Business Cycles: The Classical Approach

Size: px
Start display at page:

Download "Business Cycles: The Classical Approach"

Transcription

1 San Francisco State University ECON 302 Business Cycles: The Classical Approach Introduction Michael Bar Recall from the introduction that the output per capita in the U.S. is groing steady, but there are uctuations about the trend. These uctuations are called business cycles. Figure shos the ln of real GNP per capita in the U.S. in the last century, together ith a linear trend. The linear trend ts the data pretty ell, hich means that the original variable, GNP per capita, as groing at constant rate. Figure : n of real GNP per capita in U.S. 4 ln(real GNP per capita) Year The study of the long run groth trend belongs to the eld of economic groth. In these notes e focus on the uctuations of the output around the trend. Subtracting the groth trend from the time series in gure, results in a series of deviations from trend, displayed in gure 2. The series of deviations from trend is called detrended real output, or the cyclical part of the real output. The questions that e ant to ask in these notes are:. What causes business cycles? 2. Can the government smooth out the business cycles? 3. Should the government smooth out the business cycles? In order to anser these questions, economists use models. We ill see that di erent models give di erent ansers to those questions.

2 Figure 2: Cyclical part of GNP per capita in U.S. 0.3 Deviations from trend Year 2 The Classical Model 2. The description of the model The model consists of a representative consumer, representative rm, and a government. The consumer receives income from supplying his labor and from dividends from the rm he ons. The consumer chooses his consumption and time allocation beteen labor and leisure. The rm is oned by the consumer, it ons a xed amount of capital, and it chooses the optimal amount of labor to maximize pro ts. The government consumption is exogenous to the model. The government balances its budget by collecting taxes at the amount of expenditures. The formal description of the model economy:. Consumer: max ln C + ( C;l s:t: ) ln l C = [(h l) + ] ( t) here C is consumption, l is leisure, is real age, h is time endoment (say 00 hours per eek), is the pro ts or dividends from the rm, t is the at tax rate. Thus, the time spent orking (labor supply) is S = h l 2. Firm: max = AK D D D 2

3 here A is productivity parameter (called Total Factor Productivity, TFP), K is the capital stock, and D is labor employed by the rm. The productivity parameter re- ects the idea that ith technological improvement (A ") more output can be produced ith the same inputs. The total output in the economy is thus Y = AK. 3. Government: collects taxes on all income at the rate of t, and spends them on government consumption. The government budget is G = t ( + ) 4. De nition: Competitive equilibrium consists of (; C; G; ; l; ; Y ) such that (a) Given ;, the values of (C; l) solve the consumer s problem, (b) Given, the value of solves the rm s problem, (c) Markets are cleared: i. D = S = (labor market), ii. C + G = Y ( nal goods market). 2.2 Important remarks about models in general This section is a philosophical discussion of our approach in general. It is essential to read it in order to understand the material of this entire course, and many other courses that you are taking. You should come back and read this again after you have practiced orking ith the classical model.. The competitive equilibrium is the model s prediction about the endogenous variables. Endogenous variables are determined inside the model, i.e. the variables hich the model is trying to explain. The exogenous variables are those that are determined outside of the model. For example, in the model of a market the endogenous variables are price and quantity traded, and exogenous variables are those that determine the location of supply and demand curves (such as income, prices of related goods, etc.). In the classical model the exogenous variables are: (A; t; K), and the endogenous variables are: (; C; G; ; l; ; Y ). 2. Causality: hat causes hat? In any model, the exogenous variables are causing the endogenous variables. For example, e can change A (the technology level) and observe the changes in real age, employment, consumption, output, etc. All the endogenous variables are caused by the exogenous variables. If e don t change any of the exogenous variables, no change in the endogenous variables can occur. Thus, in this model e cannot say that output causes employment, since both output and employment are endogenous variables, and cannot change unless e change some of the exogenous. Be very careful about making statements of causality in the real orld. 3. Why models? 3

4 (a) Models can explain some features of the real orld. Models don t tell us hat the orld looks like. Instead, they tell us hat e can expect to happen in the orld if the orld as like the model. For example, the supply and demand diagram doesn t look anything like the markets in the real orld. The diagram does not sho the identities of the buyers and sellers, their feelings and emotions, their physical appearance. The supply and demand diagram only captures to features of real markets: () buyers typically ant to buy less hen the price goes up, and (2) sellers ant to produce more hen the price goes up. It turns out the supply and demand diagram is very useful in explaining hy prices di er across goods and hy there are changes in prices. After testing the predictions of the model ith the data e conclude that indeed the to features of buyers and sellers that e included in the model ere important. (b) Models can be used to perform controlled experiments. In the real orld many things change at the same time; the technology changes, government policies change, etc. In the model e can perform controlled experiments of changing one thing at a time. This is impossible to do ith actual economies. 4. Models are not realistic and are not supposed to be. When the object of study is very complicated, e need models that ill highlight some important features of the object and leave out many other features. For example, hen e study the economy of an entire country ith millions of people, thousands of markets and rms, it is di cult for us to understand the behavior of the economy by just looking at it. Moreover, if e don t have any models to ork ith, e don t even kno hat data should be collected about the object of our study. For example, the model of supply and demand tells us that e don t need to collect data of all the names of buyers and sellers of the market in order to understand ho it orks. 2.3 Working ith the classical model The de nition of competitive equilibrium is instructive about ho the model should be solved. The de nition suggests the folloing steps: () solve the consumer s problem to get the labor supply, (2) solve the rm s problem to get the labor demand, and (3) use the market clearing conditions to nd the real age, the equilibrium employment, and the rest of the endogenous variables Mathematical solution Step : solving the consumer problem The consumer s problem can be ritten as max ln C + ( C;l s:t: ) ln l C + ( t) l = (h + ) ( t) 4

