounting for long-run growth. The chapter then incorporates technological progress into the Solow model by including labor-augmenting technological change. It discusses how this affects the model's predictions and steady states. Later sections examine empirical evidence on growth, including balanced growth, conditional convergence between countries, and the roles of capital accumulation and productivity in determining income differences. The chapter concludes by considering how policies like free trade may impact productivity and long-run growth.
The document discusses government debt and perspectives on it. It covers measurement problems with the deficit figure due to inflation, business cycles, and uncounted liabilities. It also summarizes the traditional view that debt lowers national saving versus the Ricardian view that it does not affect saving. Most economists oppose a balanced budget rule as it hinders fiscal policy goals like stabilization.
This document summarizes Harrod's growth model, which argues that steady economic growth is inherently unstable due to entrepreneurs' inability to accurately predict the warranted rate of growth. It outlines Harrod's key assumptions and shows how the actual growth rate diverging from the warranted rate leads to boom/bust cycles. The model concludes that full employment steady growth is impossible to achieve due to exogenous factors like savings, technology, and population growth being rigid over time.
Joan Robinson developed growth models that rejected many neoclassical assumptions. Her models considered capital as durable and heterogeneous, not easily substitutable for labor. She argued the value of capital depends on distribution and cannot be estimated without knowing interest rates. Robinson built multiple models to analyze growth under different economic conditions. Her key model showed the relationship between the actual and desired rates of accumulation and profit. Steady growth required these rates to be equal, but various factors could cause them to diverge, making sustained steady growth difficult to achieve.
This document provides an overview of investment. It discusses three types of investment: business fixed investment, residential investment, and inventory investment. It then explains the neoclassical model of business fixed investment, which shows how investment depends on the marginal product of capital, interest rate, and tax rules. It also discusses Tobin's q theory of investment and factors that can influence investment like the stock market, financing constraints, and the housing market.
(1) Saving is income not consumed or paid in taxes, and is channeled to firms through bonds/stocks or bank deposits for investment.
(2) Investment adds to physical capital stock or replaces old assets, including private and fixed investment like structures and machinery.
(3) The saving-investment theory explains how equality between saving and investment determines the price level, with disequilibrium causing price fluctuations through changes in income.
Permanent and Life Cycle Income HypothesisJosephAsafo1
The document discusses the Permanent Income Hypothesis (PIH) and Life Cycle Hypothesis (LCH). It explains that according to PIH, consumption is based on permanent income rather than current income. Current income has both permanent and transitory components. The LCH suggests that consumption varies over a person's life cycle as they save when young and spend when retired to maintain smooth consumption levels. The LCH consumption function shows consumption depends on both wealth and income levels over a person's lifetime.
1) Several economists have proposed theories to explain the relationship between consumption and income over time. Keynes proposed that current consumption depends on current income, while Fisher argued that consumption depends on lifetime income and consumers smooth consumption over periods.
2) Modigliani built on Fisher's model with the life-cycle hypothesis, arguing consumption depends on lifetime wealth and income that varies over one's career. Friedman's permanent income hypothesis claims consumption depends on permanent rather than transitory income, allowing consumers to smooth consumption.
3) Hall's random walk hypothesis adds that if consumers have rational expectations, then consumption changes should be unpredictable and only change with unanticipated income or wealth fluctuations. Laibson challenged the assumption of
In economics, the theory of the second best concerns the situation when one or more optimality conditions cannot be satisfied.
The economists Richard Lipsey and Kelvin Lancaster showed in 1956, that if one optimality condition in an economic model cannot be satisfied, it is possible that the next-best solution involves changing other variables away from the values that would otherwise be optimal.
Politically, the theory implies that if it is infeasible to remove a particular market distortion, introducing a second (or more) market distortion may partially counteract the first, and lead to a more efficient outcome.
The Solow-Swan model assumes constant returns to scale in production using capital and labor. It predicts an economy will reach a steady state equilibrium where the savings rate equals the investment needed to maintain the capital-labor ratio. The key assumptions include diminishing returns to individual inputs, exogenous population growth and technological progress, and savings being a constant fraction of income. The model shows how an economy converges over time to this steady state level of capital per worker and output per worker, regardless of its starting point.
The document discusses the Keynesian multiplier theory and the concept of the multiplier. It explains that the multiplier captures the cumulative effect of a change in investment on national income through induced consumption. The value of the multiplier depends on the marginal propensity to consume (MPC) and is determined as 1/(1-MPC). The document provides an example of the multiplier process showing how an initial investment leads to increasing rounds of consumption and income. It also discusses some assumptions and limitations of the multiplier model.
