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.
Domar's growth model from 1946 analyzes how a capitalist economy can grow at a constant rate after reaching full employment. It assumes aggregate supply equals aggregate demand during steady growth. The model shows that for steady growth, the rates of investment, capital stock growth, output growth, and employment growth must all be equal. It derives the equation that the growth rate equals the savings ratio multiplied by the incremental output-capital ratio. Investment has dual effects of increasing both aggregate demand and productive capacity in the long-run.
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.
This chapter introduces the Solow growth model, which examines how capital accumulation and population growth impact economic growth and living standards over the long run. The key aspects covered include:
- The Solow model framework of production, consumption, investment, and capital accumulation over time.
- How economies converge to a steady state level of capital per worker and output per worker.
- How factors like the saving rate can impact the steady state level and long-run growth.
- The "Golden Rule" concept of finding the optimal saving rate and capital stock that maximizes long-run consumption per person.
Concept and application of cd and ces production function in resource managem...Nar B Chhetri
The document defines production functions and describes the Cobb-Douglas and CES production functions. It provides the mathematical forms and properties of each. The Cobb-Douglas production function relates output to labor and capital inputs. It is widely used in empirical analyses. The CES production function generalizes the Cobb-Douglas by allowing the elasticity of substitution to vary. Both functions exhibit constant returns to scale under certain parameter values. Examples are given of estimating production functions for various industries and crops using regression analysis.
This document summarizes Ricardo's theory of economic growth. It states that growth occurs through capital accumulation fueled by profits. However, as growth proceeds, wages and rents increase which squeeze profits. Eventually profits fall to zero, halting further investment and growth, reaching a stationary state. The stationary state can be avoided through international trade that imports corn, preventing rising domestic corn prices from cutting into profits.
The Lewis dual sector model of development describes an economy transitioning from subsistence agriculture to a more modern, urbanized structure. It consists of two sectors: a traditional subsistence sector with zero marginal productivity of labor, providing surplus labor; and a modern industrial sector where labor is transferred from the traditional sector, expanding output and employment through reinvested profits. However, the model is criticized for assuming profits are always reinvested when they could enable labor-saving investments or capital flight, and for assuming perfect competition in labor markets and unlimited surplus labor, which is inconsistent with historical evidence from developing countries.
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.
Domar's growth model from 1946 analyzes how a capitalist economy can grow at a constant rate after reaching full employment. It assumes aggregate supply equals aggregate demand during steady growth. The model shows that for steady growth, the rates of investment, capital stock growth, output growth, and employment growth must all be equal. It derives the equation that the growth rate equals the savings ratio multiplied by the incremental output-capital ratio. Investment has dual effects of increasing both aggregate demand and productive capacity in the long-run.
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.
This chapter introduces the Solow growth model, which examines how capital accumulation and population growth impact economic growth and living standards over the long run. The key aspects covered include:
- The Solow model framework of production, consumption, investment, and capital accumulation over time.
- How economies converge to a steady state level of capital per worker and output per worker.
- How factors like the saving rate can impact the steady state level and long-run growth.
- The "Golden Rule" concept of finding the optimal saving rate and capital stock that maximizes long-run consumption per person.
Concept and application of cd and ces production function in resource managem...Nar B Chhetri
The document defines production functions and describes the Cobb-Douglas and CES production functions. It provides the mathematical forms and properties of each. The Cobb-Douglas production function relates output to labor and capital inputs. It is widely used in empirical analyses. The CES production function generalizes the Cobb-Douglas by allowing the elasticity of substitution to vary. Both functions exhibit constant returns to scale under certain parameter values. Examples are given of estimating production functions for various industries and crops using regression analysis.
This document summarizes Ricardo's theory of economic growth. It states that growth occurs through capital accumulation fueled by profits. However, as growth proceeds, wages and rents increase which squeeze profits. Eventually profits fall to zero, halting further investment and growth, reaching a stationary state. The stationary state can be avoided through international trade that imports corn, preventing rising domestic corn prices from cutting into profits.
The Lewis dual sector model of development describes an economy transitioning from subsistence agriculture to a more modern, urbanized structure. It consists of two sectors: a traditional subsistence sector with zero marginal productivity of labor, providing surplus labor; and a modern industrial sector where labor is transferred from the traditional sector, expanding output and employment through reinvested profits. However, the model is criticized for assuming profits are always reinvested when they could enable labor-saving investments or capital flight, and for assuming perfect competition in labor markets and unlimited surplus labor, which is inconsistent with historical evidence from developing countries.
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 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 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 Harrod-Domar model of economic growth extends Keynesian analysis to the long run by considering the dual effects of investment on aggregate demand and productive capacity. It seeks to determine the unique growth rate of investment and income needed to maintain full employment. The Domar version presents a fundamental growth equation showing that the increase in national income depends on the increase in capital stock multiplied by the marginal output-capital ratio. Harrod's model treats growth more dynamically, with the warranted growth rate determined by the population growth rate, output per capita based on investment level, and capital accumulation. Equilibrium is achieved when the actual incremental capital-output ratio equals the required ratio warranted by technology.
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.
This document provides an overview of the AK model of endogenous economic growth. It discusses how the AK model addresses limitations of previous exogenous growth models. The key aspects of the AK model are:
- It models economic output as a linear function of capital stock, without diminishing returns to capital.
- This allows for perpetual long-run growth, unlike exogenous models which predict convergence to a steady state.
- The growth rate depends on savings rate and the level of technology, represented by the parameter A. Improvements in A can permanently increase the growth rate.
The Harrod-Domer model theorizes that a country's economic growth rate is defined by its savings level and capital-output ratio. It suggests there is no natural balanced growth. The model was developed independently by Roy Harrod and Evsey Domar to explain growth in terms of savings and capital productivity. It requires continuous net investment to sustain real income and production growth. The model's assumptions include no government intervention, full initial employment, a closed economy, fixed capital-labor ratios and constant savings and interest rates. Its main criticism is the unrealistic assumption of no reason for sufficient growth to maintain full employment.
Restatement of quantity theory of moneyNayan Vaghela
Milton Friedman proposed a restatement of the Quantity Theory of Money (QTM) that incorporated permanent real income and wealth. He argued that the demand for money depends on total wealth, expected returns on various assets, and tastes/preferences. Friedman defined permanent real income as the sustainable level of income without reducing wealth over time. His equation for the QTM included factors like the money stock, the price level, permanent income, expected rates of return on different assets, and other variables. While improving on prior theories, Friedman's restatement still had limitations like subjective terms that are hard to measure and challenges maintaining a steady money supply in a modern economy.