5 This is a standard consumer choice problem ith to goods: C and l, the prices of the goods are and ( t) respectively, and the consumer s income is (h + ) ( t). We kno already ho to solve a consumer choice problem ith Cobb-Douglas preferences. Thus, the demand is C = (h + ) ( t) (h + ) ( t) l = ( ) ( t) = ( ) h + and the labor supply is S = h ( ) h + () Observe that consumption is increasing in and, and decreases in t. The labor supply is increasing in, decreasing in and does not depend on taxes. The intuition hy the labor supply is decreasing in goes as follos. The dividend income is non labor income, so hen it goes up the consumer does not need to ork as much. Figure 3 shos the graph of the labor supply curve. i.e. ho much labor the consumer ants to supply at any given age, holding everything else xed. This means that changes in are re ected by movements along the curve, hile changes in ill shift the entire curve. Figure 3: abor supply curve Real age () abor Supply Curve abor (N) s Step 2: Solving the rm s problem The rm s problem is max = AK D D The rst order condition = ( ) AK D = D ( ) AK D = (2) 5

6 hich tells us that the rm maximizes pro t hen it equates the marginal product of labor the the real age. Equation (2) thus gives us the labor demand of the rm. We can solve for D explicitly from equation (2) to get ( D = ) AK = Observe that this curve is decreasing in. Figure 4 shos the labor demand curve, i.e. ho much labor the rm ants to employ at any given age, holding everything else constant. Thus, changes in are re ected by movements along the curve hile changes in A ill shift the entire curve. The pro t is therefore given by Figure 4: abor demand curve Real age () abor Deamand curve abor (N) d = AK D ( ) AK D D = AK D (3) Step 3: equilibrium in the labor market etting S = D = and substituting equations (2) and (3) into equation () gives = h ( ) h + AK ( ) AK Solving for equilibrium : = h ( ) h + ( ) ( ) = h ( ) h ( ) 6

7 + ( ) ( ) = h ( ) + = h + ( ) = h = h Equilibrium employment: = ( ) h Once e found the equilibrium employment, all the other endogenous variables can be found in terms of. Equilibrium leisure: l = h To solve for equilibrium age, use equation (2): = ( ) AK Equilibrium output: Y = AK Equilibrium pro t, using equation (3): = AK To nd equilibrium consumption e use the budget constraint: Equilibrium government expenditures: C = [ + ] ( t) C = ( ) AK + AK D ( t) C = ( t) Y G = Y C = ty Summary of equilibrium: ( ) h = l = h = ( ) AK Y = AK = AK C = Y ( t) G = ty 7

8 As you can see, an increase in productivity A, causes an increase in equilibrium output, equilibrium real age, equilibrium consumption, equilibrium government consumption, and equilibrium pro t. Equilibrium employment does not depend on the level of technology, even though the real age ent up. The e ect of higher K is similar because A and K alays appear together in the equations. An increase in the tax rate a ects only the distribution of the total output beteen the private sector and the government sector. If t = 30% for example, then the government consumes 30% of the total output, hile the private consumers get to consume the rest 70%. 8

9 2.3.2 Graphical analysis The classical model can be analyzed graphically ith only to diagrams, the labor market and the production function, as shon in gure 5. Figure 5: Classical model: graphical illustration Y Production function Y * * S abor market * D * These graphs correspond to the folloing equations: Production function : Y = AK abor supply curve : S = h ( ) h +, here = AK ( abor demand curve : D = ) AK = It is important to repeat here that labor supply curve is increasing in. On the other hand, if increases, this leads to a shift of the entire supply curve to the left. The labor demand curve is decreasing in. If A or K increase, the entire labor demand curve ill shift to the right. No e use this graphical frameork in order to perform 3 experiments ith the model:. An increase in productivity (A "). 9

