I. The Solow model. Dynamic Macroeconomic Analysis. Universidad Autónoma de Madrid. Autumn 2014

Size: px
Start display at page:

Download "I. The Solow model. Dynamic Macroeconomic Analysis. Universidad Autónoma de Madrid. Autumn 2014"

Transcription

1 I. The Solow model Dynamic Macroeconomic Analysis Universidad Autónoma de Madrid Autumn 2014 Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

2 Objectives In this first lecture we will study the Solow growth model. The Solow model is the basis for modern growth theory. It offers a simplified representation of the mechanics of growth, placing particular emphasis on the role of capital accumulation. Households own the capital stock and save a fixed proportion of their income. In later themes we will construct a genuine dynamic general equilibrium models with almost identical predictions. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

3 Proximate vs fundamental causes of growth The Solow model helps us understand how capital accumulation, population growth and technological change contribute to the growth of living standards. In the terminology of Acemoglu these are proximate causes of economic growth. They fail to explain the persistence of the pronounced differences in living standards. The study of the fundamental causes of these income differences, such as the quality of institutions, is left for future study. Even so, a thorough understanding of the mechanics of growth is essential. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

4 Main assumptions A closed economy without a government Y t = C t + I t Y t C t S t = I t A neo-classical production function (see below) Y t = F (K t, L t, A t ) The final good can be consumed or used as capital. Technology, A t, is non-rival and non-excludable. Households save a fraction s (0, 1) of their income. S t = I t = sy t while capital depreciates at a constant rate δ so that D t = δk t Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

5 Technology A neo-classical production function F (K, L, A) with F (0, 0, A) = 0 has the following features: 1 Positive but decreasing marginal products F K = F K > 0 ; 2 F K 2 = F KK < 0 ; 2 Constant returns to scale in K and L F L = F L > 0 2 F L 2 = F LL < 0 F (λk, λl, A) = λf (K, L, A) 3 The function F satisfies the Inada conditions lim K 0 F K = lim L 0 F L = ; lim K F K = lim L F L = 0 Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

6 Production side of the economy Essentially, there are two alternative interpretations of the production side Autarky (each household owns its own firm) A representative firm hires capital and labour on a competitive labour market In the latter case, the representative s problem is given by max K,L Π = F (K t, L t, A t ) r t K t w t L t r t = F K (.,.,.) w t = F L (.,.,.) F (K t, L t, A t ) = r t K t + w t L t where the last line follows from CTS. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

7 Continuous time For convenience we analyze the model in continuous time The instantaneous change in any variable X t is denoted by X t = dx ( ) t X = t+ X t lim 0 dt Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

8 Law of motion of the capital stock The change in the capital stock at t, K t, is the difference between gross investment I t, and depreciation, D t : K t = I t D t = sy t K t = sf (K t, L t, A t ) δk t Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

9 Units For future purposes, it is convenient to convert all aggregate variables in per capita quantities. We denote the quantities per capita by lower-case letters. For simplicity, let L t denote both the size of the population and the labour force. Then κ t = K t L t y t = Y t L t = 1 L t F (K t, L t, A t ) = F (K t /L t, 1, A t ) = F (κ t, 1, A t ) = f (κ t, A t ) Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

10 Benchmark In our benchmark, we abstract from population growth or technical progress. So, L t = L A t = A while κ t = δ δt ( ) Kt = L K t K t 0 K L L 2 = t L Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

11 The Fundamental Equation of the Solow Model Combining the expressions for K t and κ t we obtain: K t = sf (K t, L, A) δk t K t L = 1 L sf (K t, L, A) δ K t L κ t = sf (κ t ) δκ t Formally, this is a non-linear first-order differential equation. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

12 Example: Cobb-Douglas production function The Cobb-Douglas production function is a convenient example of a neo-classical production function: Y = AK α L 1 α y = AK α L 1 α = AK α L α L = Aκ α = f (κ, A) The function f (.,.) is a strictly concave function of κ with δf (κ, A) = f (κ, A) = αaκ α 1 = αa δκ κ 1 α lim κ 0 f (κ, A) = lim κ f (κ, A) = 0 Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

13 Convergence to steady state Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

14 Convergence to steady state The previous slide has demonstrated that the economy converges (monotonically) to a steady state with κ t = κ. The economy replicates itself because each agent (or household) saves a quantity i = sf (κ ) that exactly compensates for the depreciation of her capital d = δκ. Formally, for any initial capital stock κ 0 (0, κ ) the economy will experience a period of growth in which κ t and ẏ t are strictly positive. Once the economy reaches the steady state, growth comes to an end. Note, convergence to k will occur for any κ > 0, including the cases in which the economy starts out with a κ 0 > κ (see below). Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

15 What guarantees convergence? The assumption of a neo-classical production technology is a sufficient condition to guarantee convergence to a unique steady state: The Inada condition lim K 0 F K = guarantees that the curve sf (κ) is steeper than δκ near the origin; The diminishing marginal returns to capital guarantee that sf (κ) is a strictly concave function; The second Inada condition, lim K F K = 0, guarantees that the curve sf (κ) intersects deltaκ for some finite κ. The intersection is unique because the slope of sf (κ) is a strictly decreasing function of κ. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

16 Relevant features of the steady state Our assumptions about technology guarantee that there is a unique steady state with a positive capital-labour ratio κ. There is also a trivial steady state with κ equal to zero, but we will ignore this unstable steady state. It is common to talk about steady-state equilibria. But formally the entire trajectory from κ 0 to κ should be part of any equilibrium definition. The unique positive levels of κ and y are strictly increasing in s and A, and decreasing in δ. By contrast, consumption per capita, c, is increasing in A but non-monotonic in s (lim s 0 c = lim s 1 c = 0). Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