Adam Smith is considered the Father of Economics. In his seminal book, The Wealth of Nations, he argued that a country's wealth comes from the total value of goods and services produced, not just gold or agriculture. Smith identified two key drivers of economic growth: the division of labor and capital accumulation. The division of labor leads to specialization and higher productivity, while capital accumulation raises productivity by increasing capital per worker. This starts a virtuous cycle of growth, but eventually diminishing returns set in and growth slows, reaching a stationary state.
The document summarizes Kuznets' hypothesis that income inequality within countries initially rises and then falls with economic development. It provides evidence from Kuznets' 1955 study showing higher inequality in less developed countries (LDCs) like India compared to developed countries (DCs) like the UK and US. Kuznets attributed the inverted-U shape relationship between development and inequality to structural changes in early industrialization benefiting high-income groups before policies and social changes in later stages reduced the gap. The document also discusses measures of inequality like the Gini coefficient and debates around Kuznets' hypothesis.
The document summarizes Samuelson's model of business cycles, which relates economic fluctuations to the interaction between the multiplier and accelerator effects. It explains that the multiplier amplifies changes in autonomous investment and consumption, while the accelerator reinforces increases in income through further induced investment. The model is represented mathematically to show how different combinations of the multiplier and accelerator can produce equilibrium, damped cycles, explosive cycles, or cycles of constant amplitude to describe business cycle patterns.
The document summarizes the Ramsey-Cass-Koopmans model of economic growth. It describes the key assumptions of the model including representative consumers who maximize utility subject to a budget constraint. The model endogenizes savings by allowing for intertemporal consumer optimization. It presents the optimal growth conditions including the Euler equation and transitional dynamics towards a steady state equilibrium with constant capital-labor ratio and consumption.
Meaning, definition, nature, scope, importance and limitation of macro econo...Ashutosh Deshmukh
The document provides an overview of macroeconomics concepts taught by Dr. Ashutosh A. Deshmukh. It defines macroeconomics as the study of aggregates and averages covering the economy as a whole, such as total income, employment, output, prices. It discusses key events that influenced the development of macroeconomics like the Great Depression. It also outlines several macroeconomic topics, theories and models covered, including classical employment theory, Keynesian economics, economic growth, and limitations of the macroeconomic approach.
The document discusses two theories of consumption:
1. Permanent Income Hypothesis by Milton Friedman which argues that consumers base their consumption on their permanent income rather than temporary fluctuations in income. Consumption remains constant even if temporary income changes in the short run.
2. Life Cycle Hypothesis by Modigliani which proposes that long-term consumption is related to lifetime average income and depends on factors like wealth, future earnings, age, and rate of return on capital. It suggests consumption and savings patterns vary at different stages of life and are influenced by the age distribution of the population.
This document discusses macroeconomics and macroeconomic policy debates from classical and Keynesian perspectives. It covers unemployment, price stability, and exchange rates. On unemployment, classical economists believe full employment is always achieved through flexible wages, while Keynesians believe unemployment is normal and government intervention is needed. On price stability, classical economists see prices adjusting to maintain full employment while Keynesians see stable prices with variable output. Exchange rates are influenced by demand and supply factors in both frameworks.
Harrod – Domar Model - Development Model.pptxNithin Kumar
The document discusses the Harrod-Domar model of economic growth developed by Roy Harrod and Evsey Domar. Some key points:
1. The model focuses on the role of capital accumulation and investment in driving economic growth.
2. It uses the capital-output ratio and investment ratio to determine the rate of economic growth.
3. Harrod identified the actual, warranted, and natural rates of growth and argued stability requires equality between these rates.
4. The warranted rate depends on capital-output ratio and savings ratio matching the demand and supply of capital.
5. The natural rate is determined by long-term factors like population and technology.
1. The document discusses general equilibrium theory (GET) and defines general equilibrium as a state where all markets and decision-making units are in simultaneous equilibrium.
2. It presents a simple two-sector general equilibrium model of an economy with two consumers, two goods, and two factors of production. Equations represent consumer demand, factor supply, factor demand, good supply, and market clearing for goods and factors.
3. With the number of equations equal to the number of unknowns, a general equilibrium solution exists in this Walrasian model under certain assumptions. GET provides a framework for understanding the complexity of economic systems through interdependent markets.
The classical growth theory argues that economic growth will decrease or end because of an increasing population and limited resources Classical growth theory economists believed that temporary increases in real GDP per person would cause a population explosion that would consequently decrease real GDP.
This document discusses stabilization policy, which aims to stabilize the economy and prevent fluctuations in output, employment, and prices that occur during business cycles. Stabilization policy uses monetary policy, fiscal policy, and international measures. Monetary policy involves tools like changing interest rates, reserve ratios, and open market operations to influence the money supply. Fiscal policy involves manipulating public expenditure, taxation, and debt to stimulate or contract the economy. International measures coordinate import/export policies and currency values with other countries. The overall goal is to counteract inflation during booms and spur growth during recessions.
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.
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.
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 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 Harrod-Domar model of economic growth extends Keynesian analysis to the long run by considering the dual effects of investment on aggregate demand and productive capacity. It seeks to determine the unique growth rate of investment and income needed to maintain full employment. The Domar version presents a fundamental growth equation showing that the increase in national income depends on the increase in capital stock multiplied by the marginal output-capital ratio. Harrod's model treats growth more dynamically, with the warranted growth rate determined by the population growth rate, output per capita based on investment level, and capital accumulation. Equilibrium is achieved when the actual incremental capital-output ratio equals the required ratio warranted by technology.
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.
This document provides an overview of the AK model of endogenous economic growth. It discusses how the AK model addresses limitations of previous exogenous growth models. The key aspects of the AK model are:
- It models economic output as a linear function of capital stock, without diminishing returns to capital.
- This allows for perpetual long-run growth, unlike exogenous models which predict convergence to a steady state.
- The growth rate depends on savings rate and the level of technology, represented by the parameter A. Improvements in A can permanently increase the growth rate.
The Harrod-Domer model theorizes that a country's economic growth rate is defined by its savings level and capital-output ratio. It suggests there is no natural balanced growth. The model was developed independently by Roy Harrod and Evsey Domar to explain growth in terms of savings and capital productivity. It requires continuous net investment to sustain real income and production growth. The model's assumptions include no government intervention, full initial employment, a closed economy, fixed capital-labor ratios and constant savings and interest rates. Its main criticism is the unrealistic assumption of no reason for sufficient growth to maintain full employment.