10 Figure 6: An increase in productivity (A ") Y Y 2 Production function Y S abor market W 2 W D Figure 6 shos the e ects of an increase in A in the classical model. As A ", there is an increase in labor demand (shift of the labor demand curve to the right) and a decrease in labor supply (shift of the supply curve to the left) and an increase in production function. The e ect of the increase in labor demand on employment is an increase in employment, hile the e ect of a decrease in labor supply on employment is a decrease in employment. Thus, ithout solving the model ith particular functional forms e cannot tell hat is the e ect of A " on equilibrium employment. In the pervious section hoever e solved the model ith Cobb-Douglas technology and preferences and found that the equilibrium employment does not change as A ". In other ords, the e ect on employment of a decline in labor demand and of an increase in labor supply cancel each other. Both e ects hoever increase the equilibrium real age. 2. An increase in K. The e ect of an increase in K is the same as the e ect of an increase in A. Notice that A and K alays appear together as AK. 3. An increase in the tax rate (t "). 0

11 Neither the labor demand nor the labor supply depend on the tax rate, hence nothing ill change in the labor market. The production function does not depend on the tax rate as ell, and therefore none of the curves in gure 5 ill shift. As e have seen before, the only e ect that an increase in the tax rate has on the economy is the increase in the government share of the total output Ansering the questions No e are ready to anser the questions e posed in the beginning of these notes, ithin the frameork of the classical model.. What causes business cycles? The exogenous variables in this model are (A; t; K). As e have seen before, a positive shock to productivity (A ") increases the equilibrium output hile a negative shock to productivity (A #) decreases it. We can think of shocks to productivity as agglomeration of many factors such as innovations, shocks to oil prices, eather, political events, etc., that change the amount produced ith the same inputs. So this model suggests that business cycles might be a result of productivity shocks. As e have seen before, changes in t do not a ect the equilibrium output. Ho about K? It is possible that a hurricane, or a terrorist attack ould destroy part of the nation s capital and cause a decline in output. It is harder to think of ho the stock of capital can experience a sudden increase. In any case, hen e look at the data on capital stock, it looks very smooth and does not exhibit uctuations that can potentially be the cause of business cycles. Moreover, in applied versions of this model, K is endogenous (accumulated ithin the maodel through investment), and therefore, in such models e can t exogenously change K. 2. Can the government smooth out the business cycles? We have seen before that changes in the tax rate in this economy do not a ect the equilibrium output. Changes in the tax rate only a ect the fraction of total output that is consumed by the government. Recall that C = ( t) Y G = ty So the anser to the question is, NO, the government cannot smooth the business cycles (in this model). 3. Should the government smooth out the business cycles? It shouldn t because it can t (in this model). For a more detailed discussion about productivity shocks see the next section.

12 2.4 Real business cycle doctrine Real business cycle theory suggests that the main source of business cycles is shocks to productivity. The real business cycle school is led by Edard Prescott and Finn Kydland. They ere aarded a Nobel Prize in Economics in economics in 2004 "for their contributions to dynamic macroeconomics: the time consistency of economic policy and the driving forces behind business cycles". Finn Kydland and Edard Prescott developed a methodology that allos them to anser the folloing quantitative equation: "ho much of the uctuations in output around a trend can be accounted for by random shocks to productivity?". Their anser as 2/3. Kydland and Prescott used a model that is a more complex version of the classical model (their model is called "the Neoclassical Groth Model"). But the idea can be illustrated ith the classical model. Step : Choose functional forms for utility and production function. In the data, although the real age ent up in the last decades, the average orktime did not change. Notice that in our model ith Cobb-Douglas utility function, e get the same result, i.e. in equilibrium the orktime is constant and does not depend on the real age. In the data, the labor share of total output is roughly constant over time. The Cobb- Douglas production function delivers this property. Recall that the capital share is and the labor share is, and these are constant. Step 2: Choose the parameter values for the utility and production functions. In the data the labor share is about 2=3 of the total output. Thus, set = =3 so that ( = 2=3). In the real orld people have approximately 00 hours per eek that they can allocate beteen labor and leisure activity (24 hours per day, minus 8 hours of sleep and 2 hours of maintenance such as bathroom, eating, resting). In the data the average orktime is 40 hours per eek, so using our equilibrium equation for employment e can nd as follos: ( ) h = 40 = :4 = :4 0:4 3 = 2 3 :2 0:4 = 2a :2 = 2:4a = 0:5 Thus, = 0:5, = 3. Step 3: Estimate the shocks to productivity We assume that aggregate output is produced ith Y = AK (4) 2

13 We have data on real GDP (Y ), on capital (K) and labor employed (). This means that e can nd A from the above equation as a residual. Because of this procedure A is called the Solo Residual, since e nd it as the residual that ould equate the left hand side and the right hand side of equation (4). Step 4: Model simulation Having found the time series of A e can simulate the model and generate time series of consumption and output. We have seen that an increase in A causes an increase in output in the classical model and a decline in A ill cause a decline in output. It turns out that the time series of Y generated by the model is very similar to the data in gure 2. In fact, the variance of the output generated by the model is about 2/3 of the actual variance of the real GDP/capita in the data. This means that random shocks to productivity can explain most, but not all the variation in real GDP/capita over the business cycles. 3