17 The Golden Rule We cannot perform a formal welfare analysis as we have not specified agents preferences over consumption and labour. Nonetheless, we can ask ourselves whether the steady-state allocation generates the maximum feasible level of steady-state consumption. In any steady state, i = I t /L = δκ. Since c = f (κ ) i we can therefore define the golden-rule capital stock as argmax κ c = f (κ ) δκ The FOC that implicitly defines κ gold is: f (κ gold ) = δ Let s gold denote the savings rate required to attain a steady state with κ gold. There are no forces in the model to guarantee that s = s gold. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

18 Steady-state consumption and the Golden Rule Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

19 Dynamic inefficiency The concept of the Golden Rule is not just useful to identify the allocation with the highest steady-state consumption level. It also allows us to recognize inefficient allocations. In particular, any steady state with κ > κ gold (or s > s gold ) is inefficient. If the agents were to reduce their savings rate to s gold consumption will converge to the maximum level c gold. And along the transition to steady state the agents will enjoy even higher consumption levels. In other words, if agents value consumption they must be unambiguously better off than under the initial steady state. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

20 Intertemporal tradeoffs Now suppose the economy is located in a steady state with κ < κ gold (and s < s gold ). Once more c < c gold, but this time we cannot make unambiguous efficiency statements. To reach the Golden Rule capital stock, the agents have to raise their savings rate. This generates an immediate reduction in consumption from c = (1 s)f (κ ) to c = (1 s gold )f (κ ). Consumption will grow over time and will eventually exceed c. In other words, the agents have to trade off lower consumption today against higher consumption in the future. A formal analysis of the welfare consequences requires a fully specified model with preferences. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

21 Population growth Once we allow for population growth, the economy converges to a steady state in which all aggregate variables grow at the same rate as L t, but again there is no growth in per capita variables. Constant population growth L t L t = n κ t = δ δt ( Kt L t = K t L t κ t ) = L t K t K t L t ( ) L t L t L 2 t = K t L t κ t n Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

22 The fundamental equation with population growth Recall that the evolution of the capital stock is governed by K t = sf (K t, L t, A) δ K t L t L t L t κ t = K t L t κ t n Combining these expressions, we obtain In steady state ( κ t = 0) κ t = sf (κ t ) (n + δ)κ t sf (κ ) = (n + δ)κ Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

23 Steady state with population growth Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

24 Characteristics of the steady state In steady state all per capita variables, such as κ t, y t, i t or c t, remain constant over time. By contrast, all aggregate variables grow at the same rate as the population. For example, K t = κ L t log(k t ) = log(κ ) + log(l t ) Taking derivatives with respect to t yields K t K t = 0 + L t L t = n From CRTS, it follows that Y t and hence C t and I t also grow at rate n. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

25 Transitional dynamics Since y t is stricly increasing in κ t, the growth rate of y (ẏ t / t ) is proportional to the growth rate of κ γ κ κ κ = s f (κ, A) κ (n + δ) The concavity of f (.,.) implies that the average output per unit of capital is decreasing in κ. Hence the growth rate of κ is strictly decreasing in κ with γ κ > 0 for all κ t < κ and γ κ < 0 for κ t > κ. This combined with lim κ 0 (f (κ, A)/κ) = guarantees existence and uniqueness. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

26 Growth and convergence Correct interpretation: g=0 Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

27 Technological progress In the basic Solow model we can only have sustained growth if there is sustained technological progress. Moreover, balanced growth is only possible if technological progress is labour-augmenting. Formally, we will assume Y t = F (K t, A t L t ) Ȧ t A t = x Next, we let ˆL t = A t L t denote the efficiency units of labour and ˆκ t = K t ˆL t = K t A t L t yˆ t = F (K t, ˆL t ) = f ( ˆκ t ) ˆL t Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

28 Balanced growth with exogenous technological change Following the same procedure like before, we arrive at ( δ Kt δt A t L t ) = K t ˆL t ˆκ t (x + n) K t ˆL t = sf ( ˆκ t ) δ ˆκ t Combing the above equations we arrive at the fundamental equation with technological growth δ ˆκ t δt = sf ( ˆκ t) (n + δ + x) ˆκ t Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

29 Interpretation of the balanced growth path Once the economy reaches the steady state, All quantities per efficiency unit (ŷ, ĉ and ˆκ) are constant over time All quantities per capita (y, c and κ) grow at the rate n. All aggregate variables (Y, C and K) grow at the rate n + x. However, it should be reminded that the growth of A t is generated exogenously. Eventually, we would like to understand the drivers behind technological progress (investments in human capital, R&D, etc. ). In order to generate endogenous growth with investment in R&D we need to abandon the assumption of perfect competition. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

30 Conditional convergence The model predicts that the growth rate of capital and income per capita are falling in the level of capital. Hence, if the level of capital is the ONLY difference between two countries, then: The poor country should grow at a faster rate than the rich country Both countries should eventually converge to the same steady state. The conditional convergence of income levels is a prediction of the model that is verified by the data. Similarly, nothing prevents the divergence between countries with different fundamentals. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

31 Sustained growth The AK model In order to generate sustained growth without exogenous technological change, we need to relax some of the assumptions of the Solow model. A logical candidate is to consider alternatives to the assumption of a neo-classical production technology In the Solow model growth vanishes due to the decreasing marginal product of capital We can show that perpetual growth is feasible if output is linear in K so that Y t = AK t This interpretation is acceptable if we use a broad concept of capital that includes both human and physical capital. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

32 Sustained growth The AK model In the AK-model, per capita output is equal to y = AK /L = Aκ. In other words, the fundamental equation remains valid κ = sy (n + δ)κ = saκ (n + δ)κ and so the growth rate of κ can be written as κ κ = sa (n + δ) which is constant and independent of κ. Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