Restatement of quantity theory of moneyNayan Vaghela
Milton Friedman proposed a restatement of the Quantity Theory of Money (QTM) that incorporated permanent real income and wealth. He argued that the demand for money depends on total wealth, expected returns on various assets, and tastes/preferences. Friedman defined permanent real income as the sustainable level of income without reducing wealth over time. His equation for the QTM included factors like the money stock, the price level, permanent income, expected rates of return on different assets, and other variables. While improving on prior theories, Friedman's restatement still had limitations like subjective terms that are hard to measure and challenges maintaining a steady money supply in a modern economy.
Adam Smith is considered the Father of Economics. In his seminal book, The Wealth of Nations, he argued that a country's wealth comes from the total value of goods and services produced, not just gold or agriculture. Smith identified two key drivers of economic growth: the division of labor and capital accumulation. The division of labor leads to specialization and higher productivity, while capital accumulation raises productivity by increasing capital per worker. This starts a virtuous cycle of growth, but eventually diminishing returns set in and growth slows, reaching a stationary state.
The document summarizes Kuznets' hypothesis that income inequality within countries initially rises and then falls with economic development. It provides evidence from Kuznets' 1955 study showing higher inequality in less developed countries (LDCs) like India compared to developed countries (DCs) like the UK and US. Kuznets attributed the inverted-U shape relationship between development and inequality to structural changes in early industrialization benefiting high-income groups before policies and social changes in later stages reduced the gap. The document also discusses measures of inequality like the Gini coefficient and debates around Kuznets' hypothesis.
The document summarizes Samuelson's model of business cycles, which relates economic fluctuations to the interaction between the multiplier and accelerator effects. It explains that the multiplier amplifies changes in autonomous investment and consumption, while the accelerator reinforces increases in income through further induced investment. The model is represented mathematically to show how different combinations of the multiplier and accelerator can produce equilibrium, damped cycles, explosive cycles, or cycles of constant amplitude to describe business cycle patterns.
The document summarizes the Ramsey-Cass-Koopmans model of economic growth. It describes the key assumptions of the model including representative consumers who maximize utility subject to a budget constraint. The model endogenizes savings by allowing for intertemporal consumer optimization. It presents the optimal growth conditions including the Euler equation and transitional dynamics towards a steady state equilibrium with constant capital-labor ratio and consumption.
Meaning, definition, nature, scope, importance and limitation of macro econo...Ashutosh Deshmukh
The document provides an overview of macroeconomics concepts taught by Dr. Ashutosh A. Deshmukh. It defines macroeconomics as the study of aggregates and averages covering the economy as a whole, such as total income, employment, output, prices. It discusses key events that influenced the development of macroeconomics like the Great Depression. It also outlines several macroeconomic topics, theories and models covered, including classical employment theory, Keynesian economics, economic growth, and limitations of the macroeconomic approach.
The document discusses two theories of consumption:
1. Permanent Income Hypothesis by Milton Friedman which argues that consumers base their consumption on their permanent income rather than temporary fluctuations in income. Consumption remains constant even if temporary income changes in the short run.
2. Life Cycle Hypothesis by Modigliani which proposes that long-term consumption is related to lifetime average income and depends on factors like wealth, future earnings, age, and rate of return on capital. It suggests consumption and savings patterns vary at different stages of life and are influenced by the age distribution of the population.
This document discusses macroeconomics and macroeconomic policy debates from classical and Keynesian perspectives. It covers unemployment, price stability, and exchange rates. On unemployment, classical economists believe full employment is always achieved through flexible wages, while Keynesians believe unemployment is normal and government intervention is needed. On price stability, classical economists see prices adjusting to maintain full employment while Keynesians see stable prices with variable output. Exchange rates are influenced by demand and supply factors in both frameworks.
Harrod – Domar Model - Development Model.pptxNithin Kumar
The document discusses the Harrod-Domar model of economic growth developed by Roy Harrod and Evsey Domar. Some key points:
1. The model focuses on the role of capital accumulation and investment in driving economic growth.
2. It uses the capital-output ratio and investment ratio to determine the rate of economic growth.
3. Harrod identified the actual, warranted, and natural rates of growth and argued stability requires equality between these rates.
4. The warranted rate depends on capital-output ratio and savings ratio matching the demand and supply of capital.
5. The natural rate is determined by long-term factors like population and technology.
1. The document discusses general equilibrium theory (GET) and defines general equilibrium as a state where all markets and decision-making units are in simultaneous equilibrium.
2. It presents a simple two-sector general equilibrium model of an economy with two consumers, two goods, and two factors of production. Equations represent consumer demand, factor supply, factor demand, good supply, and market clearing for goods and factors.
3. With the number of equations equal to the number of unknowns, a general equilibrium solution exists in this Walrasian model under certain assumptions. GET provides a framework for understanding the complexity of economic systems through interdependent markets.
The classical growth theory argues that economic growth will decrease or end because of an increasing population and limited resources Classical growth theory economists believed that temporary increases in real GDP per person would cause a population explosion that would consequently decrease real GDP.
This document discusses stabilization policy, which aims to stabilize the economy and prevent fluctuations in output, employment, and prices that occur during business cycles. Stabilization policy uses monetary policy, fiscal policy, and international measures. Monetary policy involves tools like changing interest rates, reserve ratios, and open market operations to influence the money supply. Fiscal policy involves manipulating public expenditure, taxation, and debt to stimulate or contract the economy. International measures coordinate import/export policies and currency values with other countries. The overall goal is to counteract inflation during booms and spur growth during recessions.
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.
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 summarizes key concepts from Chapter 8 of an economics textbook on economic growth. It discusses how to incorporate technological progress into the Solow growth model by including a variable for labor efficiency that grows exogenously over time. It then reviews empirical evidence on growth, including balanced growth, conditional convergence between countries, and the relationship between factor accumulation and production efficiency. Finally, it examines policy issues such as evaluating a country's saving rate and how to increase savings and allocate investment between different types of capital.
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.
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 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.
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.
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.
The document summarizes several classical development theories from the post-World War 2 period, including linear stages of growth, structural change, and dependency theories. It focuses on describing the linear stages of growth theory, including Rostow's stages of growth model and the Harrod-Domar growth model. It notes that these theories viewed development as a series of successive stages involving increasing investment, savings, and capital accumulation. They argued countries could develop by following the path historically taken by more advanced nations. However, the theories were criticized for ignoring structural conditions within developing countries and external forces beyond their control.