This document provides an introduction to panel data analysis and regression models for panel data. It defines panel data as longitudinal data collected on the same units (like individuals, firms, countries) over multiple time periods. Panel data allow researchers to study changes over time and estimate causal effects. The document outlines common panel data structures, reasons for using panel data analysis, and basic estimation techniques like fixed effects and random effects models to account for unobserved heterogeneity across units. It also discusses assumptions and limitations of different panel data models.
Macro Economics -II Chapter Two AGGREGATE SUPPLYZegeye Paulos
1) The document discusses four models of short-run aggregate supply: the sticky-price model, imperfect information model, and sticky-wage model.
2) In the sticky-price model, some prices are fixed in the short-run due to contracts or costs of changing prices. This can cause output to deviate from natural levels when demand changes.
3) The imperfect information model assumes suppliers don't know the overall price level when making decisions. Output will rise if actual prices are above expected prices.
4) In the sticky-wage model, nominal wages are fixed by contracts in the short-run. A price rise will lower real wages and induce firms to hire more workers and produce more output
The document summarizes key growth models:
1) The Harrod-Domar model assumes fixed capital-output and capital-labor ratios and that the growth rate is determined by the savings ratio. However, it fails to account for substitutability between factors.
2) The Solow-Swan model introduces variable factor ratios and exogenous technological progress. It shows how capital accumulation, labor force growth, and technology affect output over time.
3) Endogenous growth models developed by Romer relax the assumption of diminishing returns to capital and allow technological progress to be endogenous.
The document summarizes key concepts from macroeconomic growth models including the Harrod-Domar, Solow-Swan, and endogenous growth models. It discusses the Harrod-Domar model which relates an economy's growth rate to its capital stock and savings ratio. It then summarizes the Solow-Swan model which incorporates technological progress and assumes diminishing returns to capital. The model predicts economies will eventually reach a steady state level of capital and output. Finally, it briefly mentions endogenous growth models which seek to explain technological progress.
This document summarizes key concepts from the Solow growth model. It explains that the model builds on the Cobb-Douglas production function by adding capital accumulation over time. The model shows how capital stock, output, and consumption per capita converge to steady-state levels. It also explains that while capital accumulation drives short-run growth, diminishing returns prevent long-run growth unless productivity or population increase. The document analyzes how changes to investment rates or depreciation rates impact the steady state and transition path of the economy.
This document outlines an economics course on the economics of less developed countries. It covers several key theories of economic growth, including Harrod-Domar, Solow, and exogenous growth models. The Solow model incorporates diminishing returns to capital and predicts economies will eventually reach a steady state level of output unless productivity or population growth occurs. The course will examine international trade, finance, development aid, government institutions, and their relationship to economic growth. Readings are drawn from Todaro and Smith's economic development textbook.
The document summarizes the Solow growth model of macroeconomics. It explains that the model focuses on long-run economic growth driven by capital accumulation from savings and investment. While higher savings can increase growth in the short-run, in the long-run the economy reaches a steady-state where population growth determines the rate of growth and savings only impacts output levels, not growth rates. The model uses mathematical equations to represent capital accumulation and its impact on output over time.
Page 2 of 41
THE MODEL SETUP AND QUESTIONS
GDP (the demand side of the economy) is given simply by
our standard expenditure equation:
Y = C + I + G +NX
For these notes we make the simplifying assumption that
there is no government or exchange of goods and
services with the rest of the world. Hence, G = NX = 0 and
GDP (again, the demand side of the economy) is given
simply by:
Y = C + I.
You might be asked to think about what happens if there
is government and exchange with the rest of the world at
some point though. So you have to fully understand the
model to be able to tweak it, in case and answer those
questions.
We’ll look at an economy with given “structural
characteristics”:
A given production function ==> the Cobb Douglas
production function that we have studied already.
This represents the supply side of the economy.
A given exogenous savings rate for the economy: s
A given population growth rate: n
A given depreciation rate of capital: d
Page 3 of 41
With this info we want to analyze the economy long run
behavior…that’s what growth is all about. We want to try
to understand the evolution of GDP and other
macroeconomic variable with a long time horizon
perspective.