33 Distinctive features of the AK model 1 The model produces sustained growth without sustained growth in an exogenous variable like A 2 The growth rate is increasing in the savings rate 3 No transitional dynamics the growth rate is constant and equal to sa (n + δ) 4 No convergence 5 Recessions produce permanent effects on living conditions 6 The economy is never dynamically inefficient Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn / 33

I. The Solow model. Dynamic Macroeconomic Analysis. Universidad Autónoma de Madrid. Autumn 2014

I. The Solow model. Dynamic Macroeconomic Analysis. Universidad Autónoma de Madrid. Autumn 2014 I. The Solow model Dynamic Macroeconomic Analysis Universidad Autónoma de Madrid Autumn 2014 Dynamic Macroeconomic Analysis (UAM) I. The Solow model Autumn 2014 1 / 38 Objectives In this first lecture

More information

I. The Solow model. Dynamic Macroeconomic Analysis. Universidad Autónoma de Madrid. September 2015

I. The Solow model. Dynamic Macroeconomic Analysis. Universidad Autónoma de Madrid. September 2015 I. The Solow model Dynamic Macroeconomic Analysis Universidad Autónoma de Madrid September 2015 Dynamic Macroeconomic Analysis (UAM) I. The Solow model September 2015 1 / 43 Objectives In this first lecture

More information

1 The Solow Growth Model

1 The Solow Growth Model 1 The Solow Growth Model The Solow growth model is constructed around 3 building blocks: 1. The aggregate production function: = ( ()) which it is assumed to satisfy a series of technical conditions: (a)

More information

202: Dynamic Macroeconomics

202: Dynamic Macroeconomics 202: Dynamic Macroeconomics Solow Model Mausumi Das Delhi School of Economics January 14-15, 2015 Das (Delhi School of Economics) Dynamic Macro January 14-15, 2015 1 / 28 Economic Growth In this course

More information

Economic Growth: Lectures 1 (second half), 2 and 3 The Solow Growth Model

Economic Growth: Lectures 1 (second half), 2 and 3 The Solow Growth Model 14.452 Economic Growth: Lectures 1 (second half), 2 and 3 The Solow Growth Model Daron Acemoglu MIT Oct. 31, Nov. 5 and 7, 2013. Daron Acemoglu (MIT) Economic Growth Lectures 1-3 Oct. 31, Nov. 5 and 7,

More information

Economic Growth: Lectures 2 and 3 The Solow Growth Model

Economic Growth: Lectures 2 and 3 The Solow Growth Model 14.452 Economic Growth: Lectures 2 and 3 The Solow Growth Model Daron Acemoglu MIT November 1 and 3. Daron Acemoglu (MIT) Economic Growth Lectures 2-3 November 1 and 3. 1 / 87 Solow Growth Model Solow

More information

004: Macroeconomic Theory

004: Macroeconomic Theory 004: Macroeconomic Theory Lecture 14 Mausumi Das Lecture Notes, DSE October 21, 2014 Das (Lecture Notes, DSE) Macro October 21, 2014 1 / 20 Theories of Economic Growth We now move on to a different dynamics

More information

004: Macroeconomic Theory

004: Macroeconomic Theory 004: Macroeconomic Theory Lecture 16 Mausumi Das Lecture Notes, DSE October 28, 2014 Das (Lecture Notes, DSE) Macro October 28, 2014 1 / 24 Solow Model: Golden Rule & Dynamic Ineffi ciency In the last

More information

Introduction to economic growth (2)

Introduction to economic growth (2) Introduction to economic growth (2) EKN 325 Manoel Bittencourt University of Pretoria M Bittencourt (University of Pretoria) EKN 325 1 / 49 Introduction Solow (1956), "A Contribution to the Theory of Economic

More information

Lecture 5: Growth Theory

Lecture 5: Growth Theory Lecture 5: Growth Theory See Barro Ch. 3 Trevor Gallen Spring, 2015 1 / 60 Production Function-Intro Q: How do we summarize the production of five million firms all taking in different capital and labor

More information

Macroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PROBLEM SET 1

Macroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PROBLEM SET 1 Macroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PROBLEM SET 1 1.1 (from Romer Advanced Macroeconomics Chapter 1) Basic properties of growth rates which will be used over and over again. Use the

More information

). In Ch. 9, when we add technological progress, k is capital per effective worker (k = K

). In Ch. 9, when we add technological progress, k is capital per effective worker (k = K Economics 285 Chris Georges Help With Practice Problems 3 Chapter 8: 1. Questions For Review 1,4: Please see text or lecture notes. 2. A note about notation: Mankiw defines k slightly differently in Chs.

More information

Lecture Notes 1: Solow Growth Model

Lecture Notes 1: Solow Growth Model Lecture Notes 1: Solow Growth Model Zhiwei Xu (xuzhiwei@sjtu.edu.cn) Solow model (Solow, 1959) is the starting point of the most dynamic macroeconomic theories. It introduces dynamics and transitions into

More information

Chapter 2 Savings, Investment and Economic Growth

Chapter 2 Savings, Investment and Economic Growth George Alogoskoufis, Dynamic Macroeconomic Theory Chapter 2 Savings, Investment and Economic Growth The analysis of why some countries have achieved a high and rising standard of living, while others have

More information

The Facts of Economic Growth and the Introdution to the Solow Model

The Facts of Economic Growth and the Introdution to the Solow Model The Facts of Economic Growth and the Introdution to the Solow Model Lorenza Rossi Goethe University 2011-2012 Course Outline FIRST PART - GROWTH THEORIES Exogenous Growth The Solow Model The Ramsey model

More information

Growth Theory: Review

Growth Theory: Review Growth Theory: Review Lecture 1, Endogenous Growth Economic Policy in Development 2, Part 2 March 2009 Lecture 1, Endogenous Growth 1/28 Economic Policy in Development 2, Part 2 Outline Review: From Solow

More information

Macroeconomics Lecture 2: The Solow Growth Model with Technical Progress

Macroeconomics Lecture 2: The Solow Growth Model with Technical Progress Macroeconomics Lecture 2: The Solow Growth Model with Technical Progress Richard G. Pierse 1 Introduction In last week s lecture we considered the basic Solow-Swan growth model (Solow (1956), Swan (1956)).