Solow Growth Model. Michael Bar. February 28, Introduction Some facts about modern growth Questions... 4

Solow Growth Model. Michael Bar. February 28, Introduction Some facts about modern growth Questions... 4 Solow Growth Model Michael Bar February 28, 208 Contents Introduction 2. Some facts about modern growth........................ 3.2 Questions..................................... 4 2 The Solow Model 5

More information

4- Current Method of Explaining Business Cycles: DSGE Models. Basic Economic Models

4- Current Method of Explaining Business Cycles: DSGE Models. Basic Economic Models 4- Current Method of Explaining Business Cycles: DSGE Models Basic Economic Models In Economics, we use theoretical models to explain the economic processes in the real world. These models de ne a relation

More information

Consider this problem. A person s utility function depends on consumption and leisure. Of his market time (the complement to leisure), h t

Consider this problem. A person s utility function depends on consumption and leisure. Of his market time (the complement to leisure), h t VI. INEQUALITY CONSTRAINED OPTIMIZATION Application of the Kuhn-Tucker conditions to inequality constrained optimization problems is another very, very important skill to your career as an economist. If

More information

Neoclassical Business Cycle Model

Neoclassical Business Cycle Model Neoclassical Business Cycle Model Prof. Eric Sims University of Notre Dame Fall 2015 1 / 36 Production Economy Last time: studied equilibrium in an endowment economy Now: study equilibrium in an economy

More information

Econ 201: Problem Set 3 Answers

Econ 201: Problem Set 3 Answers Econ 20: Problem Set 3 Ansers Instructor: Alexandre Sollaci T.A.: Ryan Hughes Winter 208 Question a) The firm s fixed cost is F C = a and variable costs are T V Cq) = 2 bq2. b) As seen in class, the optimal

More information

Equilibrium in a Production Economy

Equilibrium in a Production Economy Equilibrium in a Production Economy Prof. Eric Sims University of Notre Dame Fall 2012 Sims (ND) Equilibrium in a Production Economy Fall 2012 1 / 23 Production Economy Last time: studied equilibrium in

More information

A Summary of Economic Methodology

A Summary of Economic Methodology A Summary of Economic Methodology I. The Methodology of Theoretical Economics All economic analysis begins with theory, based in part on intuitive insights that naturally spring from certain stylized facts,

More information

Elements of Economic Analysis II Lecture VII: Equilibrium in a Competitive Market

Elements of Economic Analysis II Lecture VII: Equilibrium in a Competitive Market Elements of Economic Analysis II Lecture VII: Equilibrium in a Competitive Market Kai Hao Yang 10/31/2017 1 Partial Equilibrium in a Competitive Market In the previous lecture, e derived the aggregate

More information

Econ Review Set 2 - Answers

Econ Review Set 2 - Answers Econ 4808 Review Set 2 - Answers EQUILIBRIUM ANALYSIS 1. De ne the concept of equilibrium within the con nes of an economic model. Provide an example of an economic equilibrium. Economic models contain

More information

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Fall, 202 Answer Key to Section 2 Questions Section. (Suggested Time: 45 Minutes) For 3 of

More information

Macroeconomics IV Problem Set I

Macroeconomics IV Problem Set I 14.454 - Macroeconomics IV Problem Set I 04/02/2011 Due: Monday 4/11/2011 1 Question 1 - Kocherlakota (2000) Take an economy with a representative, in nitely-lived consumer. The consumer owns a technology

More information

Advanced Economic Growth: Lecture 8, Technology Di usion, Trade and Interdependencies: Di usion of Technology

Advanced Economic Growth: Lecture 8, Technology Di usion, Trade and Interdependencies: Di usion of Technology Advanced Economic Growth: Lecture 8, Technology Di usion, Trade and Interdependencies: Di usion of Technology Daron Acemoglu MIT October 3, 2007 Daron Acemoglu (MIT) Advanced Growth Lecture 8 October 3,

More information

Real Business Cycle Model (RBC)

Real Business Cycle Model (RBC) Real Business Cycle Model (RBC) Seyed Ali Madanizadeh November 2013 RBC Model Lucas 1980: One of the functions of theoretical economics is to provide fully articulated, artificial economic systems that

More information

problem. max Both k (0) and h (0) are given at time 0. (a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming

problem. max Both k (0) and h (0) are given at time 0. (a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming 1. Endogenous Growth with Human Capital Consider the following endogenous growth model with both physical capital (k (t)) and human capital (h (t)) in continuous time. The representative household solves