In particular, we want to analyze changes in the economy
over time:
We have seen so far that to affect productivity we need
to understand physical capital and investment so:
– How do these structural characteristics interact
to determine the investment level, and the
evolution of the capital stock?
– How does the evolution of the capital stock
interact with population in determining the
change in production?
– We’ll discuss how these factors determine the
behavior of the economy period after period,
and the implication of this for its long run
evolution.
What are the level of physical capital, output,
investment and consumption in the long run for
a specific economy?
Page 4 of 41
THE EQUATIONS OF THE MODEL
We have 5 basic ingredients (equations) in the Solow
model (yes, you need to memorize those and be able to
work the math out). Thankfully, we have seen 4 of these
5 equations previously at some point during this course
so it is just a matter of putting them together, and
understanding how they interact:
1) The production function: We have seen this equation
concerning the production function already in the slides
for chapter 12. For these notes we will use the Cobb
Douglas production function which, again, you have seen
in details. It has the constant returns to scale property.
Formally:
A is the TFP (or technology).
is physical capital at period t
is labor at period t
0 < < 1 is called the capital share you should know
this already.
1 is called the labor share you should know this
already.
Only 2 factors of productions (K, L) are analyzed jointly
with technology (A) here. This is for simplicity. It is
Page 5 of 41
possible to make the model more complicated and
consider more factor of productions such as human
capital, knowledge capital, organiz.
1. The document provides an overview of the Solow growth model, which shows how capital accumulation, labor force growth, and technological advances interact in an economy and affect total output.
2. It examines how the model treats the accumulation of capital over time and how savings, depreciation, population growth, and technological progress influence the long-run capital stock and output.
3. The model predicts that economies with higher savings rates or population growth rates will reach different steady-state levels of capital and output per worker.
This document provides an overview of the IS curve model. It begins with an introduction that defines the IS curve and establishes the negative relationship between interest rates and short-run output. It then sets up the basic model, deriving the IS curve equation, and exploring how to use the IS curve to analyze changes in interest rates and aggregate demand shocks. Finally, it discusses the microeconomic foundations of consumption, investment, and government spending behaviors that underlie the aggregate demand components of the IS curve model.
This document summarizes key aspects of the Solow growth model and endogenous growth theory. It discusses how technological progress is incorporated in the Solow model and its effects on variables like output per worker. It also examines empirical evidence about balanced growth and the relationship between factor prices and productivity in the US. The document analyzes the US saving rate using the Solow model and considers the impacts of different public policies on economic growth. Finally, it introduces endogenous growth theory and how it rejects the exogenous technological progress assumption of the Solow model.
This document provides an overview of key concepts relating to analyzing an economy in the short run, including:
- The difference between potential output in the long run and actual output which can fluctuate in the short run due to economic shocks.
- How the gap between actual and potential GDP indicates the state of the economy and whether it is in a recession.
- The relationship between output and inflation shown through the Phillips Curve, where higher output leads to increased inflation.
- Okun's Law which describes the inverse relationship between changes in output and the unemployment rate.
This document provides an overview of the Solow growth model, which examines how economic growth and standards of living are determined in the long run. It introduces key concepts such as the production function, saving rate, depreciation rate, capital accumulation, and steady state. The steady state is the level of capital where investment just offsets depreciation and capital remains constant. The model predicts that countries with higher saving and investment rates will have higher levels of capital and income per worker in the long run. It also discusses finding the optimal saving rate and capital stock, known as the Golden Rule, which maximizes consumption.
This document provides an overview of key concepts from Chapter Seven of the textbook Macroeconomics by N. Gregory Mankiw. It discusses the Solow growth model and how it treats capital accumulation. It then explains how population growth and technological progress can be incorporated into the model. The summary concludes by noting that the Solow model predicts balanced growth and convergence between economies in the long run.
This document contains slides from a chapter on economic growth from a macroeconomics textbook. It introduces the Solow growth model, which examines how a closed economy's saving rate and population growth affect its long-run standard of living and capital stock. The model shows diminishing returns to capital as capital per worker increases. It defines concepts like the steady state, where investment just offsets depreciation, keeping the capital stock constant. Numerical examples demonstrate how the capital stock approaches the steady state over time as investment exceeds depreciation when capital is below the steady state level.
1) The document summarizes key aspects of the Solow growth model, including how capital accumulation, depreciation, investment, and population growth determine an economy's steady state level of output.
2) It shows graphically how the steady state is reached through the balance of investment and depreciation, and how population growth lowers the steady state.