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.
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.
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.
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 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 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.
This document discusses endogenous growth theory and compares it to the neoclassical growth model. It summarizes two core endogenous growth models: the AK model and a "learning by doing" model. The AK model endogenizes long-run growth by having output be a linear function of capital alone. This causes savings rates to permanently impact the growth rate. The "learning by doing" model features knowledge spillovers that increase productivity based on average capital levels. Both models generate sustained long-run growth, unlike the neoclassical model. The document then discusses how international capital market integration can further boost growth by allowing more efficient global allocation of capital.
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.
LO1. Explain how sticky prices relate to the AE model.
LO2. Explain how an economy’s investment schedule is derived from the investment demand curve & an interest rate.
LO3. The table shows different levels of output and the corresponding levels of consumption, investment, exports and aggregate expenditures to determine the equilibrium level of output where aggregate expenditures equals output.
LO4. Equilibrium is also characterized by savings equaling investment and consumption being less than output due to savings being a leakage from the circular flow of spending.
While financial globalization could theoretically allow capital to flow from rich to poor countries to take advantage of higher returns, this does not fully occur in practice. There are several reasons for this:
1) Productivity levels differ across countries, with poor countries generally having lower productivity, meaning the returns to investment are not as high as predicted once productivity is accounted for.
2) Risk premiums charged for investing in emerging markets are often substantial and high enough to cause capital flows in the opposite direction.
3) Transaction costs are often much higher for poor countries to acquire capital goods from abroad.
Therefore, complete convergence of capital levels and incomes between rich and poor countries is unlikely through financial globalization alone. Other
1. The document discusses the difference between economic growth and development. Growth refers to increases in production, while development encompasses improvements in living standards.
2. It examines factors that influence economic growth according to neoclassical growth models, including capital accumulation, technological progress, savings rates, and human capital. The Solow and Romer growth models are described.
3. Empirical evidence suggests that differences in total factor productivity and institutional quality best explain variations in growth between rich and poor countries. Geography and institutions have significant impacts on development.
[4:55 p.m.] Bryan Oates
OJPs are becoming a critical resource for policy-makers and researchers who study the labour market. LMIC continues to work with Vicinity Jobs’ data on OJPs, which can be explored in our Canadian Job Trends Dashboard. Valuable insights have been gained through our analysis of OJP data, including LMIC research lead
Suzanne Spiteri’s recent report on improving the quality and accessibility of job postings to reduce employment barriers for neurodivergent people.
Decoding job postings: Improving accessibility for neurodivergent job seekers
Improving the quality and accessibility of job postings is one way to reduce employment barriers for neurodivergent people.
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
Solution Manual For Financial Accounting, 8th Canadian Edition 2024, by Libby...Donc Test
Solution Manual For Financial Accounting, 8th Canadian Edition 2024, by Libby, Hodge, Verified Chapters 1 - 13, Complete Newest Version Solution Manual For Financial Accounting, 8th Canadian Edition by Libby, Hodge, Verified Chapters 1 - 13, Complete Newest Version Solution Manual For Financial Accounting 8th Canadian Edition Pdf Chapters Download Stuvia Solution Manual For Financial Accounting 8th Canadian Edition Ebook Download Stuvia Solution Manual For Financial Accounting 8th Canadian Edition Pdf Solution Manual For Financial Accounting 8th Canadian Edition Pdf Download Stuvia Financial Accounting 8th Canadian Edition Pdf Chapters Download Stuvia Financial Accounting 8th Canadian Edition Ebook Download Stuvia Financial Accounting 8th Canadian Edition Pdf Financial Accounting 8th Canadian Edition Pdf Download Stuvia
Independent Study - College of Wooster Research (2023-2024) FDI, Culture, Glo...AntoniaOwensDetwiler
"Does Foreign Direct Investment Negatively Affect Preservation of Culture in the Global South? Case Studies in Thailand and Cambodia."
Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
My study abroad in Bali, Indonesia, inspired this research topic as I noticed how globalization is changing the culture of its people. I learned their language and way of life which helped me understand the beauty and importance of cultural preservation. I believe we could all benefit from learning new perspectives as they could help us ideate solutions to contemporary issues and empathize with others.
In a tight labour market, job-seekers gain bargaining power and leverage it into greater job quality—at least, that’s the conventional wisdom.
Michael, LMIC Economist, presented findings that reveal a weakened relationship between labour market tightness and job quality indicators following the pandemic. Labour market tightness coincided with growth in real wages for only a portion of workers: those in low-wage jobs requiring little education. Several factors—including labour market composition, worker and employer behaviour, and labour market practices—have contributed to the absence of worker benefits. These will be investigated further in future work.
"Does Foreign Direct Investment Negatively Affect Preservation of Culture in the Global South? Case Studies in Thailand and Cambodia."
Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
My study abroad in Bali, Indonesia, inspired this research topic as I noticed how globalization is changing the culture of its people. I learned their language and way of life which helped me understand the beauty and importance of cultural preservation. I believe we could all benefit from learning new perspectives as they could help us ideate solutions to contemporary issues and empathize with others.
Abhay Bhutada, the Managing Director of Poonawalla Fincorp Limited, is an accomplished leader with over 15 years of experience in commercial and retail lending. A Qualified Chartered Accountant, he has been pivotal in leveraging technology to enhance financial services. Starting his career at Bank of India, he later founded TAB Capital Limited and co-founded Poonawalla Finance Private Limited, emphasizing digital lending. Under his leadership, Poonawalla Fincorp achieved a 'AAA' credit rating, integrating acquisitions and emphasizing corporate governance. Actively involved in industry forums and CSR initiatives, Abhay has been recognized with awards like "Young Entrepreneur of India 2017" and "40 under 40 Most Influential Leader for 2020-21." Personally, he values mindfulness, enjoys gardening, yoga, and sees every day as an opportunity for growth and improvement.
1. CHAPTER FOUR
The neo-Keynesian Harrod–Domar model;
The Solow–Swan neoclassical model; and
The Romer–Lucas-inspired endogenous growth models.
1 Macro Economics-II CH-4 WSU By Zegeye Paulos
2. 4.1 The Harrod- Domar Growth
Model Harrod (1939, 1948) and Evsey Domar (1946, 1947) independently
developed theories that relate an economy’s rate of growth to its
capital stock.
