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.
This document provides an overview of several prominent theories of consumption, including:
1) John Maynard Keynes' theory that current consumption depends on current income. Later theories found problems with Keynes' prediction that consumption would grow more slowly than income over time.
2) Irving Fisher's intertemporal choice theory, which assumes consumers maximize lifetime satisfaction subject to an intertemporal budget constraint. This theory formed the basis for later work on consumption.
3) Franco Modigliani's life-cycle hypothesis, which proposes consumption depends on lifetime resources and income varies systematically over a consumer's life cycle, allowing saving to achieve smooth consumption. This theory helped solve the "consumption puzzle."
4)
The document discusses the Mundell-Fleming model of the open economy and exchange rate regimes. It provides an overview of the key assumptions and components of the Mundell-Fleming model, including the IS* and LM* curves. It then analyzes the effects of fiscal policy, monetary policy, and trade policy under both floating and fixed exchange rate systems. The document concludes with two case studies on financial crises in Mexico and Southeast Asia that illustrate the model.
Policymakers debate whether monetary and fiscal policy should be active or passive in response to economic fluctuations, and whether policy should be set by rule or at the discretion of officials. Arguments for active policy include reducing economic hardship during recessions, while critics argue policies have long and variable lags. Policy rules aim to increase credibility and reduce time inconsistency problems, like central banks targeting an inflation rate or following the Taylor rule. The optimal approach remains an open debate among economists.
Here are the key impacts of an increase in investment demand in a small open economy:
- Investment demand I(r*) increases.
- Saving S does not change.
- Net capital outflow decreases as domestic investment increases and saving remains the same.
- Net exports NX decrease as the trade balance deteriorates to finance the higher investment through net capital inflows.
So in summary, an increase in investment demand leads to a deterioration in the trade balance (lower NX) and lower net capital outflow, while saving remains unchanged.
CHAPTER 5 The Open Economy slide 23
This document provides an overview of aggregate supply and the short-run tradeoff between inflation and unemployment known as the Phillips curve. It discusses three models of aggregate supply - the sticky-wage model, imperfect-information model, and sticky-price model - and how they each imply a positive relationship between output and the price level in the short run. The Phillips curve relationship is then derived from the aggregate supply relationship. The document also discusses concepts like adaptive expectations, inflation inertia, cost-push vs demand-pull inflation, and the sacrifice ratio.
1) The chapter uses the IS-LM model to analyze the effects of fiscal and monetary policy shocks on aggregate output and the interest rate in the short run.
2) Fiscal policy like increases in government spending or tax cuts shift the IS curve right, raising output. Monetary policy like increases in the money supply shift the LM curve down, lowering interest rates and raising output.
3) Shocks like increases in wealth from a stock market boom shift the IS curve right, raising output, while shocks that increase money demand like credit card fraud shift the LM curve left, lowering output.
4) In the long run, price adjustments return output to potential as the price level falls to accommodate any short
The Mundell-Fleming model is an extension of the IS-LM model that includes the joint determination of net exports and currency value. It suggests that fiscal expansion with monetary contraction would boost the currency value and reduce net exports, while fiscal contraction and monetary expansion would boost net exports and reduce the currency value. However, expectations play a major role in determining outcomes. Under Reagan, expectations of growth from tax cuts led to a higher dollar and lower net exports, while under Clinton, expectations of growth from spending cuts had the same effect despite different policies.
The Mundell-Fleming model is an extension of the IS-LM model that accounts for an open economy with international capital flows and exchange rates. It shows how fiscal and monetary policy can affect output and exchange rates under both fixed and flexible exchange rate regimes. Under flexible exchange rates, expansionary domestic policies may be offset by currency appreciation, while under fixed rates they may lead to balance of payments deficits. The model suggests using different combinations of fiscal and monetary policies to achieve objectives like boosting output while maintaining a stable currency value.
This document provides an overview of several prominent theories of consumption, including:
1) John Maynard Keynes' theory that current consumption depends on current income. Later theories found problems with Keynes' prediction that consumption would grow more slowly than income over time.
2) Irving Fisher's intertemporal choice theory, which assumes consumers maximize lifetime satisfaction subject to an intertemporal budget constraint. This theory formed the basis for later work on consumption.
3) Franco Modigliani's life-cycle hypothesis, which proposes consumption depends on lifetime resources and income varies systematically over a consumer's life cycle, allowing saving to achieve smooth consumption. This theory helped solve the "consumption puzzle."
4)
The document discusses the Mundell-Fleming model of the open economy and exchange rate regimes. It provides an overview of the key assumptions and components of the Mundell-Fleming model, including the IS* and LM* curves. It then analyzes the effects of fiscal policy, monetary policy, and trade policy under both floating and fixed exchange rate systems. The document concludes with two case studies on financial crises in Mexico and Southeast Asia that illustrate the model.
Policymakers debate whether monetary and fiscal policy should be active or passive in response to economic fluctuations, and whether policy should be set by rule or at the discretion of officials. Arguments for active policy include reducing economic hardship during recessions, while critics argue policies have long and variable lags. Policy rules aim to increase credibility and reduce time inconsistency problems, like central banks targeting an inflation rate or following the Taylor rule. The optimal approach remains an open debate among economists.
Here are the key impacts of an increase in investment demand in a small open economy:
- Investment demand I(r*) increases.
- Saving S does not change.
- Net capital outflow decreases as domestic investment increases and saving remains the same.
- Net exports NX decrease as the trade balance deteriorates to finance the higher investment through net capital inflows.
So in summary, an increase in investment demand leads to a deterioration in the trade balance (lower NX) and lower net capital outflow, while saving remains unchanged.
CHAPTER 5 The Open Economy slide 23
This document provides an overview of aggregate supply and the short-run tradeoff between inflation and unemployment known as the Phillips curve. It discusses three models of aggregate supply - the sticky-wage model, imperfect-information model, and sticky-price model - and how they each imply a positive relationship between output and the price level in the short run. The Phillips curve relationship is then derived from the aggregate supply relationship. The document also discusses concepts like adaptive expectations, inflation inertia, cost-push vs demand-pull inflation, and the sacrifice ratio.
1) The chapter uses the IS-LM model to analyze the effects of fiscal and monetary policy shocks on aggregate output and the interest rate in the short run.