3) The "Golden Rule level of capital" is defined as the steady state that maximizes consumption, where the marginal product of capital equals the depreciation rate.
Chapter 3-2 Growth Models and Developement Strategies.pptxselam49
The document summarizes key aspects of endogenous growth models. It discusses limitations of exogenous growth models in explaining long-term economic growth. Endogenous growth models assume technological progress is determined within the economic system, rather than imposed from outside. This allows for sustained growth without diminishing returns. The models focus on increasing returns to scale through complementary investments in human capital, infrastructure, and research and development.
This document provides an outline and overview of growth theory. It discusses the empirical picture of economic growth, including some stylized facts about growth rates, capital intensity, returns, and income distribution over time. It also examines convergence across countries and uses growth accounting to measure the contributions of capital, labor, and total factor productivity to output growth. The document reviews relevant literature on these topics and provides empirical examples and results.
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1. Chapter 5: Solow Growth Model
Ryan W. Herzog
Spring 2021
Ryan W. Herzog (GU) Solow Spring 2021 1 / 59
2. 1 Introduction
2 Setting up the Model
3 Prices and the Real Interest Rate
4 Solving the Solow Model
5 Looking at Data through the Lens of the Solow Model
6 Understanding the Steady State
7 Economic Growth in the Solow Model
8 Some Economic Experiments
9 The Principle of Transition Dynamics
10 Strengths and Weaknesses of the Solow Model
Ryan W. Herzog (GU) Solow Spring 2021 2 / 59
3. Introduction
Learning Objectives
How capital accumulates over time.
How diminishing MPK explains differences in growth rates across
countries.
The principle of transition dynamics.
The limitations of capital accumulation, and how it leaves a
significant part of economic growth unexplained.
Ryan W. Herzog (GU) Solow Spring 2021 3 / 59
4. Introduction
The Solow Growth Model
Builds on the production model by adding a theory of capital
accumulation
Was developed in the mid-1950s by Robert Solow of MIT
Was the basis for the Nobel Prize he received in 1987
Ryan W. Herzog (GU) Solow Spring 2021 4 / 59
5. Introduction
Changes in the Solow Model
Capital stock is no longer exogenous.
Capital stock is now “endogenized”
The accumulation of capital is a possible engine of long-run economic
growth.
Ryan W. Herzog (GU) Solow Spring 2021 5 / 59
6. Setup
Production
Start with the previous production model and add an equation
describing the accumulation of capital over time.
The production function:
Cobb-Douglas
Constant returns to scale in capital and labor
Exponent of one-third on K
Yt = F(Kt, Lt) = AK
1/3
t L
2/3
t (1)
Ryan W. Herzog (GU) Solow Spring 2021 6 / 59
7. Setup
Output
We assume a closed economy so output can be used for either
consumption or investment
Ct + It = Yt (2)
This is called the resource constraint (how an economy can use its
resources).
Ryan W. Herzog (GU) Solow Spring 2021 7 / 59
8. Setup
Capital Accumulation
Goods invested for the future determines the accumulation of capital.
Capital accumulation equation:
Kt+1 = Kt + It − dKt (3)
where
Kt+1 is next year’s capital stock
Kt is this year’s capital stock
It is investment this year
d is the depreciation rate
Ryan W. Herzog (GU) Solow Spring 2021 8 / 59
9. Setup
Depreciation Rate
The amount of capital that wears out each period
Mathematically must be between 0 and 1 in this setting
Often viewed as approximately 10 percent (some examples assume
d = 0.07).
Ryan W. Herzog (GU) Solow Spring 2021 9 / 59
10. Setup
Evolution of Capital
Let ∆Kt+1 ≡ Kt+1 − Kt
Thus:
Kt+1 − Kt = It − dKt
or
∆Kt+1 = It − dKt (4)
Ryan W. Herzog (GU) Solow Spring 2021 10 / 59
11. Setup
An Example of Capital Accumulation
Assume the economy begins with an initial level of capital, k0 of
1,000 units:
Time, t Capital, Kt Investment, It Depreciation, dKt ∆Kt+1
0 1,000 200 100 100
1 1,100 200 110 90
2 1,190 200 119 81
3 1,271 200 127 73
4 1,344 200 134 66
5 1,410 200 141 59
Ryan W. Herzog (GU) Solow Spring 2021 11 / 59
12. Setup
Labor
To keep things simple, labor demand and supply not included
The amount of labor in the economy is given exogenously at a
constant level (L = L).