The model assumes
an exogenous rate of labour force growth (n),
a given technology exhibiting fixed factor proportions
i.e. - constant capital–labour ratio, K/L) and
- a fixed capital–output ratio (K/Y).
Assuming a two-sector economy (households and firms),
we can write the simple national income equation as (4.1):
Yt = Ct + St -----------------------------------------------------4.1
where Yt = GDP, Ct = consumption and St = saving.
Equilibrium in this simple economy requires (4.2):
It = St ------------------------------------------4.22
Macro Economics-II CH-4 WSU By Zegeye Paulos
3. Substituting (4.2) into (4.1) yields (4.3):
Yt = Ct + It ----------------------------------------------------4.3
Within the Harrod–Domar framework the growth of real GDP
is assumed to be proportional to
The share of investment spending (I) in GDP and
For an economy to grow, net additions to the capital
stock are required.
The capital stock over time is given in equation as
Kt+1 = (1− δ)Kt + It ---------------------------------4.4
where δ is the rate of depreciation of the capital stock.
The relationship between
the size of the total capital stock (K) and total GDP (Y)
is known as the capital–output ratio (K/Y = v) and is assumed fixed.
3 Macro Economics-II CH-4 WSU By Zegeye Paulos
4. Given that we have defined v = K/Y, it also follows that v = ΔK/ΔY
Assume that total saving is some proportion (s) of GDP (Y)
St = sYt ----------------------------------------------------------------4.5
Since K = vY and It = St, it follows that we can rewrite equation (4.4) as
equation (4.6):
vYt+1 = (1− δ)vYt + sYt --------------------------------------------------4.6
Dividing by v, and subtracting Yt from both sides of equation (4.6) yields
equation (4.7):
Yt+1 − Yt = [s/v − δ]Yt -----------------------------------------------------4.7
Dividing through by Y t gives us equation (4.8):
[Yt+1 − Yt ]/Yt = (s/v) − δ -------------------------------------------------4.8
Here [Yt + 1 – Yt]/Yt is the growth rate of GDP. Letting G = [Yt + 1 –
Yt]/Yt,
We can write the Harrod–Domar growth equation as (4.9):
G = s/v − δ ------------------------------------------------------------4.9
4 Macro Economics-II CH-4 WSU By Zegeye Paulos
5. G = s/v − δ --------------------------------------4.9
NB: This simply states that the growth rate (G) of GDP is
jointly determined by
the savings ratio (s) divided by the capital–output
ratio (v).
The higher the savings ratio and the lower the capital–
output ratio and depreciation rate, the faster will an
economy grow.
By ignoring depreciation rate Harrod–Domar model as
G = s/v ---------------------------------------------4.10
5 Macro Economics-II CH-4 WSU By Zegeye Paulos
6. For example, if a developing country desired to achieve a growth
rate of per capita income of 2 per cent per annum and
population is estimated to be growing at 2 per cent, then economic
planners would need to set a target rate of GDP growth (G*) equal
to 4 per cent. G/ pop%= Percapita income
4%/2% = 2%
If v = 4, this implies that G* can only be achieved with a desired
savings ratio (s*) of 0.16, or 16 per cent of GDP.
If s* > s, there is a ‘savings gap’, and planners needed to devise
policies for plugging this gap.
6 Macro Economics-II CH-4 WSU By Zegeye Paulos
7. Since the rate of growth in the Harrod–Domar model
is positively related to the savings ratio,
If domestic sources of finance were inadequate to achieve the
desired growth target,
then foreign aid could fill the ‘savings gap’
Aid requirements (Ar) would simply be calculated as
s* – s = Ar
7 Macro Economics-II CH-4 WSU By Zegeye Paulos
8. However, a major weakness of the Harrod–Domar
It’s assumption of a fixed capital– output ratio. K/Y
The model assumed that aid inflows would go into investment one to one.
But it soon became apparent that inflows of foreign aid, with the objective of
closing the savings gap, did not necessarily boost total savings.
The assumption of zero substitutability between capital and labour (that is, a fixed
factor proportions production function).
This is a ‘crucial’ but inappropriate assumption for a model concerned with
long-run growth.
8 Macro Economics-II CH-4 WSU By Zegeye Paulos
9. In the Harrod–Domar model the capital–output ratio (K/Y) and the
capital–labour ratio (K/L) are assumed constant.
In a growth setting this means that K and Y must always grow at the same rate
to maintain equilibrium.
However, because the model also assumes a constant capital–labour ratio
(K/L), K and L must also grow at the same rate.
Therefore, if we assume that the labour force (L) grows at the same rate
as the rate of growth of population (n), then we can conclude that the only
way that equilibrium can be maintained in the model is
for n = G = s/v.
It would only be by pure coincidence that n = G.
If n > G, the result will be continually rising unemployment.
If G > n, the capital stock will become increasingly idle and the growth
rate of output will slow down to G = n.
Thus, whenever K and L do not grow at the same rate, the economy falls
off its equilibrium ‘knife-edge’ growth path.
9 Macro Economics-II CH-4 WSU By Zegeye Paulos
10. Increasing the saving ratio in lower-income countries is not
easy.
Many developing countries has lower marginal propensity to
save
Many developing countries lack reliable and strong financial
system and institutions
More challenging to achieve efficiency(K/Y) in developing
countries
Research and development(R/D) is under funded
Borrowing money abroad to close the saving gap can cause
external debt in the long run
10 Macro Economics-II CH-4 WSU By Zegeye Paulos
11. 4.2. The Solow Neoclassical Growth Model
In Solow model
capital,
labor, and key determinants of production of goods &services
technology
we developed the Solow model to show
how changes in capital (through S and I)
& affect economy’s output.
changes in the labor force (pon growth)
We are now ready to add the third source of growth
changes in technology—to the mix.
The Solow model does not explain technological progress but,
instead, takes it as exogenously given and
shows how it interacts with other variables in the process of economic
growth.
11 Macro Economics-II CH-4 WSU By Zegeye Paulos
12. The key assumptions of the Solow model are:
The economy consists of one sector producing one type of
commodity that can be used for either
investment or consumption purposes;
The economy is closed and the government sector is ignored;
all output that is saved is invested;
The economy is always producing its potential (natural) level
of total output;
Solow abandons the H-D assumptions of a fixed capital–output
ratio (K/Y) and fixed capital–labour ratio (K/L);
The rate of technological progress, population growth and the
depreciation rate of the capital stock are all determined
exogenously.