2) Fiscal policy like increases in government spending or tax cuts shift the IS curve right, raising output. Monetary policy like increases in the money supply shift the LM curve down, lowering interest rates and raising output.
3) Shocks like increases in wealth from a stock market boom shift the IS curve right, raising output, while shocks that increase money demand like credit card fraud shift the LM curve left, lowering output.
4) In the long run, price adjustments return output to potential as the price level falls to accommodate any short
The Mundell-Fleming model is an extension of the IS-LM model that includes the joint determination of net exports and currency value. It suggests that fiscal expansion with monetary contraction would boost the currency value and reduce net exports, while fiscal contraction and monetary expansion would boost net exports and reduce the currency value. However, expectations play a major role in determining outcomes. Under Reagan, expectations of growth from tax cuts led to a higher dollar and lower net exports, while under Clinton, expectations of growth from spending cuts had the same effect despite different policies.
The Mundell-Fleming model is an extension of the IS-LM model that accounts for an open economy with international capital flows and exchange rates. It shows how fiscal and monetary policy can affect output and exchange rates under both fixed and flexible exchange rate regimes. Under flexible exchange rates, expansionary domestic policies may be offset by currency appreciation, while under fixed rates they may lead to balance of payments deficits. The model suggests using different combinations of fiscal and monetary policies to achieve objectives like boosting output while maintaining a stable currency value.
This document provides an overview of a macroeconomic model that examines national income. It discusses how total output is determined by factors of production like capital and labor. It then explains how factor prices, like wages and rental rates, are set through supply and demand in factor markets. The model shows how total national income is distributed to factor payments. It also outlines the components of aggregate demand, like consumption, investment, and government spending, and how their equilibrium in the goods market determines total output.
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 provides an overview of key concepts in international macroeconomics and the open economy model. It introduces accounting identities that apply to an open economy, where spending does not necessarily equal output and saving does not necessarily equal investment due to trade flows. It then presents the small open economy model, where the domestic economy is too small to affect global interest rates. In this model, the trade balance and exchange rate are determined by the interaction of domestic saving and investment with the exogenous world interest rate. Fiscal and monetary policies can influence the trade balance and exchange rate through their impact on saving and investment.
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.
This document summarizes key concepts from Chapter 12 of Mankiw's Macroeconomics textbook on open economy macroeconomics. It introduces the Mundell-Fleming model, which uses the IS-LM framework to analyze the effects of fiscal and monetary policy in a small open economy. It discusses the implications of floating versus fixed exchange rates and how this determines the effectiveness of different policies. It also examines the impacts of interest rate differentials and trade policies. The summary slides provide a concise overview of the model and the main policy conclusions.
This document provides an overview of classical theories of inflation and the quantity theory of money. It defines key concepts like money, inflation, the money supply, and velocity. The quantity theory of money posits that inflation is primarily caused by increases in the money supply that outpace economic growth. It predicts a direct relationship between money growth and inflation. The document uses graphs and international data to show this relationship generally holds in practice and discusses implications for interest rates.
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.
The life cycle income hypothesis asserts that consumers save and consume based on their optimal consumption pattern over their lifetime, subject to resource constraints. It emphasizes saving during working years to fund consumption in retirement years when income is lower. The hypothesis divides a person's life into three stages - childhood, middle age, and old age - with consumption gradually rising and income peaking in middle age then declining in retirement, resulting in dissaving early and late in life and saving in middle years.
An offer curve shows the quantities of imports and exports that a country is willing to trade at different relative prices (terms-of-trade). It combines a country's demand for imports and supply of exports. Offer curves can be drawn for two countries trading two goods to determine the trading equilibrium and equilibrium terms-of-trade. The equilibrium occurs where the quantities exported and imported are equal for both goods and countries.
This document discusses the natural rate of unemployment and its causes. It begins by defining the natural rate of unemployment as the average rate around which the actual unemployment rate fluctuates over the business cycle. It then presents a model showing how the natural rate is determined by the rates of job separation and job finding. Frictional unemployment results from the time it takes to search for and transition between jobs, while structural unemployment stems from wage rigidities that prevent wages from adjusting downward to clear the labor market. The document explores factors like minimum wages, unions, efficiency wages, and sectoral shifts that contribute to real wage rigidity and the natural rate of unemployment.
This document provides an overview of macroeconomic theory regarding short-term fluctuations in output and employment (i.e. the business cycle) using aggregate demand/aggregate supply models. It explains that in the short-run, prices are sticky but flexible in the long-run, leading to different aggregate supply curves (SRAS, LRAS). The AD/AS framework is used to analyze how demand and supply shocks can cause fluctuations and how stabilization policy aims to minimize changes in output and employment.
Don Patinkin criticized the neoclassical assumptions of homogeneity and dichotomization. He proposed the real balance effect to reconcile goods and money markets. The real balance effect posits that changes in the price level affect real purchasing power, which impacts demand for goods. When prices rise, real balances and goods demand fall, pushing prices back down. This feedback loop between prices, real balances, and goods demand is represented using the IS-LM model, where a fall in prices shifts the LM curve right, raising output and employment until full employment is reached. Patinkin argues this real balance effect denies the homogeneity assumption and integrates goods and money markets.
The document summarizes the relative income hypothesis proposed by Dusenberry in 1949. The key points are:
1) Dusenberry argued that consumption depends more on a person's relative income position compared to others in their community, rather than their absolute income level. People will consume more if they live in wealthier communities to maintain their standard of living.
2) In the short run, the average propensity to consume is greater than the marginal propensity to consume and the relationship between income and consumption is not proportional. In the long run, consumption increases proportionally with income and the average propensity to consume equals the marginal propensity to consume.
3) Dusenberry also believed consumption
This chapter introduces the concepts of the business cycle, aggregate demand, aggregate supply, and the model of aggregate demand and aggregate supply. It discusses how the economy behaves differently in the short-run versus long-run. In the short-run, many prices are sticky so the aggregate supply curve is horizontal, but in the long-run prices are flexible so the aggregate supply curve is vertical. The model can be used to analyze how shocks like changes in the money supply, velocity, or supply shocks impact output and inflation in both the short-run and long-run. An example is given of the 1970s oil shocks, which were adverse supply shocks that increased costs and shifted the short-run aggregate supply curve
This document discusses equilibrium in consumption and production using an Edgeworth box model. It explains that equilibrium occurs where the indifference curves of two consumers are tangent, known as the contract curve. General equilibrium is achieved when the contract curve touches the production possibility frontier in the Edgeworth box, establishing equilibrium in both markets simultaneously. However, general equilibrium is not unique and depends on given prices; the model assumes perfect competition and does not explain price determination.