Ryan W. Herzog (GU) Solow Spring 2021 12 / 59
13. Setup
Investment
In our single firm economy (i.e. farmers) we assume a constant
portion of the output is consumed and the rest is investment:
It = sYt (5)
Therefore:
Ct = (1 − s)Yt
You can think of s as a constant saving rate. In this model saving
equal investment, implicitly assuming a closed economy (in reality,
use the investment rate).
Ryan W. Herzog (GU) Solow Spring 2021 13 / 59
14. Setup
The Solow Model
The model has five endogenous variables (Yt, Kt, Lt, Ct, It)
The model has five equations:
Production function: Y = AK1/3
L2/3
Capital accumulation: ∆Kt+1 = It − dKt
Labor force: L = L
Resource constraint: Ct + It = Yt
Allocation of resources: It = sYt
Exogenous parameters: A, s, d, L, K0
Ryan W. Herzog (GU) Solow Spring 2021 14 / 59
15. Setup
Questions/Differeces in the Solow Model
Differences between Solow model and production model in previous
chapter:
Dynamics of capital accumulation added
Left out capital and labor markets, along with their prices
Why include the investment share but not the consumption share?
No need to − it would be redundant
Preserve five equations and five unknowns
Ryan W. Herzog (GU) Solow Spring 2021 15 / 59
16. Setup
Key Definitions
Stock: A quantity that survives from period to period.
Flow: A quantity that lasts a single period
A change in the stock of capital is the flow of investment.
Ryan W. Herzog (GU) Solow Spring 2021 16 / 59
17. Prices
The Real Interest Rate
The amount a person can earn by saving one unit of output for a year
Or, the amount a person must pay to borrow one unit of output for a
year
Measured in constant dollars, not in nominal dollars
Ryan W. Herzog (GU) Solow Spring 2021 17 / 59
18. Prices
Saving
The difference between income and consumption
Is equal to investment
Yt − Ct
| {z }
saving
= It
The closed economy assumptions forces all saving to flow into
domestic investment.
In an open economy saving could fund domestic or foreign
investment, plus foreign saving can fund domestic investment.
Ryan W. Herzog (GU) Solow Spring 2021 18 / 59
19. Prices
Return on Saving and MPK
A unit of investment becomes a unit of capital which means the
return on saving must equal the rental price of capital.
The real interest rate equals the rental price of capital which equals
the MPK.
Ryan W. Herzog (GU) Solow Spring 2021 19 / 59
20. Solving
Solving the Model
The model needs to be solved at every point in time, which cannot be
done algebraically.
Two ways to make progress
1 Show a graphical solution
2 Solve the model in the long run
We can start by combining equations to go as far as we can with
algebra.
Ryan W. Herzog (GU) Solow Spring 2021 20 / 59
21. Solving
Solving the Model
Let’s start by combining the investment allocation (It = sYt) with the
capital accumulation equation (∆Kt+1 = It − dKt)
∆Kt+1
| {z }
change in capital
= sYt − dKt
| {z }
net investment
(6)
We can interpret equation 6 as the change in capital equals
investment less depreciation.
Ryan W. Herzog (GU) Solow Spring 2021 21 / 59
22. Solving
Production
Since we assume the supply of labor is constant (L = L) we can
reduce the production function down to two unknowns (Yt, Kt).
Y = AK1/3
L
2/3
(7)
We can now combine our two equations by plugging in equation 7
into equation 6.
This would provide us with a single dynamic equation that describes
the evolution of the capital stock.
Ryan W. Herzog (GU) Solow Spring 2021 22 / 59
23. Solving
Creating the Solow Diagram
The Solow Diagram plots the two terms (sY and dK)
New investment looks like the production functions previously
graphed but scaled down by the investment rate.
sY = sAK1/3
L
2/3
Depreciation is constant so dK is linear with an intercept of 0 and
slope of d
Ryan W. Herzog (GU) Solow Spring 2021 23 / 59
25. Solving
Using the Solow Diagram
If the amount of investment is greater than the amount of
depreciation the capital stock will increase until investment equals
depreciation.
When they equal the change in capital is equal to 0
the capital stock will stay at this value of capital forever
this is called the steady state
If depreciation is greater than investment, the economy converges to
the same steady state as above.
Ryan W. Herzog (GU) Solow Spring 2021 25 / 59
26. Solving
Dynamics of the Model
When not in the steady state, the economy exhibits a movement of
capital toward the steady state.