12 Macro Economics-II CH-4 WSU By Zegeye Paulos
13. The Solow growth model is designed to show how growth
in the capital stock,
growth in the labor force, and
advances in technology
affect a nation’s total output of goods and services.
We will build this model in a series of steps.
Our first step is to examine how the supply and demand for goods
determine the accumulation of capital.
In this first step, we assume that
the labor force and
technology are fixed.
We then relax these assumptions by introducing changes in the
labor force later in this chapter and by introducing changes in
technology in the next.
13 Macro Economics-II CH-4 WSU By Zegeye Paulos
14. The supply of goods in the Solow model is based on the production function,
which states that output depends on
capital stock and
labor force:
Y = F(K, L).
The Solow growth model assumes that the production function
has constant returns to scale. zY = F(zK, zL)
That is, if both capital and labor are multiplied by z, the amount of output is also multiplied by z.
Production functions with constant returns to scale allow us to analyze all quantities in the economy
relative to the size of the labor force.
To see that this is true, set z = 1/L in the preceding equation to obtain
Y/L = F(K/L, 1).
14 Macro Economics-II CH-4 WSU By Zegeye Paulos
15. This equation shows that the amount of output per worker Y/L
is a function of the amount of capital per worker K/L.
(The number 1 is constant and thus can be ignored.)
The assumption of constant returns to scale implies that
the size of the economy as measured by the number of
workers does not affect the relationship between
output per worker and capital per worker.
y = Y/L is output per worker, and k = K/L is capital per worker.
We can then write the production function as
y = f (k),
15 Macro Economics-II CH-4 WSU By Zegeye Paulos
16. Note that in Figure 4.1, as the amount of capital increases,
the production function becomes flatter, indicating that the production
function exhibits diminishing marginal product of capital.
When k is low, the average worker has only a little capital to work
with, so an extra unit of capital is very useful and produces a lot of
additional output.
When k is high, the average worker has a lot of capital already, so
an extra unit increases production only slightly.
16
Macro Economics-II CH-4 WSU By Zegeye
Paulos
18. The Demand for Goods and the Consumption Function
The demand for goods in the Solow model comes from
consumption and
investment.
In other words, output per worker y is divided between
consumption per worker c and
investment per worker i:
y = c + i.
This equation is the per-worker version of the national income accounts identity for an economy.
The Solow model assumes that
each year people save a fraction s of their income and
consume a fraction (1 – s)
We can express this idea with the following consumption function:
c = (1 − s)y,
where s, the saving rate, is a number between zero and one.
For now, however, we just take the saving rate s as given.
To see what this consumption function implies for investment,
substitute (1 – s)y for c in the national income accounts identity:
y = (1 − s)y + i.
Rearrange the terms to obtain i = sy.18
19. For any given capital stock k, the production function y = f(k)
determines how much output the economy produces, and
The saving rate s determines the allocation of that output between
consumption and investment.
Growth in the Capital Stock and the Steady State
At any moment, the capital stock is a key determinant of the economy’s output,
but the capital stock can change over time, and
those changes can lead to economic growth.
In particular, two forces influence the capital stock:
investment and
depreciation.
Investment is expenditure on new plant and equipment, and it causes the capital stock
to rise.
Depreciation is the wearing out of old capital, and it causes the capital stock to fall.
Let’s consider each of these forces in turn. As we have already noted, investment per
worker i equals sy.
By substituting the production function for y, we can express investment per worker as
a function of the capital stock per worker:
i = sf(k).19
20. This equation relates the existing stock of capital k to the
accumulation of new capital i.
The production function f(k), and the allocation of that output between
consumption
and is determined by the saving rate s.
saving
To incorporate depreciation into the model, we assume that a certain
fraction of the capital stock wears out each year.
For example, if capital lasts an average of 25 years, then the
depreciation rate is 4 percent per year ( = 0.04).
The amount of capital that depreciates each year is k .
Change in Capital Stock = Investment − Depreciation
k = i −k
where k is the change in the capital stock between one year and the
next.
Because investment i equals sf(k), we can write this as
k = sf (k) − k .
20
21. Regardless of the level of capital with which the economy begins, it ends up with the
steady-state level of capital.
To see why an economy always ends up at the steady state,
suppose that the economy starts with less than the steady-state level of capital, such as
level k1 in Figure 4.2.
In this case, the level of investment exceeds the amount of depreciation.
Over time, the capital stock will rise and will continue to rise- along with output
f(k)—until it approaches the steady state k*.
Similarly, suppose that the economy starts with more than the steady-state level of
capital, such as level k2.
In this case, investment is less than depreciation: capital is wearing out faster than
it is being replaced.
The capital stock will fall, again approaching the steady-state level.
Once the capital stock reaches the steady state, investment equals depreciation, and
there is no pressure for the capital stock to either increase or decrease.
21 Macro Economics-II CH-4 WSU By Zegeye Paulos
22. Figure 4-2 graphs the terms of this equation—investment and
depreciation—for different levels of the capital stock k.
The higher the capital stock, the greater the amounts of output and
investment.
Yet the higher the capital stock, the greater also the amount of
depreciation.
As Figure 4.2 shows, there is a single capital stock k* at which the
amount of investment equals the amount of depreciation.
If the economy finds itself at this level of the capital stock, the capital
stock will not change because the two forces acting on it
investment and
depreciation—just balance.
That is, at k*, k = 0, so the capital stock k and output f(k) are steady
over time (rather than growing or shrinking).
We therefore call k* the steady-state level of capital.
The steady state is significant for two reasons.
As we have just seen, an economy at the steady state will stay there.
In addition, and just as important, an economy not at the steady state
will go there.22
24. Approaching the Steady State: A Numerical Example
Let’s use a numerical example to see how the Solow
model works and how the economy approaches the
steady state.
we assume that the production function is
The Cobb–Douglas production function with the
capital-share parameter α equal to 1/2.
24
Macro Economics-II CH-4 WSU CBE, Economics By Zegeye
Paulos
25. To derive the per-worker production function f(k),
divide both sides of the production function by the
labor force L:
Rearrange to obtain
Because y = Y/L and k = K/L, this equation becomes
which can also be written as
25
Macro Economics-II CH-4 WSU CBE, Economics, By Zegeye
Paulos
26. This form of the production function states that
output per worker equals the square root of the amount of capital per
worker.
To complete the example, let’s assume that 30 percent of
output is saved (s = 0.3), that 10 percent of the capital stock
depreciates every year ( = 0.1), and that the economy starts
off with 4 units of capital per worker (k = 4). Given these
numbers, we can now examine what happens to this
economy over time.