More information

Long run economic growth, part 2. The Solow growth model

Long run economic growth, part 2. The Solow growth model Long run economic growth, part 2. The Solow growth model The Solow growth model The seminal Solow growth model dates bac to 1950 s and belongs to the fundamentals of growth theory The Solow model is remarable

More information

The Role of Physical Capital

The Role of Physical Capital San Francisco State University ECO 560 The Role of Physical Capital Michael Bar As we mentioned in the introduction, the most important macroeconomic observation in the world is the huge di erences in

More information

LEC 2: Exogenous (Neoclassical) growth model

LEC 2: Exogenous (Neoclassical) growth model LEC 2: Exogenous (Neoclassical) growth model Development of the model The Neo-classical model was an extension to the Harrod-Domar model that included a new term productivity growth The most important

More information

Foundations of Economics for International Business Supplementary Exercises 2

Foundations of Economics for International Business Supplementary Exercises 2 Foundations of Economics for International Business Supplementary Exercises 2 INSTRUCTOR: XIN TANG Department of World Economics Economics and Management School Wuhan University Fall 205 These tests are

More information

The Ramsey Model. Lectures 11 to 14. Topics in Macroeconomics. November 10, 11, 24 & 25, 2008

The Ramsey Model. Lectures 11 to 14. Topics in Macroeconomics. November 10, 11, 24 & 25, 2008 The Ramsey Model Lectures 11 to 14 Topics in Macroeconomics November 10, 11, 24 & 25, 2008 Lecture 11, 12, 13 & 14 1/50 Topics in Macroeconomics The Ramsey Model: Introduction 2 Main Ingredients Neoclassical

More information

Road Map to this Lecture

Road Map to this Lecture Economic Growth 1 Road Map to this Lecture 1. Steady State dynamics: 1. Output per capita 2. Capital accumulation 3. Depreciation 4. Steady State 2. The Golden Rule: maximizing welfare 3. Total Factor

More information

CHAPTER SEVEN - Eight. Economic Growth

CHAPTER SEVEN - Eight. Economic Growth CHAPTER SEVEN - Eight Economic Growth 1 The Solow Growth Model is designed to show how: growth in the capital stock, growth in the labor force, and advances in technology interact in an economy, and how

More information

Ch.3 Growth and Accumulation. Production function and constant return to scale

Ch.3 Growth and Accumulation. Production function and constant return to scale 1 Econ 30 Intermediate Macroeconomics Chul-Woo Kwon Ch.3 Growth and Accumulation I. Introduction A. Growth accounting and source of economic growth B. The neoclassical growth model: the Simple Solow growth

More information

Chapter 2 Savings, Investment and Economic Growth

Chapter 2 Savings, Investment and Economic Growth Chapter 2 Savings, Investment and Economic Growth In this chapter we begin our investigation of the determinants of economic growth. We focus primarily on the relationship between savings, investment,

More information

Lecture 2: Intermediate macroeconomics, autumn 2012

Lecture 2: Intermediate macroeconomics, autumn 2012 Lecture 2: Intermediate macroeconomics, autumn 2012 Lars Calmfors Literature: Mankiw, Chapters 3, 7 and 8. 1 Topics Production Labour productivity and economic growth The Solow Model Endogenous growth

More information

The Solow Growth Model

The Solow Growth Model The Solow Growth Model Seyed Ali Madanizadeh Sharif U. of Tech. April 25, 2017 Seyed Ali Madanizadeh Sharif U. of Tech. () The Solow Growth Model April 25, 2017 1 / 46 Economic Growth Facts 1 In the data,

More information

ECON 3020: ACCELERATED MACROECONOMICS. Question 1: Inflation Expectations and Real Money Demand (20 points)

ECON 3020: ACCELERATED MACROECONOMICS. Question 1: Inflation Expectations and Real Money Demand (20 points) ECON 3020: ACCELERATED MACROECONOMICS SOLUTIONS TO PRELIMINARY EXAM 03/05/2015 Instructor: Karel Mertens Question 1: Inflation Expectations and Real Money Demand (20 points) Suppose that the real money

More information

ECON 3560/5040 Week 3

ECON 3560/5040 Week 3 ECON 3560/5040 Week 3 ECONOMIC GROWTH - Understand what causes differences in income over time and across countries - Sources of economy s output: factors of production (K, L) and production technology

More information

ECON 256: Poverty, Growth & Inequality. Jack Rossbach

ECON 256: Poverty, Growth & Inequality. Jack Rossbach ECON 256: Poverty, Growth & Inequality Jack Rossbach What Makes Countries Grow? Common Answers Technological progress Capital accumulation Question: Should countries converge over time? Models of Economic

More information

Intermediate Macroeconomics

Intermediate Macroeconomics Intermediate Macroeconomics Lecture 5 - Endogenous growth models Zsófia L. Bárány Sciences Po 2014 February Recap: Why go beyond the Solow model? we looked at the Solow model with technological progress

More information

Problem set 7: Economic Growth: The Solow Model

Problem set 7: Economic Growth: The Solow Model Dr Michał Broowski MACROECONOMICS II Problem set 7: Economic Growth: The Solow Model Problem (HOMEWORK) The production function is given by the following equation Y F( K, N ) ( K + N ) = =, where K Y,