At the rest point of the economy, all endogenous variables are steady.
Transition dynamics take the economy from its initial level of capital
to the steady state.
Ryan W. Herzog (GU) Solow Spring 2021 26 / 59
27. Solving
Output and Consumption
As K moves to its steady state by transition dynamics, output will
also move to its steady state.
Y = AK(1/3)
L
2/3
Consumption can also be seen in the diagram since it is the difference
between output and investment.
Ct = Yt − It
Ryan W. Herzog (GU) Solow Spring 2021 27 / 59
29. Solving
Solving Mathematically for the Steady State
In the steady state, investment equals depreciation.
sY ∗
= dK∗
Substitute in the production function
sAK∗1/3
L
2/3
= dK∗
Ryan W. Herzog (GU) Solow Spring 2021 29 / 59
30. Solving
Solve for K∗
Solve for K∗
K∗
=
sA
d
3/2
L (8)
The steady-state level of capital is positively related with the
investment rate
the size of the workforce
the productivity of the economy
Negatively correlated with the depreciation rate
Ryan W. Herzog (GU) Solow Spring 2021 30 / 59
31. Solving
Solve for Y ∗
We can plug K∗ into the production function:
Y ∗
= AK∗1/3
L
2/3
Doing so yields:
Y ∗
=
s
d
1/2
A
3/2
L (9)
Higher steady-state production caused by higher productivity and
investment rate
Lower steady-state production caused by faster depreciation
Ryan W. Herzog (GU) Solow Spring 2021 31 / 59
32. Solving
Output per Worker (Person)
Finally, divide both sides of the last equation by labor to get output
per person (y) in the steady state.
y∗
≡
Y ∗
L∗
=
s
d
1/2
A
3/2
(10)
Note the exponent on productivity is different here (3/2) than in the
production model (1).
Higher productivity has additional effects in the Solow model by
leading the economy to accumulate more capital.
Ryan W. Herzog (GU) Solow Spring 2021 32 / 59
33. Data
The Capital-Output Ratio
Recall the steady state, where ∆Kt+1 = 0 and sY ∗ = dK∗
The capital to output ratio is the ratio of the investment rate to the
depreciation rate:
K∗
Y ∗
=
s
d
(11)
Investment rates vary across countries.
It is assumed that the depreciation rate is relatively constant.
Ryan W. Herzog (GU) Solow Spring 2021 33 / 59
35. Data
Differences in Y /L
The Solow model gives more weight to TFP in explaining per capita
output than the production model.
We can use this formula to understand why some countries are so
much richer.
Take the ratio of y* for two countries and assume the depreciation
rate is the same:
y∗
rich
y∗
poor
| {z }
70
=
Arich
Apoor
3/2
| {z }
35
×
srich
spoor
1/2
| {z }
2
(12)
Ryan W. Herzog (GU) Solow Spring 2021 35 / 59
36. Data
Explaining Differences in TFP and investment
Investment rates in rich countries are approximately 25 to 30 percent.
Investment rates in poor countries are approximately 7 percent.
Then
srich
spoor
1/2
= (28/7)1/2 = 41/2 ≈ 2
We can then find the ratio of TFP as 70/2 ≈ 35
Ryan W. Herzog (GU) Solow Spring 2021 36 / 59
37. Steady State
The Steady State
The economy reaches a steady state because investment has
diminishing returns.
The rate at which production and investment rise is smaller as the
capital stock is larger.
Also, a constant fraction of the capital stock depreciates every period.
Depreciation is not diminishing as capital increases.
Eventually, net investment is zero.
The economy rests in steady state.
Ryan W. Herzog (GU) Solow Spring 2021 37 / 59
38. Growth
Economic Growth in the Solow Model
Important result: there is no long-run economic growth in the Solow
model.
In the steady state, growth stops, and all of the following are
constant:
Output
Capital
Output per person
Consumption per person
Ryan W. Herzog (GU) Solow Spring 2021 38 / 59
39. Growth
Economic Growth
Empirically, however, economies appear to continue to grow over
time. Thus, we see a drawback of the model.
According to the model:
Capital accumulation is not the engine of long-run economic growth.
After we reach the steady state, there is no long-run growth in output.
Saving and investment are beneficial in the short-run but do not
sustain long-run growth due to diminishing returns
Ryan W. Herzog (GU) Solow Spring 2021 39 / 59
40. Growth
Adding Population Growth to The Model
Can growth in the labor force lead to overall economic growth?