We begin by looking at the production and allocation of
output in the first year,
when the economy has 4 units of capital per worker. Here are
the steps we follow.
According to the production function y = , the 4 units of capital
per worker (k) produce 2 units of output per worker (y).
Because 30 percent of output is saved and invested and 70
percent is consumed, i = 0.6 and c = 1.4.
Because 10 percent of the capital stock depreciates, dk = 0.4.
With investment of 0.6 and depreciation of 0.4, the change in the
capital stock is k = 0.2.26
Macro Economics-II CH-4 WSU CBE, Economics By
Zegeye Paulos
27. Thus, the economy begins its second year with 4.2 units of capital
per worker.
We can do the same calculations for each subsequent year.
Table 4.3 shows how the economy progresses. Every year, because
investment exceeds depreciation, new capital is added and output
grows.
Over many years, the economy approaches a steady state with 9
units of capital per worker.
In this steady state, investment of 0.9 exactly offsets depreciation of
0.9, so the capital stock and output are no longer growing.
Following the progress of the economy for many years is one way
to find the steady-state capital stock, but there is another way that
requires fewer calculations.
Recall that
k = sf(k) − k.
This equation shows how k evolves over time. Because the steady
state is (by definition) the value of k at which k = 0, we know that
0 = sf (k*) − k*,
27
Macro Economics-II CH-4 WSU CBE, Economics By Zegeye
Paulos
29. How Saving Affects Growth
To understand more fully the international differences in economic performance, we must consider the effects of
different saving rates.
Consider what happens to an economy when its saving rate increases.
Figure 4-3shows such a change. The economy is assumed to begin in a steady state with saving rate s1 and capital
stock k*1.
When the saving rate increases from s1 to s2, the sf(k) curve shifts upward.
At the initial saving rate s1 and the initial capital stock k*1, the amount of investment just offsets the amount of
depreciation.
capital stock will gradually rise until the economy reaches the new steady state k*2, which has a higher capital
stock and a higher level of output than the old steady state.
The Solow model shows that the saving rate is a key determinant of the steady-state capital stock.
If the saving rate is high, the economy will have a large capital stock and a high level of output in the steady state.
If the saving rate is low, the economy will have a small capital stock and a low level of output in the steady state.
29
Macro Economics-II CH-4 WSU CBE, Economics By Zegeye
Paulos
31. The Golden Rule Level of Capital
So far, we have used the Solow model to examine how an
economy’s rate of saving and investment determines
its steady-state levels of capital and income.
This analysis is might lead you to think that higher saving is
always a good thing
because it always leads to greater income.
Yet suppose a nation had a saving rate of 100 percent. That
would lead to the
largest possible capital stock and the largest possible
income.
But if all of this income is saved and none is ever consumed,
what good is it?
This section uses the Solow model to discuss the optimal
amount of capital accumulation
from the standpoint of economic well-being.
31 Macro Economics-II CH-4 WSU CBE, Economics By Zegeye
Paulos
33. Different values of s lead to different steady states.
How do we know which is the “best” steady state?
Economic well-being depends on consumption, so the “best”
steady state has
the highest possible value of consumption per person:
c* = (1–s) f(k*)
An increase in s
o leads to higher k* and y*, which may raise c*
o reduces consumption’s share of income (1–s),
which may lower c*
So, how do we find the s and k* that maximize c* ?
33 Macro Economics-II CH-4 WSU CBE Economics By Zegeye Paulos
34. K*
golden= the Golden Rule level of capital
the steady state value of k that maximizes consumption.
To find it, first express c* in terms of k*:
c* = y* i* Consumption is output minus
investment.
= f (k*) i*
= f (k*) k*
In general:
i = k + k
In the steady state:
i* = k* because k = 0.
At the golden rule level the slope of production
function (MPK) equals to the slope of k* line that
is .34
Macro Economics-II CH-4 WSU CBE, Economics By
Zegeye Paulos
36. The transition to the Golden Rule Steady State
The economy does NOT have a tendency to move toward
the Golden Rule steady state.
Achieving the Golden Rule requires that policymakers
adjust s.
This adjustment leads to a new steady state with higher
consumption.
But what happens to consumption during the transition to
the Golden Rule?
36
Macro Economics-II CH-4 WSU CBE, Economics By
Zegeye Paulos
39. Population Growth
Assume that the population--and labor force-- grow at rate
n. (n is exogenous)
EX: Suppose L = 1000 in year 1 and the population is growing at
2%/year (n=0.02).
Then L = n L = 0.02 1000 = 20, so L = 1020 in year 2.
Break-even investment
( + n)k = break-even investment, the amount of investment necessary to keep
k constant.
With population growth, the equation of motion for k is
k = s f(k) ( + n) k
Actual invesment break even investment
L
n
L
39
Macro Economics-II CH-4 WSU By Zegeye
Paulos
41. The Effects of Population Growth
An increase in n = break-even investment, leading to a lower steady-state level of k.
Higher n lower k*. And since y = f(k) , lower k* lower y* .
Thus, Solow model predicts that countries with higher popn growth will
have lower levels of capital and income per worker in the long run.
41
42. The Golden Rule with Population Growth
To find the Golden Rule capital stock,
we again express c* in terms of k*:
c* = y* i*
= f (k* ) ( + n) k*
c* is maximized when
MPK = + n
or equivalently,
MPK = n
In the Golden Rule Steady
State,
The marginal product of
capital net of depreciation
equals
The population growth rate.
42
Macro Economics-II CH-4 WSU By Zegeye
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43. Technological Progress in Solow Model
Previously, in the Solow model
the production technology was held constant
income per capita was constant in the steady state.
Neither point is true in the real world
Tech. progress in the Solow model
A new variable: E = labor efficiency
Assume:
Technological progress is labor-augmenting:
o it increases labor efficiency at the exogenous rate g:
(assumption about techn progress is that it causes the efficiency
of labor E to grow at some constant rate g.)
We have to incorporate technological progress to production
function
E
g
E
43
( , )Y F K L E
Macro Economics-II CH-4 WSU By Zegeye
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44. We now write the production function as
where L E = the number of effective workers.
– Hence, increases in labor efficiency have the same effect on output as increases
in the labor force.
Notation:
y = Y/LE = output per effective worker
k = K/LE = capital per effective worker
Production function per effective worker:
y = f(k)
Saving and investment per effective worker:
s y = s f(k)
( + n + g)k = break-even investment:
The amount of investment necessary to keep k constant.