More information

The Solow Model. Prof. Lutz Hendricks. January 26, Econ520

The Solow Model. Prof. Lutz Hendricks. January 26, Econ520 The Solow Model Prof. Lutz Hendricks Econ520 January 26, 2017 1 / 28 Issues The production model measures the proximate causes of income gaps. Now we start to look at deep causes. The Solow model answers

More information

RBC Model with Indivisible Labor. Advanced Macroeconomic Theory

RBC Model with Indivisible Labor. Advanced Macroeconomic Theory RBC Model with Indivisible Labor Advanced Macroeconomic Theory 1 Last Class What are business cycles? Using HP- lter to decompose data into trend and cyclical components Business cycle facts Standard RBC

More information

FEDERAL RESERVE BANK of ATLANTA

FEDERAL RESERVE BANK of ATLANTA FEDERAL RESERVE BANK of ATLANTA On the Solution of the Growth Model with Investment-Specific Technological Change Jesús Fernández-Villaverde and Juan Francisco Rubio-Ramírez Working Paper 2004-39 December

More information

1 Bewley Economies with Aggregate Uncertainty

1 Bewley Economies with Aggregate Uncertainty 1 Bewley Economies with Aggregate Uncertainty Sofarwehaveassumedawayaggregatefluctuations (i.e., business cycles) in our description of the incomplete-markets economies with uninsurable idiosyncratic risk

More information

Macroeconomics II Dynamic macroeconomics Class 1: Introduction and rst models

Macroeconomics II Dynamic macroeconomics Class 1: Introduction and rst models Macroeconomics II Dynamic macroeconomics Class 1: Introduction and rst models Prof. George McCandless UCEMA Spring 2008 1 Class 1: introduction and rst models What we will do today 1. Organization of course

More information

The Ramsey Model. (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 2013)

The Ramsey Model. (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 2013) The Ramsey Model (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 213) 1 Introduction The Ramsey model (or neoclassical growth model) is one of the prototype models in dynamic macroeconomics.

More information

(a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming

(a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming 1. Government Purchases and Endogenous Growth Consider the following endogenous growth model with government purchases (G) in continuous time. Government purchases enhance production, and the production

More information

Public Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model. Burkhard Heer University of Augsburg, Germany

Public Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model. Burkhard Heer University of Augsburg, Germany Public Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model Burkhard Heer University of Augsburg, Germany October 3, 2018 Contents I 1 Central Planner 2 3 B. Heer c Public Economics: Chapter

More information

Lecture 1: Ricardian Theory of Trade

Lecture 1: Ricardian Theory of Trade Lecture 1: Ricardian Theory of Trade Alfonso A. Irarrazabal University of Oslo September 25, 2007 Contents 1 Simple Ricardian Model 3 1.1 Preferences................................. 3 1.2 Technologies.................................

More information

Advanced Economic Growth: Lecture 3, Review of Endogenous Growth: Schumpeterian Models

Advanced Economic Growth: Lecture 3, Review of Endogenous Growth: Schumpeterian Models Advanced Economic Growth: Lecture 3, Review of Endogenous Growth: Schumpeterian Models Daron Acemoglu MIT September 12, 2007 Daron Acemoglu (MIT) Advanced Growth Lecture 3 September 12, 2007 1 / 40 Introduction

More information

One-Sector Models of Endogenous Growth. Instructor: Dmytro Hryshko

One-Sector Models of Endogenous Growth. Instructor: Dmytro Hryshko One-Sector Models of Endogenous Growth Instructor: Dmytro Hryshko 1 Mid-1980s: dissatisfaction with exogenously driven explanations of long-run productivity growth. 2 It led to construction of models in

More information

New Notes on the Solow Growth Model

New Notes on the Solow Growth Model New Notes on the Solow Growth Model Roberto Chang September 2009 1 The Model The firstingredientofadynamicmodelisthedescriptionofthetimehorizon. In the original Solow model, time is continuous and the

More information

Addendum to: New Trade Models, Same Old Gains?

Addendum to: New Trade Models, Same Old Gains? Addendum to: New Trade Models, Same Old Gains? Costas Arkolakis Yale and NBER Arnaud Costinot MIT and NBER September 5, 200 Andrés Rodríguez-Clare Penn State and NBER Abstract This addendum provides generalizations

More information

Housing and the Business Cycle

Housing and the Business Cycle Housing and the Business Cycle Morris Davis and Jonathan Heathcote Winter 2009 Huw Lloyd-Ellis () ECON917 Winter 2009 1 / 21 Motivation Need to distinguish between housing and non housing investment,!

More information

Macroeconomics Qualifying Examination

Macroeconomics Qualifying Examination Macroeconomics Qualifying Examination January 2016 Department of Economics UNC Chapel Hill Instructions: This examination consists of 3 questions. Answer all questions. If you believe a question is ambiguously

More information

1 The Basic RBC Model

1 The Basic RBC Model IHS 2016, Macroeconomics III Michael Reiter Ch. 1: Notes on RBC Model 1 1 The Basic RBC Model 1.1 Description of Model Variables y z k L c I w r output level of technology (exogenous) capital at end of

More information

The TransPacific agreement A good thing for VietNam?