Through this slide I try hard to explain it in as simple as possible, so you guys easily understand what IL-SM curve is & its derivation graphically & mathematically, and I hope you guys no need to open you books after you go through with it.
1. The document discusses using the IS-LM model to analyze the effects of shocks, fiscal policy, and monetary policy. It provides examples of analyzing different policy changes using the IS-LM diagram.
2. It then discusses how the IS-LM model can be used to derive the aggregate demand curve and analyze short-run and long-run effects of shocks. Price level adjustments move the economy from short-run to long-run equilibrium.
3. The document contains an example analyzing the 2001 US recession using the IS-LM framework, examining the effects of stock market decline, 9/11, accounting scandals, and fiscal and monetary policy responses.
Kaldor and Hicks developed the compensation principle to evaluate changes in social welfare resulting from economic changes that help some and harm others. Their principle states that if those who gain can compensate the losers and still be better off, the change increases social welfare. They used utility possibility curves to illustrate this, showing how compensation could move individuals to a higher indifference curve. Their theory was criticized for requiring interpersonal utility comparisons and assuming compensation actually occurs.
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.
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 a macroeconomic model that examines national income. It discusses how total output is determined by factors of production like capital and labor. It then explains how factor prices, like wages and rental rates, are set through supply and demand in factor markets. The model shows how total national income is distributed to factor payments. It also outlines the components of aggregate demand, like consumption, investment, and government spending, and how their equilibrium in the goods market determines total output.
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 provides an overview of key concepts in international macroeconomics and the open economy model. It introduces accounting identities that apply to an open economy, where spending does not necessarily equal output and saving does not necessarily equal investment due to trade flows. It then presents the small open economy model, where the domestic economy is too small to affect global interest rates. In this model, the trade balance and exchange rate are determined by the interaction of domestic saving and investment with the exogenous world interest rate. Fiscal and monetary policies can influence the trade balance and exchange rate through their impact on saving and investment.
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.
This document summarizes key concepts from Chapter 12 of Mankiw's Macroeconomics textbook on open economy macroeconomics. It introduces the Mundell-Fleming model, which uses the IS-LM framework to analyze the effects of fiscal and monetary policy in a small open economy. It discusses the implications of floating versus fixed exchange rates and how this determines the effectiveness of different policies. It also examines the impacts of interest rate differentials and trade policies. The summary slides provide a concise overview of the model and the main policy conclusions.
This document provides an overview of classical theories of inflation and the quantity theory of money. It defines key concepts like money, inflation, the money supply, and velocity. The quantity theory of money posits that inflation is primarily caused by increases in the money supply that outpace economic growth. It predicts a direct relationship between money growth and inflation. The document uses graphs and international data to show this relationship generally holds in practice and discusses implications for interest rates.
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.
The life cycle income hypothesis asserts that consumers save and consume based on their optimal consumption pattern over their lifetime, subject to resource constraints. It emphasizes saving during working years to fund consumption in retirement years when income is lower. The hypothesis divides a person's life into three stages - childhood, middle age, and old age - with consumption gradually rising and income peaking in middle age then declining in retirement, resulting in dissaving early and late in life and saving in middle years.
An offer curve shows the quantities of imports and exports that a country is willing to trade at different relative prices (terms-of-trade). It combines a country's demand for imports and supply of exports. Offer curves can be drawn for two countries trading two goods to determine the trading equilibrium and equilibrium terms-of-trade. The equilibrium occurs where the quantities exported and imported are equal for both goods and countries.
This document discusses the natural rate of unemployment and its causes. It begins by defining the natural rate of unemployment as the average rate around which the actual unemployment rate fluctuates over the business cycle. It then presents a model showing how the natural rate is determined by the rates of job separation and job finding. Frictional unemployment results from the time it takes to search for and transition between jobs, while structural unemployment stems from wage rigidities that prevent wages from adjusting downward to clear the labor market. The document explores factors like minimum wages, unions, efficiency wages, and sectoral shifts that contribute to real wage rigidity and the natural rate of unemployment.
This document provides an overview of macroeconomic theory regarding short-term fluctuations in output and employment (i.e. the business cycle) using aggregate demand/aggregate supply models. It explains that in the short-run, prices are sticky but flexible in the long-run, leading to different aggregate supply curves (SRAS, LRAS). The AD/AS framework is used to analyze how demand and supply shocks can cause fluctuations and how stabilization policy aims to minimize changes in output and employment.
Don Patinkin criticized the neoclassical assumptions of homogeneity and dichotomization. He proposed the real balance effect to reconcile goods and money markets. The real balance effect posits that changes in the price level affect real purchasing power, which impacts demand for goods. When prices rise, real balances and goods demand fall, pushing prices back down. This feedback loop between prices, real balances, and goods demand is represented using the IS-LM model, where a fall in prices shifts the LM curve right, raising output and employment until full employment is reached. Patinkin argues this real balance effect denies the homogeneity assumption and integrates goods and money markets.
The document summarizes the relative income hypothesis proposed by Dusenberry in 1949. The key points are:
1) Dusenberry argued that consumption depends more on a person's relative income position compared to others in their community, rather than their absolute income level. People will consume more if they live in wealthier communities to maintain their standard of living.
2) In the short run, the average propensity to consume is greater than the marginal propensity to consume and the relationship between income and consumption is not proportional. In the long run, consumption increases proportionally with income and the average propensity to consume equals the marginal propensity to consume.