Consists of:
k to replace depreciating capital
n k to provide capital for new workers
g k to provide capital for the new “effective” workers
created by technological progress
( , )Y F K L E
44 Macro Economics-II CH-4 WSU CBE, Economics By Zegeye
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45. In effective workers due to Tech - Tend to decrease
in k
In steady state , investment sf(k) exactly offset the
reduction in k attributable to – depreciation, popn
growth and tech progress
45
Macro Economics-II CH-4 WSU By Zegeye Paulos
46. Policies to promote growth
Four policy questions:
1. Are we saving enough? Too much?
2. What policies might change the saving rate?
3. How should we allocate our investment between privately
owned physical capital, public infrastructure, and “human
capital”?
4. What policies might encourage faster technological
progress?
1. Evaluating the Rate of Saving
Use the Golden Rule to determine whether
our saving rate and capital stock are too high, too low, or about
right.
To do this, we need to compare
(MPK ) to (n + g ).46
47. To estimate (MPK ), we use three facts about an
economy;
1. k = 2.5 y
The capital stock is about 2.5 times one year’s GDP.
2. k = 0.1 y
About 10% of GDP is used to replace depreciating
capital.
3. MPK k = 0.3 y
Capital income is about 30% of GDP
1. k = 2.5 y
2. k = 0.1 y
3. MPK k = 0.3 y
To determine , divided 2 by 1:
0 1
2 5
.
.
k y
k y
0 1
0 04
2 5
.
.
.
47
Macro Economics-II CH-4 WSU By Zegeye Paulos
48. 1. k = 2.5 y
2. k = 0.1 y
3. MPK k = 0.3 y
To determine MPK, divided 3 by 1:
Hence, MPK = 0.12 0.04 = 0.08
Real GDP grows an average of 3%/year,
so n + g = 0.03
Thus, in this economy,
MPK = 0.08 > 0.03 = n + g
Conclusion
The economy is below the Golden Rule steady state:
if we increase saving rate of this economy, the economy will
have faster growth until it reaches to a new steady state with
higher consumption per capita
MPK 0 3
2 5
.
.
k y
k y
0 3
MPK 0 12
2 5
.
.
.
48
Macro Economics-II CH-4 WSU By Zegeye Paulos
49. 2. Policies to increase the saving rate
49
Reduce the government budget deficit (or increase the budget
surplus)
Increase incentives for private saving:
reduce capital gains tax, corporate income tax,
estate tax as they discourage saving
replace federal income tax with a consumption
tax
expand tax incentives for individual retirement
accounts and other retirement savings accounts
Macro Economics-II CH-4 WSU By Zegeye
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50. 3. Allocating the economy’s investment
50
In the Solow model, there’s one type of capital.
In the real world, there are many types, which we can divide into three
categories:
private capital stock
public infrastructure
human capital: the knowledge and skills that workers acquire
through education
How should we allocate investment among these types?
Allocating the economy’s investment: two viewpoints
1. Equalize tax treatment of all types of capital in all industries, then let
the market allocate investment to the type with the highest marginal
product.
2. Industrial policy: Govt. should actively encourage investment in
capital of certain types or in certain industries
Macro Economics-II CH-4 WSU By Zegeye
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51. 4. Encouraging technological progress
51
Patent laws: encourage innovation by granting
temporary monopolies to inventors of new products
Tax incentives for R&D
Grants to fund basic research at universities
Industrial policy:
encourage specific industries that are key for rapid
tech. progress
Macro Economics-II CH-4 WSU By Zegeye Paulos
52. Convergence
52
Solow model predicts that, other things equal, “poor” countries
(with lower Y/L and K/L ) should grow faster than “rich” ones.
If true, then the income gap between rich & poor countries would
shrink over time, and living standards “converge.”
In real world, many poor countries do NOT grow faster than rich
ones.
Does this mean the Solow model fails?
No, because “other things” aren’t equal.
What the Solow model really predicts is conditional
convergence –
countries converge to their own steady states, which are
determined by saving, population growth, and education.
And this prediction comes true in the real world.
Macro Economics-II CH-4 WSU By Zegeye Paulos
53. Endogenous Growth Theory
53
Solow model:
sustained growth in living standards is due to tech progress
the rate of tech progress is exogenous
Endogenous growth theory:
a set of models in which the growth rate of productivity and living
standards is endogenous
A basic model
Production function: Y = A K
where , Y is Output , K is the capital stock, A measures the amount
of output produced for each unit of capital (A is exogenous & constant)
Key difference between this model & Solow:
MPK is constant here, diminishes in Solow
Investment: sY
Depreciation: K
Equation of motion for total capital:
Δ K = s Y K
Divide through by K and use Y = A K , get:
Y K
sA
Y K
Macro Economics-II CH-4 WSU By Zegeye Paulos
54. 54
If sA > , then income will grow forever, and
investment is the “engine of growth.”
Here, the permanent growth rate depends on s. In
Solow model, it does not.
Does capital have diminishing returns or not?
Yes, if “capital” is narrowly defined (plant &
equipment).
Perhaps not, with a broad definition of “capital”
(physical & human capital, knowledge).
Some economists believe that knowledge exhibits
increasing returns.
In the endogenous growth model, the assumption
of constant returns to capital is more plausible.
55. A two-sector model
55
Two sectors:
1. manufacturing firms produce goods
2. research universities produce knowledge that
increases labor efficiency in manufacturing
u = fraction of labor in research (u is exogenous)
Mfg prod func: Y = F [K, (1-u )EL]
Res prod func: Δ E = g (u )E
Cap accumulation: Δ K = s Y K
Macro Economics-II CH-4 WSU By Zegeye Paulos
56. A two-sector model
56
In the steady state, mfg output per worker and the
standard of living grow at rate
E/E = g (u ).
Key variables:
s: affects the level of income, but not its growth rate
(same as in Solow model)
u: affects level and growth rate of income
Macro Economics-II CH-4 WSU By Zegeye
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57. Three facts about R&D in the real world
57
1.Much research is done by firms seeking profits.
2.Firms profit from research because
new inventions can be patented, creating a stream
of monopoly profits until the patent expires
there is an advantage to being the first firm on the
market with a new product
3.Innovation produces externalities that reduce the
cost of subsequent innovation.
Much of the new endogenous growth theory
attempts to incorporate these facts into models to
better understand tech progress.
Macro Economics-II CH-4 WSU By Zegeye Paulos