The TransPacific agreement A good thing for VietNam? The TransPacific agreement A good thing for VietNam? Jean Louis Brillet, France For presentation at the LINK 2014 Conference New York, 22nd 24th October, 2014 Advertisement!!! The model uses EViews The

More information

Dynamic Macroeconomics: Problem Set 4

Dynamic Macroeconomics: Problem Set 4 Dynamic Macroeconomics: Problem Set 4 Universität Siegen Dynamic Macroeconomics 1 / 28 1 Computing growth rates 2 Golden rule saving rate 3 Simulation of the Solow Model 4 Growth accounting Dynamic Macroeconomics

More information

Growth: Facts and Theories

Growth: Facts and Theories Notes on Growth: Facts and Theories Intermediate Macroeconomics Spring 2006 Guido Menzio University of Pennsylvania Growth In the last part of the course we are going to study economic growth, i.e. the

More information

Lecture 8: Aggregate demand and supply dynamics, closed economy case.

Lecture 8: Aggregate demand and supply dynamics, closed economy case. Lecture 8: Aggregate demand and supply dynamics, closed economy case. Ragnar Nymoen Department of Economics, University of Oslo October 20, 2008 1 Ch 17, 19 and 20 in IAM Since our primary concern is to

More information

TOBB-ETU - Econ 532 Practice Problems II (Solutions)

TOBB-ETU - Econ 532 Practice Problems II (Solutions) TOBB-ETU - Econ 532 Practice Problems II (Solutions) Q: Ramsey Model: Exponential Utility Assume that in nite-horizon households maximize a utility function of the exponential form 1R max U = e (n )t (1=)e

More information

Practice Questions for Mid-Term I. Question 1: Consider the Cobb-Douglas production function in intensive form:

Practice Questions for Mid-Term I. Question 1: Consider the Cobb-Douglas production function in intensive form: Practice Questions for Mid-Term I Question 1: Consider the Cobb-Douglas production function in intensive form: y f(k) = k α ; α (0, 1) (1) where y and k are output per worker and capital per worker respectively.

More information

Session 4: Money. Jean Imbs. November 2010

Session 4: Money. Jean Imbs. November 2010 Session 4: Jean November 2010 I So far, focused on real economy. Real quantities consumed, produced, invested. No money, no nominal in uences. I Now, introduce nominal dimension in the economy. First and

More information

Lecture 2: Factor Proportions Theory of Trade

Lecture 2: Factor Proportions Theory of Trade Lecture 2: Factor Proportions Theory of Trade Alfonso A. Irarrazabal University of Oslo September 25, 2007 Contents 1 Factor Proportions Model 2 1.1 Preferences................................. 2 1.2 Technologies.................................

More information

Problem 1 (30 points)

Problem 1 (30 points) Problem (30 points) Prof. Robert King Consider an economy in which there is one period and there are many, identical households. Each household derives utility from consumption (c), leisure (l) and a public

More information

14.05: Section Handout #1 Solow Model

14.05: Section Handout #1 Solow Model 14.05: Section Handout #1 Solow Model TA: Jose Tessada September 16, 2005 Today we will review the basic elements of the Solow model. Be prepared to ask any questions you may have about the derivation

More information

1. Using the model and notations covered in class, the expected returns are:

1. Using the model and notations covered in class, the expected returns are: Econ 510a second half Yale University Fall 2006 Prof. Tony Smith HOMEWORK #5 This homework assignment is due at 5PM on Friday, December 8 in Marnix Amand s mailbox. Solution 1. a In the Mehra-Prescott

More information

The economy is populated by a unit mass of infinitely lived households with preferences given by. β t u(c Mt, c Ht ) t=0

The economy is populated by a unit mass of infinitely lived households with preferences given by. β t u(c Mt, c Ht ) t=0 Review Questions: Two Sector Models Econ720. Fall 207. Prof. Lutz Hendricks A Planning Problem The economy is populated by a unit mass of infinitely lived households with preferences given by β t uc Mt,

More information

EconS Cost Structures

EconS Cost Structures EconS 425 - Cost Structures Eric Dunaway Washington State University eric.dunaway@wsu.edu Industrial Organization Eric Dunaway (WSU) EconS 425 Industrial Organization 1 / 34 Introduction Today, we ll review

More information

Foundation of (virtually) all DSGE models (e.g., RBC model) is Solow growth model

Foundation of (virtually) all DSGE models (e.g., RBC model) is Solow growth model THE BASELINE RBC MODEL: THEORY AND COMPUTATION FEBRUARY, 202 STYLIZED MACRO FACTS Foundation of (virtually all DSGE models (e.g., RBC model is Solow growth model So want/need/desire business-cycle models