More information

Intermediate Macroeconomics,Assignment 3 & 4

Intermediate Macroeconomics,Assignment 3 & 4 Intermediate Macroeconomics,Assignment 3 & 4 Due May 4th (Friday), in-class 1. In this chapter we saw that the steady-state rate of unemployment is U/L = s/(s + f ). Suppose that the unemployment rate

More information

Technical change is labor-augmenting (also known as Harrod neutral). The production function exhibits constant returns to scale:

Technical change is labor-augmenting (also known as Harrod neutral). The production function exhibits constant returns to scale: Romer01a.doc The Solow Growth Model Set-up The Production Function Assume an aggregate production function: F[ A ], (1.1) Notation: A output capital labor effectiveness of labor (productivity) Technical

More information

Chapter 6. Endogenous Growth I: AK, H, and G

Chapter 6. Endogenous Growth I: AK, H, and G Chapter 6 Endogenous Growth I: AK, H, and G 195 6.1 The Simple AK Model Economic Growth: Lecture Notes 6.1.1 Pareto Allocations Total output in the economy is given by Y t = F (K t, L t ) = AK t, where

More information

The neoclassical model of economic growth. Trevor Swan (1956) Give rise to the Solow Swan model

The neoclassical model of economic growth. Trevor Swan (1956) Give rise to the Solow Swan model The neoclassical model of economic growth Robert Solow (1956) Trevor Swan (1956) Give rise to the Solow Swan model premises Closed economy with 1 final output Exogenous labor supply Initial physical capital

More information

Testing the predictions of the Solow model:

Testing the predictions of the Solow model: Testing the predictions of the Solow model: 1. Convergence predictions: state that countries farther away from their steady state grow faster. Convergence regressions are designed to test this prediction.

More information

Ramsey s Growth Model (Solution Ex. 2.1 (f) and (g))

Ramsey s Growth Model (Solution Ex. 2.1 (f) and (g)) Problem Set 2: Ramsey s Growth Model (Solution Ex. 2.1 (f) and (g)) Exercise 2.1: An infinite horizon problem with perfect foresight In this exercise we will study at a discrete-time version of Ramsey

More information

ECONOMIC GROWTH 1. THE ACCUMULATION OF CAPITAL

ECONOMIC GROWTH 1. THE ACCUMULATION OF CAPITAL ECON 3560/5040 ECONOMIC GROWTH - Understand what causes differences in income over time and across countries - Sources of economy s output: factors of production (K, L) and production technology differences

More information

Components of Economic Growth

Components of Economic Growth Components of Economic Growth Components of Economic Growth 1. Capital Accumulation: savings from present income invested to increase future output and income New factories, equipment, etc., increase the

More information

Testing the predictions of the Solow model: What do the data say?

Testing the predictions of the Solow model: What do the data say? Testing the predictions of the Solow model: What do the data say? Prediction n 1 : Conditional convergence: Countries at an early phase of capital accumulation tend to grow faster than countries at a later

More information

Growth 2. Chapter 6 (continued)

Growth 2. Chapter 6 (continued) Growth 2 Chapter 6 (continued) 1. Solow growth model continued 2. Use the model to understand growth 3. Endogenous growth 4. Labor and goods markets with growth 1 Solow Model with Exogenous Labor-Augmenting

More information

EC 205 Macroeconomics I

EC 205 Macroeconomics I EC 205 Macroeconomics I Macroeconomics I Chapter 8 & 9: Economic Growth Why growth matters In 2000, real GDP per capita in the United States was more than fifty times that in Ethiopia. Over the period

More information

Economic Growth: Extensions

Economic Growth: Extensions Economic Growth: Extensions 1 Road Map to this Lecture 1. Extensions to the Solow Growth Model 1. Population Growth 2. Technological growth 3. The Golden Rule 2. Endogenous Growth Theory 1. Human capital

More information

Midterm Examination Number 1 February 19, 1996

Midterm Examination Number 1 February 19, 1996 Economics 200 Macroeconomic Theory Midterm Examination Number 1 February 19, 1996 You have 1 hour to complete this exam. Answer any four questions you wish. 1. Suppose that an increase in consumer confidence

More information

A Note on the Solow Growth Model with a CES Production Function and Declining Population

A Note on the Solow Growth Model with a CES Production Function and Declining Population MPRA Munich Personal RePEc Archive A Note on the Solow Growth Model with a CES Production Function and Declining Population Hiroaki Sasaki 7 July 2017 Online at https://mpra.ub.uni-muenchen.de/80062/ MPRA

More information

Overlapping Generations Model: Dynamic Efficiency and Social Security

Overlapping Generations Model: Dynamic Efficiency and Social Security Overlapping Generations Model: Dynamic Efficiency and Social Security Prof. Lutz Hendricks Econ720 August 23, 2017 1 / 28 Issues The OLG model can have inefficient equilibria. We solve the problem of a

More information

Master 2 Macro I. Lecture 3 : The Ramsey Growth Model

Master 2 Macro I. Lecture 3 : The Ramsey Growth Model 2012-2013 Master 2 Macro I Lecture 3 : The Ramsey Growth Model Franck Portier (based on Gilles Saint-Paul lecture notes) franck.portier@tse-fr.eu Toulouse School of Economics Version 1.1 07/10/2012 Changes

More information

SOLUTIONS PROBLEM SET 5

SOLUTIONS PROBLEM SET 5 Macroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PROBLEM SET 5 The Solow AK model with transitional dynamics Consider the following Solow economy production is determined by Y = F (K; L) = AK

More information

Ch.3 Growth and Accumulation. Production function and constant return to scale

Ch.3 Growth and Accumulation. Production function and constant return to scale 1 Econ 302 Intermediate Macroeconomics Chul-Woo Kwon Ch.3 Growth and Accumulation I. Introduction A. Growth accounting and source of economic growth B. The neoclassical growth model: the Simple Solow growth

More information

Lecture 3 Growth Model with Endogenous Savings: Ramsey-Cass-Koopmans Model

Lecture 3 Growth Model with Endogenous Savings: Ramsey-Cass-Koopmans Model Lecture 3 Growth Model with Endogenous Savings: Ramsey-Cass-Koopmans Model Rahul Giri Contact Address: Centro de Investigacion Economica, Instituto Tecnologico Autonomo de Mexico (ITAM). E-mail: rahul.giri@itam.mx

More information

Economic Growth: Malthus and Solow Copyright 2014 Pearson Education, Inc.