3) Dusenberry also believed consumption
This chapter introduces the concepts of the business cycle, aggregate demand, aggregate supply, and the model of aggregate demand and aggregate supply. It discusses how the economy behaves differently in the short-run versus long-run. In the short-run, many prices are sticky so the aggregate supply curve is horizontal, but in the long-run prices are flexible so the aggregate supply curve is vertical. The model can be used to analyze how shocks like changes in the money supply, velocity, or supply shocks impact output and inflation in both the short-run and long-run. An example is given of the 1970s oil shocks, which were adverse supply shocks that increased costs and shifted the short-run aggregate supply curve
This document discusses equilibrium in consumption and production using an Edgeworth box model. It explains that equilibrium occurs where the indifference curves of two consumers are tangent, known as the contract curve. General equilibrium is achieved when the contract curve touches the production possibility frontier in the Edgeworth box, establishing equilibrium in both markets simultaneously. However, general equilibrium is not unique and depends on given prices; the model assumes perfect competition and does not explain price determination.
Through this slide I try hard to explain it in as simple as possible, so you guys easily understand what IL-SM curve is & its derivation graphically & mathematically, and I hope you guys no need to open you books after you go through with it.
1. The document discusses using the IS-LM model to analyze the effects of shocks, fiscal policy, and monetary policy. It provides examples of analyzing different policy changes using the IS-LM diagram.
2. It then discusses how the IS-LM model can be used to derive the aggregate demand curve and analyze short-run and long-run effects of shocks. Price level adjustments move the economy from short-run to long-run equilibrium.
3. The document contains an example analyzing the 2001 US recession using the IS-LM framework, examining the effects of stock market decline, 9/11, accounting scandals, and fiscal and monetary policy responses.
Kaldor and Hicks developed the compensation principle to evaluate changes in social welfare resulting from economic changes that help some and harm others. Their principle states that if those who gain can compensate the losers and still be better off, the change increases social welfare. They used utility possibility curves to illustrate this, showing how compensation could move individuals to a higher indifference curve. Their theory was criticized for requiring interpersonal utility comparisons and assuming compensation actually occurs.
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.
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 differences in living standards and economic growth rates around the world. It begins by showing data on GDP per capita and other indicators for families in the UK, Mexico, and Mali to illustrate vast differences in living standards globally. Tables then show data on GDP per capita and growth rates for various countries from 1960-2005, demonstrating both differences in incomes and variation in growth rates. The document poses questions about why some countries are richer and grow faster than others and what policies may help raise growth rates and living standards. It then discusses various determinants of productivity that influence economic growth and living standards.
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 summarizes key concepts from an intermediate macroeconomics textbook chapter on long-run economic growth. It introduces growth accounting and examines the neoclassical and endogenous growth models. The neoclassical model shows output growing at the population rate unless productivity increases. The endogenous model explains productivity growth endogenously through constant or increasing returns to capital. Government policies that boost savings/investment or productivity can increase long-run growth rates.
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 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 global economic indicators and trends. It finds that while low-income countries tend to have higher GDP growth rates, this may not last as GDP per capita increases and economies "converge." Some countries defy trends, with Qatar projected to quadruple per capita income but Sudan to decline 40%. GDP can grow through increasing productivity, capital, and labor, but productivity growth has diminished in recent decades.
1) This chapter introduces the Keynesian model by adding government and foreign sectors to the analysis of aggregate expenditures and output.
2) In the Keynesian model, equilibrium occurs where total output equals total spending at the point of full employment. Disequilibrium can occur in the form of recessionary or inflationary gaps.
3) Government spending is considered autonomous because it is primarily a political decision independent of the level of output. Changes in autonomous spending, through fiscal policy tools, can be used to adjust aggregate demand and close gaps.
The document is an exam paper for a Business Studies exam containing two case studies:
1. The Travelstop Hotel is facing cash flow problems and declining tourist numbers. It must decide whether to accept a large booking that may be slow to pay.
2. The Soup Makers produces three products at different stages of the product life cycle. It is developing a new product and has identified quality control issues. The case examines production, costs, and decisions around products.
This chapter discusses macroeconomic concepts including national income, GDP, and the factors that determine and distribute total income in an economy. It presents models for how prices of labor and capital are determined by supply and demand in factor markets, and how total income is distributed to labor income and capital income based on marginal productivity. The chapter also examines the components of aggregate demand, including consumption, investment, and government spending, and how equilibrium is reached in the goods and loanable funds markets through price adjustments.
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 discusses key economic concepts including consumption, saving, the multiplier effect, investment demand, and how changes in government spending and taxes can impact GDP through the multiplier. It provides examples of how an initial $1,000 change in spending can multiply into $2,000 in total income due to subsequent rounds of spending. It also notes that the size of the multiplier depends on the marginal propensity to consume.
Duncan Green, head of research at Oxfam GB, gave a lecture on poverty and wealth at Notre Dame University in September 2009. He argued that orthodox economics must consider environmental sustainability and unpaid work. Markets are changing rapidly for the poor, with new threats and opportunities. Redistributing power in markets is key to reducing inequality and poverty. Effective states also have important roles to play in promoting growth that benefits the poor.
This document provides an overview of key macroeconomic statistics including Gross Domestic Product (GDP), the Consumer Price Index (CPI), and the unemployment rate. It discusses how GDP can be measured through expenditures, income, and value added. The components of GDP expenditures are defined as consumption, investment, government spending, and net exports. Real GDP is introduced to control for inflation. The GDP deflator and inflation rates are also explained.
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.
Policy responses to the global economic crisis: Too little, too late?Latvijas Banka
Presentation by Andrew Bosomworth, Managing Director, PIMCO, at the Bank of Latvia conference "Economic Adjustment under Sovereign Debt Crisis: Can Experience of the Baltics Be Applied to Others?"
Riga, November 2, 2012.
Chapter One Development Theory & Poicy.pdfAndnetHilnew
It deals with the fundamental questions of development and underdevelopment.
it tries to show the percapita income variations of countries across time and space
2. In this chapter, you will learn…
the closed economy Solow model
how a country’s standard of living depends on its
saving and population growth rates
how to use the “Golden Rule” to find the optimal
saving rate and capital stock
CHAPTER 7 Economic Growth I slide 2
3. Why growth matters
Data on infant mortality rates:
20% in the poorest 1/5 of all countries
0.4% in the richest 1/5
In Pakistan, 85% of people live on less than $2/day.
One-fourth of the poorest countries have had
famines during the past 3 decades.
Poverty is associated with oppression of women
and minorities.
Economic growth raises living standards and
reduces poverty….