More information

Economic Growth: Lecture 9, Neoclassical Endogenous Growth

Economic Growth: Lecture 9, Neoclassical Endogenous Growth 14.452 Economic Growth: Lecture 9, Neoclassical Endogenous Growth Daron Acemoglu MIT November 28, 2017. Daron Acemoglu (MIT) Economic Growth Lecture 9 November 28, 2017. 1 / 41 First-Generation Models

More information

Assignment #5. 1 Keynesian Cross. Econ 302: Intermediate Macroeconomics. December 2, 2009

Assignment #5. 1 Keynesian Cross. Econ 302: Intermediate Macroeconomics. December 2, 2009 Assignment #5 Econ 0: Intermediate Macroeconomics December, 009 Keynesian Cross Consider a closed economy. Consumption function: C = C + M C(Y T ) () In addition, suppose that planned investment expenditure

More information

Chapter 11 The Stochastic Growth Model and Aggregate Fluctuations

Chapter 11 The Stochastic Growth Model and Aggregate Fluctuations George Alogoskoufis, Dynamic Macroeconomics, 2016 Chapter 11 The Stochastic Growth Model and Aggregate Fluctuations In previous chapters we studied the long run evolution of output and consumption, real

More information

Assumption 5. The technology is represented by a production function, F : R 3 + R +, F (K t, N t, A t )

Assumption 5. The technology is represented by a production function, F : R 3 + R +, F (K t, N t, A t ) 6. Economic growth Let us recall the main facts on growth examined in the first chapter and add some additional ones. (1) Real output (per-worker) roughly grows at a constant rate (i.e. labor productivity

More information

Lecture 5: The neoclassical growth model

Lecture 5: The neoclassical growth model THE UNIVERSITY OF SOUTHAMPTON Paul Klein Office: Murray Building, 3005 Email: p.klein@soton.ac.uk URL: http://paulklein.se Economics 3010 Topics in Macroeconomics 3 Autumn 2010 Lecture 5: The neoclassical

More information

Long run input use-input price relations and the cost function Hessian. Ian Steedman Manchester Metropolitan University

Long run input use-input price relations and the cost function Hessian. Ian Steedman Manchester Metropolitan University Long run input use-input price relations and the cost function Hessian Ian Steedman Manchester Metropolitan University Abstract By definition, to compare alternative long run equilibria is to compare alternative

More information

Internation1al Trade

Internation1al Trade 14.581 Internation1al Trade Class notes on 3/4/2013 1 Factor Proportion Theory The law of comparative advantage establishes the relationship between relative autarky prices and trade ows But where do relative

More information

1. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1,x2) = Ax 1 a x 2

1. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1,x2) = Ax 1 a x 2 Additional questions for chapter 7 1. Suppose preferences are represented by the Cobb-Douglas utility function ux1x2 = Ax 1 a x 2 1-a 0 < a < 1 &A > 0. Assuming an interior solution solve for the Marshallian

More information

Intro to Economic analysis

Intro to Economic analysis Intro to Economic analysis Alberto Bisin - NYU 1 Rational Choice The central gure of economics theory is the individual decision-maker (DM). The typical example of a DM is the consumer. We shall assume

More information

Macroeconomics Theory II

Macroeconomics Theory II Macroeconomics Theory II Francesco Franco FEUNL February 2011 Francesco Franco Macroeconomics Theory II 1/34 The log-linear plain vanilla RBC and ν(σ n )= ĉ t = Y C ẑt +(1 α) Y C ˆn t + K βc ˆk t 1 + K

More information

Comprehensive Exam. Macro Spring 2014 Retake. August 22, 2014

Comprehensive Exam. Macro Spring 2014 Retake. August 22, 2014 Comprehensive Exam Macro Spring 2014 Retake August 22, 2014 You have a total of 180 minutes to complete the exam. If a question seems ambiguous, state why, sharpen it up and answer the sharpened-up question.

More information

ECON 5118 Macroeconomic Theory

ECON 5118 Macroeconomic Theory ECON 5118 Macroeconomic Theory Winter 013 Test 1 February 1, 013 Answer ALL Questions Time Allowed: 1 hour 0 min Attention: Please write your answers on the answer book provided Use the right-side pages

More information

Towards a Theory of Societal Co-Evolution: Individualism versus Collectivism

Towards a Theory of Societal Co-Evolution: Individualism versus Collectivism Toards a Theory of Societal Co-Evolution: Individualism versus Collectivism Kartik Ahuja, Simpson Zhang and Mihaela van der Schaar Department of Electrical Engineering, Department of Economics, UCLA Theorem

More information

Competitive Equilibrium and the Welfare Theorems

Competitive Equilibrium and the Welfare Theorems Competitive Equilibrium and the Welfare Theorems Craig Burnside Duke University September 2010 Craig Burnside (Duke University) Competitive Equilibrium September 2010 1 / 32 Competitive Equilibrium and