Economic Growth: Malthus and Solow Copyright 2014 Pearson Education, Inc. Chapter 7 Economic Growth: Malthus and Solow Copyright Chapter 7 Topics Economic growth facts Malthusian model of economic growth Solow growth model Growth accounting 1-2 U.S. Per Capita Real Income Growth

More information

Department of Economics Shanghai University of Finance and Economics Intermediate Macroeconomics

Department of Economics Shanghai University of Finance and Economics Intermediate Macroeconomics Department of Economics Shanghai University of Finance and Economics Intermediate Macroeconomics Instructor: Min Zhang Answer 2. List the stylized facts about economic growth. What is relevant for the

More information

ECONOMICS 723. Models with Overlapping Generations

ECONOMICS 723. Models with Overlapping Generations ECONOMICS 723 Models with Overlapping Generations 5 October 2005 Marc-André Letendre Department of Economics McMaster University c Marc-André Letendre (2005). Models with Overlapping Generations Page i

More information

Lastrapes Fall y t = ỹ + a 1 (p t p t ) y t = d 0 + d 1 (m t p t ).

Lastrapes Fall y t = ỹ + a 1 (p t p t ) y t = d 0 + d 1 (m t p t ). ECON 8040 Final exam Lastrapes Fall 2007 Answer all eight questions on this exam. 1. Write out a static model of the macroeconomy that is capable of predicting that money is non-neutral. Your model should

More information

Course information EC2065 Macroeconomics

Course information EC2065 Macroeconomics Course information 2015 16 This course introduces students to the most influential and compelling theories designed by macroeconomists to explain issues related to the determination of output, unemployment

More information

The Solow Model. Econ 4960: Economic Growth

The Solow Model. Econ 4960: Economic Growth The Solow Model All theory depends on assumptions which are not quite true That is what makes it theory The art of successful theorizing is to make the inevitable simplifying assumptions in such a way

More information

Savings, Investment and Economic Growth

Savings, Investment and Economic Growth Chapter 2 Savings, Investment and Economic Growth In this chapter we begin our investigation of the determinants of economic growth. We focus primarily on the relationship between savings, investment,

More information

ECN101: Intermediate Macroeconomic Theory TA Section

ECN101: Intermediate Macroeconomic Theory TA Section ECN101: Intermediate Macroeconomic Theory TA Section (jwjung@ucdavis.edu) Department of Economics, UC Davis November 4, 2014 Slides revised: November 4, 2014 Outline 1 2 Fall 2012 Winter 2012 Midterm:

More information

The Neoclassical Growth Model

The Neoclassical Growth Model The Neoclassical Growth Model 1 Setup Three goods: Final output Capital Labour One household, with preferences β t u (c t ) (Later we will introduce preferences with respect to labour/leisure) Endowment

More information

ECON Chapter 6: Economic growth: The Solow growth model (Part 1)

ECON Chapter 6: Economic growth: The Solow growth model (Part 1) ECON3102-005 Chapter 6: Economic growth: The Solow growth model (Part 1) Neha Bairoliya Spring 2014 Motivations Why do countries grow? Why are there poor countries? Why are there rich countries? Can poor

More information

Growth. Prof. Eric Sims. Fall University of Notre Dame. Sims (ND) Growth Fall / 39

Growth. Prof. Eric Sims. Fall University of Notre Dame. Sims (ND) Growth Fall / 39 Growth Prof. Eric Sims University of Notre Dame Fall 2012 Sims (ND) Growth Fall 2012 1 / 39 Economic Growth When economists say growth, typically mean average rate of growth in real GDP per capita over

More information

ECN101: Intermediate Macroeconomic Theory TA Section

ECN101: Intermediate Macroeconomic Theory TA Section ECN101: Intermediate Macroeconomic Theory TA Section (jwjung@ucdavis.edu) Department of Economics, UC Davis October 27, 2014 Slides revised: October 27, 2014 Outline 1 Announcement 2 Review: Chapter 5

More information

AK and reduced-form AK models. Consumption taxation.

AK and reduced-form AK models. Consumption taxation. Chapter 11 AK and reduced-form AK models. Consumption taxation. In his Chapter 11 Acemoglu discusses simple fully-endogenous growth models in the form of Ramsey-style AK and reduced-form AK models, respectively.