It can in the aggregate.
It can’t in output per person.
The presence of diminishing returns leads capital per person and
output per person to approach the steady state even with more
workers
Ryan W. Herzog (GU) Solow Spring 2021 40 / 59
41. Experiments
An Increase in the Investment Rate
Suppose investment increases from s to s
0
, then...
The investment curve rotates upward
The depreciation curve remains unchanged.
The capital stock increases by transition dynamics to reach the new
steady state because investment exceeds depreciation
The new steady state is located to the right where s
0
Y = dK.
Ryan W. Herzog (GU) Solow Spring 2021 41 / 59
43. Experiments
Output
The rise in investment leads capital to accumulate over time.
This higher capital causes output to rise as well.
Output increases from its initial steady-state level Y ∗ to the new
steady state Y ∗∗.
Ryan W. Herzog (GU) Solow Spring 2021 43 / 59
45. Experiments
A Rise in the Depreciation Rate
Suppose depreciation rate is exogenously shocked to a higher rate
from d to d
0
, then...
The depreciation curve rotates upward
The investment curve remains unchanged.
The capital stock declines by transition dynamics until it reaches the
new steady state this happens because depreciation exceeds investment
The new steady state is located to the left where sY = d
0
K.
Ryan W. Herzog (GU) Solow Spring 2021 45 / 59
47. Experiments
Output in Response to a Change in Depreciation
The decline in capital reduces output.
Output declines rapidly at first, and then gradually settles down at its
new, lower steady-state level Y ∗∗.
Ryan W. Herzog (GU) Solow Spring 2021 47 / 59
49. Experiments
What Else Can Change?
We looked at changes to depreciation and investment rates. What
happens if...
Technology increase?
Labor decreases?
A country has a lower level of initial capital.
Ryan W. Herzog (GU) Solow Spring 2021 49 / 59
50. Transition
Transition Dynamics
If an economy is below steady state then economic growth will be
positive.
If an economy is above steady state then economic growth will be
negative.
When graphing this, a ratio scale is used. This allows us to see that
output changes more rapidly if we are further from the steady state
As the steady state is approached, growth shrinks to zero.
Ryan W. Herzog (GU) Solow Spring 2021 50 / 59
51. Transition
The Principle of Transition Dynamics
The farther below its steady state an economy is, (in percentage
terms) the faster the economy will grow
The farther above its steady state the slower the economy will grow
Allows us to understand why economies grow at different rates
Ryan W. Herzog (GU) Solow Spring 2021 51 / 59
52. Transition
Understanding Differences in Growth Rates
Empirically, for OECD countries, transition dynamics holds:
Countries that were poor in 1960 grew quickly.
Countries that were relatively rich grew slower.
Looking at the world as whole, on average, rich and poor countries
grow at the same rate.
Most countries have already reached their steady states.
Countries are poor not because of a bad shock, but because they have
parameters that yield a lower steady state.
Ryan W. Herzog (GU) Solow Spring 2021 52 / 59
55. Transition
South Korea and Philippines
South Korea
Grew at 6 percent per year
Income increases from 15 percent to 75 percent of US income
Philippines
Grew at 1.7 percent per year
Stayed at 15 percent of U.S. income
Ryan W. Herzog (GU) Solow Spring 2021 55 / 59
56. Transition
Comparing US and Korea
Assuming equal depreciation rates
y∗
Korea
y∗
US
=
AKorea
AUS
3/2
×
sKorea
sUS
1/2
(13)
The long-run ratio of per capita incomes depends on the ratio of
productivities (TFP levels) and the ratio of investment rates
Ryan W. Herzog (GU) Solow Spring 2021 56 / 59
58. Strengths and Weaknesses
Strengths
It provides a theory that determines how rich a country is in the long
run.
The long run occurs at the steady state
The principle of transition dynamics allows for an understanding of
differences in growth rates across countries
A country further from the steady state will grow faster
Ryan W. Herzog (GU) Solow Spring 2021 58 / 59
59. Strengths and Weaknesses
Weaknesses
It focuses on investment and capital but the much more important
factor of TFP is still unexplained
It does not explain why different countries have different investment
and productivity rates.
A more complicated model could endogenize the investment rate
The model does not provide a theory of sustained long-run economic
growth.
Ryan W. Herzog (GU) Solow Spring 2021 59 / 59