CHAPTER 7 Economic Growth I slide 3
4. Income and poverty in the world
selected countries, 2000
100
Madagascar
90
India
living on $2 per day or less
80 Nepal
70 Bangladesh
% of population
60 Kenya Botswana
50 China
40 Peru
Mexico
30 Thailand
20
Brazil Chile
10 Russian
S. Korea
Federation
0
$0 $5,000 $10,000 $15,000 $20,000
Income per capita in dollars
5. Why growth matters
Anything that effects the long-run rate of economic
growth – even by a tiny amount – will have huge
effects on living standards in the long run.
annual growth percentage increase in
rate of income standard of living after…
per capita …25 years …100 years
…50 years
2.0% 64.0% 169.2% 624.5%
2.5% 85.4% 243.7% 1,081.4%
CHAPTER 7 Economic Growth I slide 5
6. Why growth matters
If the annual growth rate of U.S. real GDP per
capita had been just one-tenth of one percent
higher during the 1990s, the U.S. would have
generated an additional $496 billion of income
during that decade.
CHAPTER 7 Economic Growth I slide 6
7. The lessons of growth theory
…can make a positive difference in the lives of
hundreds of millions of people.
These lessons help us
understand why poor
countries are poor
design policies that
can help them grow
learn how our own
growth rate is affected
by shocks and our
government’s policies
CHAPTER 7 Economic Growth I slide 7
8. The Solow model
due to Robert Solow,
won Nobel Prize for contributions to
the study of economic growth
a major paradigm:
widely used in policy making
benchmark against which most
recent growth theories are compared
looks at the determinants of economic growth
and the standard of living in the long run
CHAPTER 7 Economic Growth I slide 8
9. How Solow model is different
from Chapter 3’s model
1. K is no longer fixed:
investment causes it to grow,
depreciation causes it to shrink
2. L is no longer fixed:
population growth causes it to grow
3. the consumption function is simpler
CHAPTER 7 Economic Growth I slide 9
10. How Solow model is different
from Chapter 3’s model
4. no G or T
(only to simplify presentation;
we can still do fiscal policy experiments)
5. cosmetic differences
CHAPTER 7 Economic Growth I slide 10
11. The production function
In aggregate terms: Y = F (K, L)
Define: y = Y/L = output per worker
k = K/L = capital per worker
Assume constant returns to scale:
zY = F (zK, zL ) for any z > 0
Pick z = 1/L. Then
Y/L = F (K/L, 1)
y = F (k, 1)
y = f(k) where f(k) = F(k, 1)
CHAPTER 7 Economic Growth I slide 11
12. The production function
Output per
worker, y
f(k)
MPK = f(k +1) – f(k)
1
Note: this production function
Note: this production function
exhibits diminishing MPK.
exhibits diminishing MPK.
Capital per
worker, k
CHAPTER 7 Economic Growth I slide 12
13. The national income identity
Y=C+I (remember, no G )
In “per worker” terms:
y=c+i
where c = C/L and i = I /L
CHAPTER 7 Economic Growth I slide 13
14. The consumption function
s = the saving rate,
the fraction of income that is saved
(s is an exogenous parameter)
Note: s is the only lowercase variable
that is not equal to
its uppercase version divided by L
Consumption function: c = (1–s)y
(per worker)
CHAPTER 7 Economic Growth I slide 14
15. Saving and investment
saving (per worker) = y – c
= y – (1–s)y
= sy
National income identity is y = c + i
Rearrange to get: i = y – c = sy
(investment = saving, like in chap. 3!)
Using the results above,
i = sy = sf(k)
CHAPTER 7 Economic Growth I slide 15
16. Output, consumption, and investment
Output per f(k)
worker, y
c1
y1 sf(k)
i1
k1 Capital per
worker, k
CHAPTER 7 Economic Growth I slide 16
17. Depreciation
Depreciation δ = the rate of depreciation
δ = the rate of depreciation
per worker, δ k = the fraction of the capital stock
= the fraction of the capital stock
that wears out each period
that wears out each period
δk
δ
1
Capital per
worker, k
CHAPTER 7 Economic Growth I slide 17
18. Capital accumulation
The basic idea: Investment increases the capital
stock, depreciation reduces it.
Change in capital stock = investment – depreciation
∆k = i – δk
Since i = sf(k) , this becomes:
∆ k = s f(k) – δk
CHAPTER 7 Economic Growth I slide 18
19. The equation of motion for k
∆ k = s f(k) – δk
The Solow model’s central equation
Determines behavior of capital over time…
…which, in turn, determines behavior of
all of the other endogenous variables
because they all depend on k. E.g.,
income per person: y = f(k)
consumption per person: c = (1–s) f(k)
CHAPTER 7 Economic Growth I slide 19
20. The steady state
∆ k = s f(k) – δk
If investment is just enough to cover depreciation
[sf(k) = δ k ],
then capital per worker will remain constant:
∆k = 0.
This occurs at one value of k, denoted k*,
called the steady state capital stock.
CHAPTER 7 Economic Growth I slide 20
21. The steady state
Investment
and δk
depreciation
sf(k)
k* Capital per
worker, k
CHAPTER 7 Economic Growth I slide 21
22. Moving toward the steady state
∆ k = sf(k) − δk
Investment
and δk
depreciation
sf(k)
∆k
investment
depreciation
k1 k* Capital per
worker, k
CHAPTER 7 Economic Growth I slide 22
23. Moving toward the steady state
∆ k = sf(k) − δk
Investment
and δk
depreciation
sf(k)
∆k
k1 k2 k* Capital per
worker, k
CHAPTER 7 Economic Growth I slide 24
24. Moving toward the steady state
∆ k = sf(k) − δk
Investment
and δk
depreciation
sf(k)
∆k
investment
depreciation
k2 k* Capital per
worker, k
CHAPTER 7 Economic Growth I slide 25
25. Moving toward the steady state
∆ k = sf(k) − δk
Investment
and δk
depreciation
sf(k)
∆k
k2 k3 k* Capital per
worker, k
CHAPTER 7 Economic Growth I slide 27
26. Moving toward the steady state
∆ k = sf(k) − δk
Investment
and δk
depreciation
sf(k)
Summary:
Summary:
As long as k < k**,,
As long as k < k
investment will exceed
investment will exceed
depreciation,
depreciation,
and k will continue to
and k will continue to
grow toward k**..
grow toward k
k3 k* Capital per
worker, k
CHAPTER 7 Economic Growth I slide 28
27. Now you try:
Draw the Solow model diagram,
labeling the steady state k*.