More information

Lecture 2: The Neoclassical Growth Model

Lecture 2: The Neoclassical Growth Model Lecture 2: The Neoclassical Growth Model Florian Scheuer 1 Plan Introduce production technology, storage multiple goods 2 The Neoclassical Model Three goods: Final output Capital Labor One household, with

More information

Macroeconomics. Review of Growth Theory Solow and the Rest

Macroeconomics. Review of Growth Theory Solow and the Rest Macroeconomics Review of Growth Theory Solow and the Rest Basic Neoclassical Growth Model K s Y = savings = investment = K production Y = f(l,k) consumption L = n L L exogenous population (labor) growth

More information

Intermediate Macroeconomics,Assignment 4

Intermediate Macroeconomics,Assignment 4 Intermediate Macroeconomics,Assignment 4 Due May 6th (Friday), in-class 1. Two countries, Richland and Poorland, are described by the Solow growth model. They have the same Cobb Douglas production function,,

More information

AK and reduced-form AK models. Consumption taxation. Distributive politics

AK and reduced-form AK models. Consumption taxation. Distributive politics Chapter 11 AK and reduced-form AK models. Consumption taxation. Distributive politics The simplest model featuring fully-endogenous exponential per capita growth is what is known as the AK model. Jones

More information

Part 1: Short answer, 60 points possible Part 2: Analytical problems, 40 points possible

Part 1: Short answer, 60 points possible Part 2: Analytical problems, 40 points possible Midterm #1 ECON 322, Prof. DeBacker September 25, 2018 INSTRUCTIONS: Please read each question below carefully and respond to the questions in the space provided (use the back of pages if necessary). You

More information

Equilibrium with Production and Endogenous Labor Supply

Equilibrium with Production and Endogenous Labor Supply Equilibrium with Production and Endogenous Labor Supply ECON 30020: Intermediate Macroeconomics Prof. Eric Sims University of Notre Dame Spring 2018 1 / 21 Readings GLS Chapter 11 2 / 21 Production and

More information

In this chapter, you will learn C H A P T E R National Income: Where it Comes From and Where it Goes CHAPTER 3

In this chapter, you will learn C H A P T E R National Income: Where it Comes From and Where it Goes CHAPTER 3 C H A P T E R 3 National Income: Where it Comes From and Where it Goes MACROECONOMICS N. GREGORY MANKIW 007 Worth Publishers, all rights reserved SIXTH EDITION PowerPoint Slides by Ron Cronovich In this

More information

ECON 302: Intermediate Macroeconomic Theory (Spring ) Discussion Section Week 7 March 7, 2014

ECON 302: Intermediate Macroeconomic Theory (Spring ) Discussion Section Week 7 March 7, 2014 ECON 302: Intermediate Macroeconomic Theory (Spring 2013-14) Discussion Section Week 7 March 7, 2014 SOME KEY CONCEPTS - Long-run Economic Growth - Growth Accounting - Solow Growth Model - Endogenous Growth

More information

Economic Growth I Macroeconomics Finals

Economic Growth I Macroeconomics Finals Economic Growth I Macroeconomics Finals Introduction and the Solow growth model Martin Ellison Nuffield College Hilary Term 2016 The Wealth of Nations Performance of economy over many years Growth a recent

More information

Part A: Answer question A1 (required), plus either question A2 or A3.

Part A: Answer question A1 (required), plus either question A2 or A3. Ph.D. Core Exam -- Macroeconomics 15 August 2016 -- 8:00 am to 3:00 pm Part A: Answer question A1 (required), plus either question A2 or A3. A1 (required): Macroeconomic Effects of Brexit In the wake of

More information

Lecture notes 2: Physical Capital, Development and Growth

Lecture notes 2: Physical Capital, Development and Growth Lecture notes 2: Physical Capital, Development and Growth These notes are based on a draft manuscript Economic Growth by David N. Weil. All rights reserved. Lecture notes 2: Physical Capital, Development

More information

Macroeconomic Models of Economic Growth

Macroeconomic Models of Economic Growth Macroeconomic Models of Economic Growth J.R. Walker U.W. Madison Econ448: Human Resources and Economic Growth Summary Solow Model [Pop Growth] The simplest Solow model (i.e., with exogenous population

More information

Dynamic Macroeconomics

Dynamic Macroeconomics Chapter 1 Introduction Dynamic Macroeconomics Prof. George Alogoskoufis Fletcher School, Tufts University and Athens University of Economics and Business 1.1 The Nature and Evolution of Macroeconomics

More information

ECON 6022B Problem Set 1 Suggested Solutions Fall 2011

ECON 6022B Problem Set 1 Suggested Solutions Fall 2011 ECON 6022B Problem Set Suggested Solutions Fall 20 September 5, 20 Shocking the Solow Model Consider the basic Solow model in Lecture 2. Suppose the economy stays at its steady state in Period 0 and there

More information

Intermediate Macroeconomics: Economic Growth and the Solow Model

Intermediate Macroeconomics: Economic Growth and the Solow Model Intermediate Macroeconomics: Economic Growth and the Solow Model Eric Sims University of Notre Dame Fall 2014 1 Introduction We begin the core of the course with a discussion of economic growth. Technically

More information

TOBB-ETU, Economics Department Macroeconomics II (ECON 532) Practice Problems I (Solutions)

TOBB-ETU, Economics Department Macroeconomics II (ECON 532) Practice Problems I (Solutions) TOBB-ETU, Economics Department Macroeconomics II (ECON 532) Practice Problems I (Solutions) Q: The Solow-Swan Model: Constant returns Prove that, if the production function exhibits constant returns, all

More information

SDP Macroeconomics Final exam, 2014 Professor Ricardo Reis

SDP Macroeconomics Final exam, 2014 Professor Ricardo Reis SDP Macroeconomics Final exam, 2014 Professor Ricardo Reis Answer each question in three or four sentences and perhaps one equation or graph. Remember that the explanation determines the grade. 1. Question

More information

Final Exam II (Solutions) ECON 4310, Fall 2014

Final Exam II (Solutions) ECON 4310, Fall 2014 Final Exam II (Solutions) ECON 4310, Fall 2014 1. Do not write with pencil, please use a ball-pen instead. 2. Please answer in English. Solutions without traceable outlines, as well as those with unreadable

More information

Lecture 2: Intermediate macroeconomics, autumn 2014

Lecture 2: Intermediate macroeconomics, autumn 2014 Lecture 2: Intermediate macroeconomics, autumn 2014 Lars Calmfors Literature: Mankiw, chapters 3, 8 and 9. 1 Topics Production Labour productivity and economic growth The Solow model (neoclassical growth