On the horizontal axis, pick a value greater than k*
for the economy’s initial capital stock. Label it k1.
Show what happens to k over time.
Does k move toward the steady state or
away from it?
CHAPTER 7 Economic Growth I slide 29
28. A numerical example
Production function (aggregate):
Y = F (K , L ) = K × L = K 1 / 2L1 / 2
To derive the per-worker production function,
divide through by L:
1/ 2
Y K L 1/ 2 1/ 2
K
= = ÷
L L L
Then substitute y = Y/L and k = K/L to get
y = f (k ) = k 1 / 2
CHAPTER 7 Economic Growth I slide 30
29. A numerical example, cont.
Assume:
s = 0.3
δ = 0.1
initial value of k = 4.0
CHAPTER 7 Economic Growth I slide 31
30. Approaching the steady state:
A numerical example
Assumptions: y = k; s = 0.3; δ
Year
Year k
k y
y c
c ii k
k ∆k
∆k
11 4.000
4.000 2.000 1.400
2.000 1.400 0.600
0.600 0.400
0.400 0.200
0.200
2
2 4.200
4.200 2.049 1.435
2.049 1.435 0.615
0.615 0.420
0.420 0.195
0.195
3
3 4.395
4.395 2.096 1.467
2.096 1.467 0.629
0.629 0.440
0.440 0.189
0.189
4 4.584 2.141 1.499 0.642 0.458 0.184
…
10 5.602 2.367 1.657 0.710 0.560 0.150
…
25 7.351 2.706 1.894 0.812 0.732 0.080
…
100 8.962 2.994 2.096 0.898 0.896 0.002
…
CHAPTER9.000 3.000
7 Economic Growth I 2.100 0.900 0.900 0.000 32
slide
31. Exercise: Solve for the steady state
Continue to assume
s = 0.3, δ = 0.1, and y = k 1/2
Use the equation of motion
∆k = s f(k) − δ k
to solve for the steady-state values of k, y, and c.
CHAPTER 7 Economic Growth I slide 33
32. Solution to exercise:
∆k = 0 def. of steady state
s f (k * ) = δ k * eq'n of motion with ∆k = 0
0.3 k * = 0.1k * using assumed values
k *
3= = k *
k *
Solve to get: k * = 9 and y * = k * = 3
Finally, c * = (1 − s ) y * = 0.7 × 3 = 2.1
CHAPTER 7 Economic Growth I slide 34
33. An increase in the saving rate
An increase in the saving rate raises investment…
…causing k to grow toward a new steady state:
Investment
and δk
depreciation s2 f(k)
s1 f(k)
k
CHAPTER 7 Economic Growth I
k 1* k2
*
slide 35
34. Prediction:
Higher s ⇒ higher k*.
And since y = f(k) ,
higher k* ⇒ higher y* .
Thus, the Solow model predicts that countries
with higher rates of saving and investment
will have higher levels of capital and income per
worker in the long run.
CHAPTER 7 Economic Growth I slide 36
35. International evidence on investment
rates and income per person
Income per 100,000
person in
2000
(log scale)
10,000
1,000
100
0 5 10 15 20 25 30 35
Investment as percentage of output
(average 1960-2000)
CHAPTER 7 Economic Growth I slide 37
36. The Golden Rule: Introduction
Different values of s lead to different steady states.
How do we know which is the “best” steady state?
The “best” steady state has the highest possible
consumption per person: c* = (1–s) f(k*).
An increase in s
leads to higher k* and y*, which raises c*
reduces consumption’s share of income (1–s),
which lowers c*.
So, how do we find the s and k* that maximize c*?
CHAPTER 7 Economic Growth I slide 38
37. The Golden Rule capital stock
k gold = 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*
= f (k*) − i*
In the steady state:
= f (k*) − δ k* i* = δ k*
because ∆k = 0.
CHAPTER 7 Economic Growth I slide 39
38. The Golden Rule capital stock
steady state
output and
depreciation δ k*
Then, graph
Then, graph
f(k * )
f(k*)) and δ k*,,
f(k* and δ k*
look for the
look for the
point where
point where
the gap between
the gap between c gold
*
them is biggest.
them is biggest.
i gold = δ k gold
* *
y gold = f (k gold )
* *
k gold
*
steady-state
capital per
worker, k *
CHAPTER 7 Economic Growth I slide 40
39. The Golden Rule capital stock
c* * = f(k*)) − δ k* *
c = f(k* − δ k δ k*
is biggest where the
is biggest where the
slope of the
slope of the f(k * )
production function
production function
equals
equals
the slope of the
the slope of the
depreciation line:
depreciation line:
c gold
*
MPK = δ
k gold
*
steady-state
capital per
worker, k *
CHAPTER 7 Economic Growth I slide 41
40. 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?
CHAPTER 7 Economic Growth I slide 42
41. Starting with too much capital
If k *
> k gold
*
y
then increasing c**
then increasing c
requires a fall in s.
requires a fall in s.
c
In the transition to
In the transition to
the Golden Rule,
the Golden Rule,
i
consumption is
consumption is
higher at all points
higher at all points
in time.
in time. t0 time
CHAPTER 7 Economic Growth I slide 43
42. Starting with too little capital
If k * < k gold
*
then increasing c**
then increasing c
requires an y
requires an
increase in s.
increase in s. c
Future generations
Future generations
enjoy higher
enjoy higher
consumption, i
consumption,
but the current
but the current
one experiences
one experiences t0 time
an initial drop
an initial drop
in consumption.
in consumption. Growth I
CHAPTER 7 Economic slide 44
43. Population growth
Assume that the population (and labor force)
grow at rate n. (n is exogenous.)
∆L
= n
L
EX: Suppose L = 1,000 in year 1 and the
population is growing at 2% per year (n = 0.02).
Then ∆L = n L = 0.02 × 1,000 = 20,
so L = 1,020 in year 2.