More information

Check your understanding: Solow model 1

Check your understanding: Solow model 1 Check your understanding: Solow model 1 Bill Gibson March 26, 2017 1 Thanks to Farzad Ashouri Solow model The characteristics of the Solow model are 2 Solow has two kinds of variables, state variables

More information

Exercises in Growth Theory and Empirics

Exercises in Growth Theory and Empirics Exercises in Growth Theory and Empirics Carl-Johan Dalgaard University of Copenhagen and EPRU May 22, 2003 Exercise 6: Productive government investments and exogenous growth Consider the following growth

More information

Final Exam (Solutions) ECON 4310, Fall 2014

Final Exam (Solutions) ECON 4310, Fall 2014 Final Exam (Solutions) ECON 4310, Fall 2014 1. Do not write with pencil, please use a ball-pen instead. 2. Please answer in English. Solutions without traceable outlines, as well as those with unreadable

More information

Part A: Answer Question A1 (required) and Question A2 or A3 (choice).

Part A: Answer Question A1 (required) and Question A2 or A3 (choice). Ph.D. Core Exam -- Macroeconomics 13 August 2018 -- 8:00 am to 3:00 pm Part A: Answer Question A1 (required) and Question A2 or A3 (choice). A1 (required): Short-Run Stabilization Policy and Economic Shocks

More information

Part A: Answer Question A1 (required) and Question A2 or A3 (choice).

Part A: Answer Question A1 (required) and Question A2 or A3 (choice). Ph.D. Core Exam -- Macroeconomics 10 January 2018 -- 8:00 am to 3:00 pm Part A: Answer Question A1 (required) and Question A2 or A3 (choice). A1 (required): Cutting Taxes Under the 2017 US Tax Cut and

More information

INTERMEDIATE MACROECONOMICS

INTERMEDIATE MACROECONOMICS INTERMEDIATE MACROECONOMICS LECTURE 4 Douglas Hanley, University of Pittsburgh ECONOMIC GROWTH IN THIS LECTURE Why do countries grow economically? Why do some countries grow faster than others? Why has

More information

A Two-sector Ramsey Model

A Two-sector Ramsey Model A Two-sector Ramsey Model WooheonRhee Department of Economics Kyung Hee University E. Young Song Department of Economics Sogang University C.P.O. Box 1142 Seoul, Korea Tel: +82-2-705-8696 Fax: +82-2-705-8180

More information

Incentives and economic growth

Incentives and economic growth Econ 307 Lecture 8 Incentives and economic growth Up to now we have abstracted away from most of the incentives that agents face in determining economic growth (expect for the determination of technology

More information

Generalized Taylor Rule and Determinacy of Growth Equilibrium. Abstract

Generalized Taylor Rule and Determinacy of Growth Equilibrium. Abstract Generalized Taylor Rule and Determinacy of Growth Equilibrium Seiya Fujisaki Graduate School of Economics Kazuo Mino Graduate School of Economics Abstract This paper re-examines equilibrium determinacy

More information

Chapter 9 Dynamic Models of Investment

Chapter 9 Dynamic Models of Investment George Alogoskoufis, Dynamic Macroeconomic Theory, 2015 Chapter 9 Dynamic Models of Investment In this chapter we present the main neoclassical model of investment, under convex adjustment costs. This

More information

CAPITAL ACCUMULATION AND ECONOMIC GROWTH. Dongpeng Liu Department of Economics Nanjing University

CAPITAL ACCUMULATION AND ECONOMIC GROWTH. Dongpeng Liu Department of Economics Nanjing University CAPITAL ACCUMULATION AND ECONOMIC GROWTH Dongpeng Liu Department of Economics Nanjing University ROADMAP INCOME EXPENDITURE LIQUIDITY PREFERENCE IS CURVE LM CURVE SHORT-RUN IS-LM MODEL AGGREGATE DEMAND

More information

Class Notes. Intermediate Macroeconomics. Li Gan. Lecture 7: Economic Growth. It is amazing how much we have achieved.

Class Notes. Intermediate Macroeconomics. Li Gan. Lecture 7: Economic Growth. It is amazing how much we have achieved. Class Notes Intermediate Macroeconomics Li Gan Lecture 7: Economic Growth It is amazing how much we have achieved. It is also to know how much difference across countries. Nigeria is only 1/43 of the US.

More information

Chapter 7 Externalities, Human Capital and Endogenous Growth

Chapter 7 Externalities, Human Capital and Endogenous Growth George Alogoskoufis, Dynamic Macroeconomics, 2016 Chapter 7 Externalities, Human Capital and Endogenous Growth In this chapter we examine growth models in which the efficiency of labor is no longer entirely

More information

Quantitative Techniques (Finance) 203. Derivatives for Functions with Multiple Variables

Quantitative Techniques (Finance) 203. Derivatives for Functions with Multiple Variables Quantitative Techniques (Finance) 203 Derivatives for Functions with Multiple Variables Felix Chan October 2006 1 Introduction In the previous lecture, we discussed the concept of derivative as approximation

More information

Questions for Review. CHAPTER 8 Economic Growth II

Questions for Review. CHAPTER 8 Economic Growth II CHAPTER 8 Economic Growth II Questions for Review 1. In the Solow model, we find that only technological progress can affect the steady-state rate of growth in income per worker. Growth in the capital

More information

2014/2015, week 6 The Ramsey model. Romer, Chapter 2.1 to 2.6

2014/2015, week 6 The Ramsey model. Romer, Chapter 2.1 to 2.6 2014/2015, week 6 The Ramsey model Romer, Chapter 2.1 to 2.6 1 Background Ramsey model One of the main workhorses of macroeconomics Integration of Empirical realism of the Solow Growth model and Theoretical

More information