CHAPTER 7 Economic Growth I slide 45
44. Break-even investment
(δ + n)k = break-even investment,
the amount of investment necessary
to keep k constant.
Break-even investment includes:
δ k to replace capital as it wears out
n k to equip new workers with capital
(Otherwise, k would fall as the existing capital stock
would be spread more thinly over a larger
population of workers.)
CHAPTER 7 Economic Growth I slide 46
45. The equation of motion for k
With population growth,
the equation of motion for k is
∆ k = s f(k) − (δ + n ) k
actual
break-even
investment
investment
CHAPTER 7 Economic Growth I slide 47
46. The Solow model diagram
Investment,
∆ k = s f(k) − (δ +n )k
break-even
investment
(δ + n ) k
sf(k)
k* Capital per
worker, k
CHAPTER 7 Economic Growth I slide 48
47. The impact of population growth
Investment,
break-even ( δ +n 2 ) k
investment
(δ +n 1 ) k
An increase in n
An increase in n
causes an sf(k)
causes an
increase in break-
increase in break-
even investment,
even investment,
leading to a lower
steady-state level
of k.
k 2* k 1* Capital per
worker, k
CHAPTER 7 Economic Growth I slide 49
48. Prediction:
Higher n ⇒ lower k*.
And since y = f(k) ,
lower k* ⇒ lower y*.
Thus, the Solow model predicts that countries
with higher population growth rates will have
lower levels of capital and income per worker in
the long run.
CHAPTER 7 Economic Growth I slide 50
49. International evidence on population
growth and income per person
Income 100,000
per Person
in 2000
(log scale)
10,000
1,000
100
0 1 2 3 4 5
Population Growth
(percent per year; average 1960-2000)
CHAPTER 7 Economic Growth I slide 51
50. The Golden Rule with population
growth
To find the Golden Rule capital stock,
express c* in terms of k*:
c* = y* − i*
= f (k* ) − (δ + n) k*
In the Golden
In the Golden
c* is maximized when Rule steady state,
Rule steady state,
MPK = δ + n the marginal product
the marginal product
or equivalently, of capital net of
of capital net of
MPK − δ = n depreciation equals
depreciation equals
the population
the population
CHAPTER 7 Economic Growth I
growth rate.
growth rate. slide 52
51. Alternative perspectives on
population growth
The Malthusian Model (1798)
Predicts population growth will outstrip the Earth’s
ability to produce food, leading to the
impoverishment of humanity.
Since Malthus, world population has increased
sixfold, yet living standards are higher than ever.
Malthus omitted the effects of technological
progress.
CHAPTER 7 Economic Growth I slide 53
52. Alternative perspectives on
population growth
The Kremerian Model (1993)
Posits that population growth contributes to
economic growth.
More people = more geniuses, scientists &
engineers, so faster technological progress.
Evidence, from very long historical periods:
As world pop. growth rate increased, so did rate
of growth in living standards
Historically, regions with larger populations have
enjoyed faster growth.
CHAPTER 7 Economic Growth I slide 54
53. Chapter Summary
1. The Solow growth model shows that, in the long
run, a country’s standard of living depends
positively on its saving rate
negatively on its population growth rate
2. An increase in the saving rate leads to
higher output in the long run
faster growth temporarily
but not faster steady state growth.
CHAPTER 7 Economic Growth I slide 55
54. Chapter Summary
3. If the economy has more capital than the
Golden Rule level, then reducing saving will
increase consumption at all points in time,
making all generations better off.
If the economy has less capital than the Golden
Rule level, then increasing saving will increase
consumption for future generations, but reduce
consumption for the present generation.
CHAPTER 7 Economic Growth I slide 56
Editor's Notes
Chapters 7 and 8 cover one of the most important topics in macroeconomics. The material in these chapters is more challenging than average for the book, yet Mankiw explains it especially clearly. New to the 6 th edition is a brief section at the end of the chapter on alternative perspectives on population growth. If you taught with the PowerPoint slides I prepared for the previous edition of this textbook, you will find that I’ve streamlined the introduction a bit. If you have not, you will find an introduction here, not appearing in the textbook, that provides data to motivate the study of economic growth.
This slide shows a negative relationship between income per capita and poverty. Many economists believe that the causation runs from growth to poverty, i.e. increasing growth will reduce poverty. source: The Elusive Quest for Growth , by William Easterly. (MIT Press, 2001) Note: I have searched far and wide for updated poverty statistics, including the UN and World Bank’s World Development Indicators. At the time I write this (July 2007), the poverty rate data I find are scattered – different years for different countries, and for most countries the latest available is no more recent than 2000. If you know of a source for more recent poverty statistics, I would be most grateful if you could email me at roncron@unlv.nevada.edu. Thank you!
The $496 billion is in 2006 prices. How I did this calculation: 1. Computed actual quarterly growth rate of real income per capita from 1989:4 through 1999:4. 2. Added one-fourth of one-tenth of one percent to each quarter’s actual growth rate. 3. Computed what real income per capita in would have been with the new growth rates. 4. Multiplied this hypothetical real income per capita by the population to get hypothetical real GDP. 5. Computed the difference between hypothetical and actual real GDP for each quarter. 6. Cumulated these differences over the period 1990:1-1999:4. Like the original real GDP data, the cumulative difference was in 1996 dollars. I multiplied this amount by 21%, the amount by which the GDP deflator rose between 1996 and 2006, so the final result is expressed in 2006 dollars. SOURCE of DATA: Real GDP, GDP deflator - Dept of Commerce, Bureau of Economic Analysis. Population - Dept of Commerce, Census Bureau. All obtained from “FRED” - the St. Louis Fed’s database, on the web at http://research.stlouisfed.org/fred2/
It’s easier for students to learn the Solow model if they see that it’s just an extension of something they already know, the classical model from Chapter 3. So, this slide and the next point out the differences.
The cosmetic differences include things like the notation (lowercase letters for per-worker magnitudes instead of uppercase letters for aggregate magnitudes) and the variables that are measured on the axes of the main graph.
When everything on the slide is showing on the screen, explain to students how to interpret f ( k ) : f ( k ) is the “per worker production function,” it shows how much output one worker could produce using k units of capital. You might want to point out that this is the same production function we worked with in chapter 3. We’re just expressing it differently.
The real interest rate r does not appear explicitly in any of the Solow model’s equations. This is to simplify the presentation. You can tell your students that investment still depends on r , which adjusts behind the scenes to keep investment = saving at all times.
As each assumption appears on the screen, explain it’s interpretation. I.e., “The economy saves three-tenths of income,” “every year, 10% of the capital stock wears out,” and “suppose the economy starts out with four units of capital for every worker.”
Before revealing the numbers in the first row, ask your students to determine them and write them in their notes. Give them a moment, then reveal the first row and make sure everyone understands where each number comes from. Then, ask them to determine the numbers for the second row and write them in their notes. After the second round of this, it’s probably fine to just show them the rest of the table.
Suggestion: give your students 3-5 minutes to work on this exercise in pairs. Working alone, a few students might not know that they need to start by setting k = 0. But working in pairs, they are more likely to figure it out. Also, this gives students a little psychological momentum to make it easier for them to start on the end-of-chapter exercises (if you assign them as homework). (If any need a hint, remind them that the steady state is defined by k = 0. A further hint is that they answers they get should be the same as the last row of the big table on the preceding slide, since we are still using all the same parameter values.)
The first few lines of this slide show the calculations and intermediate steps necessary to arrive at the correct answers, which are given in the last 2 lines of the slide.
Next, we see what the model says about the relationship between a country’s saving rate and its standard of living (income per capita) in the long run (or steady state). An earlier slide said that the model’s omission of G and T was only to simplify the presentation. We can still do policy analysis. We know from Chapter 3 that changes in G and/or T affect national saving. In the Solow model as presented here, we can simply change the exogenous saving rate to analyze the impact of fiscal policy changes.
After showing this slide, you might also note that the converse is true, as well: a fall in s (caused, for example, by tax cuts or government spending increases) leads ultimately to a lower standard of living. In the static model of Chapter 3, we learned that a fiscal expansion crowds out investment. The Solow model allows us to see the long-run dynamic effects: the fiscal expansion, by reducing the saving rate, reduces investment. If we were initially in a steady state (in which investment just covers depreciation), then the fall in investment will cause capital per worker, labor productivity, and income per capita to fall toward a new, lower steady state. (If we were initially below a steady state, then the fiscal expansion causes capital per worker and productivity to grow more slowly, and reduces their steady-state values.) This, of course, is relevant because actual U.S. public saving has fallen sharply since 2001.
Figure 7-6, p.197. Source: Penn World Table version 6.1. Number of countries = 97 High investment is associated with high income per person, as the Solow model predicts.
Students sometimes confuse this graph with the other Solow model diagram, as the curves look similar. Be sure to clarify the differences: On this graph, the horizontal axis measures k*, not k. Thus, once we have found k* using the other graph, we plot that k* on this graph to see where the economy’s steady state is in relation to the golden rule capital stock. On this graph, the curve measures f(k*), not sf(k). On the other diagram, the intersection of the two curves determines k*. On this graph, the only thing determined by the intersection of the two curves is the level of capital where c*=0, and we certainly wouldn’t want to be there. There are no dynamics in this graph, as we are in a steady state. In the other graph, the gap between the two curves determines the change in capital.
If your students have had a semester of calculus, you can show them that deriving the condition MPK = is straight-forward: The problem is to find the value of k* that maximizes c * = f(k * ) k * . Just take the first derivative of that expression and set equal to zero: f (k * ) = 0 where f (k * ) = MPK = slope of production function and = slope of steady-state investment line.
Remember: policymakers can affect the national saving rate: - changing G or T affects national saving - holding T constant overall, but changing the structure of the tax system to provide more incentives for private saving (e.g., a revenue-neutral shift from the income tax to a consumption tax)
t 0 is the time period in which the saving rate is reduced. It would be helpful if you explained the behavior of each variable before t 0 , at t 0 , and in the transition period (after t 0 ). Before t 0 : in a steady state, where k, y, c, and i are all constant. At t 0 : The change in the saving rate doesn’t immediately change k, so y doesn’t change immediately. But the fall in s causes a fall in investment [because saving equals investment] and a rise in consumption [because c = (1-s)y, s has fallen but y has not yet changed.]. Note that c = - i, because y = c + i and y has not changed. After t 0 : In the previous steady state, saving and investment were just enough to cover depreciation. Then saving and investment were reduced, so depreciation is greater than investment, which causes k to fall toward a new, lower steady state value. As k falls and settles on its new, lower steady state value, so will y, c, and i (because each of them is a function of k). Even though c is falling, it doesn’t fall all the way back to its initial value. Policymakers would be happy to make this change, as it produces higher consumption at all points in time (relative to what consumption would have been if the saving rate had not been reduced.
Before t 0 : in a steady state, where k, y, c, and i are all constant. At t 0 : The increase in s doesn’t immediately change k, so y doesn’t change immediately. But the increase in s causes investment to rise [because higher saving means higher investment] and consumption to fall [because we are saving more of our income, and consuming less of it]. After t 0 : Now, saving and investment exceed depreciation, so k starts rising toward a new, higher steady state value. The behavior of k causes the same behavior in y, c, and i (qualitatively the same, that is). Ultimately, consumption ends up at a higher steady state level. But initially consumption falls. Therefore, if policymakers value the current generation’s well-being more than that of future generations, they might be reluctant to adjust the saving rate to achieve the Golden Rule. Notice, though, that if they did increase s, an infinite number of future generations would benefit, which makes the sacrifice of the current generation seem more acceptable.
Of course, “actual investment” and “break-even investment” here are in “per worker” magnitudes.
This and the preceding slide establish an implication of the model. The following slide confronts this implication with data.
Figure 7-13, p.210. Number of countries = 96. Source: Penn World Table version 6.1. The model predicts that faster population growth should be associated with a lower long-run income per capital The data is consistent with this prediction. So far, we’ve now learned two things a poor country can do to raise its standard of living: increase national saving (perhaps by reducing its budget deficit) and reduce population growth.
This and the next slide cover new material in the 6 th edition. They can be omitted without loss of continuity.
Michael Kremer, “Population Growth and Technological Change: One Million B.S. to 1990,” Quarterly Journal of Economics 108 (August 1993): 681-716.