More information

Econ 5110 Solutions to the Practice Questions for the Midterm Exam

Econ 5110 Solutions to the Practice Questions for the Midterm Exam Econ 50 Solutions to the Practice Questions for the Midterm Exam Spring 202 Real Business Cycle Theory. Consider a simple neoclassical growth model (notation similar to class) where all agents are identical

More information

Economic Growth: Lecture 8, Overlapping Generations

Economic Growth: Lecture 8, Overlapping Generations 14.452 Economic Growth: Lecture 8, Overlapping Generations Daron Acemoglu MIT November 20, 2018 Daron Acemoglu (MIT) Economic Growth Lecture 8 November 20, 2018 1 / 46 Growth with Overlapping Generations

More information

Advanced Macroeconomics

Advanced Macroeconomics Advanced Macroeconomics The Ramsey Model Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 30 Introduction Authors: Frank Ramsey (1928), David Cass (1965) and Tjalling

More information

General Examination in Macroeconomic Theory SPRING 2013

General Examination in Macroeconomic Theory SPRING 2013 HARVARD UNIVERSITY DEPARTMENT OF ECONOMICS General Examination in Macroeconomic Theory SPRING 203 You have FOUR hours. Answer all questions Part A (Prof. Laibson): 48 minutes Part B (Prof. Aghion): 48

More information

Econ 204A: Section 3

Econ 204A: Section 3 Econ 204A: Section 3 Ryan Sherrard University of California, Santa Barbara 18 October 2016 Sherrard (UCSB) Section 3 18 October 2016 1 / 19 Notes on Problem Set 2 Total Derivative Review sf (k ) = (δ +

More information

u(c t, x t+1 ) = c α t + x α t+1

u(c t, x t+1 ) = c α t + x α t+1 Review Questions: Overlapping Generations Econ720. Fall 2017. Prof. Lutz Hendricks 1 A Savings Function Consider the standard two-period household problem. The household receives a wage w t when young

More information

Fluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice

Fluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice Fluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice Olivier Blanchard April 2002 14.452. Spring 2002. Topic 2. 14.452. Spring, 2002 2 Want to start with a model with two ingredients: ²

More information

Economic Growth: Lectures 10 and 11, Endogenous Technological Change

Economic Growth: Lectures 10 and 11, Endogenous Technological Change 14.452 Economic Growth: Lectures 10 and 11, Endogenous Technological Change Daron Acemoglu MIT December 1 and 6, 2011. Daron Acemoglu (MIT) Economic Growth Lectures 10 end 11 December 1 and 6, 2011. 1

More information

University of Pittsburgh Department of Economics Econ 1720: Advanced Macroeconomics Handout 3

University of Pittsburgh Department of Economics Econ 1720: Advanced Macroeconomics Handout 3 University of Pittsburgh Department of Economics Econ 1720: Advanced Macroeconomics Handout 3 This handout presents how we can use all the results obtained in handouts 1 and 2 in order to characterize

More information

Lecture Notes 8

Lecture Notes 8 14.451 Lecture Notes 8 Guido Lorenzoni Fall 29 1 Stochastic dynamic programming: an example We no turn to analyze problems ith uncertainty, in discrete time. We begin ith an example that illustrates the

More information

Solutions to Problem Set 4 Macro II (14.452)

Solutions to Problem Set 4 Macro II (14.452) Solutions to Problem Set 4 Macro II (14.452) Francisco A. Gallego 05/11 1 Money as a Factor of Production (Dornbusch and Frenkel, 1973) The shortcut used by Dornbusch and Frenkel to introduce money in

More information

Final Exam. You may not use calculators, notes, or aids of any kind.

Final Exam. You may not use calculators, notes, or aids of any kind. Professor Christiano Economics 311, Winter 2005 Final Exam IMPORTANT: read the following notes You may not use calculators, notes, or aids of any kind. A total of 100 points is possible, with the distribution

More information

Handout: Competitive Equilibrium

Handout: Competitive Equilibrium 1 Competitive equilibrium Handout: Competitive Equilibrium Definition 1. A competitive equilibrium is a set of endogenous variables (Ĉ, N s, N d, T, π, ŵ), such that given the exogenous variables (G, z,

More information

Granger Causality and Equilibrium Business Cycle Theory

Granger Causality and Equilibrium Business Cycle Theory Granger Causality and Equilibrium Business Cycle Theory Yi Wen Department of Economics Cornell University Abstract Post war US data show that consumption growth causes output and investment growth. This

More information

General motivation behind the augmented Solow model

General motivation behind the augmented Solow model General motivation behind the augmented Solow model Empirical analysis suggests that the elasticity of output Y with respect to capital implied by the Solow model (α 0.3) is too low to reconcile the model

More information

Logic Effort Revisited

Logic Effort Revisited Logic Effort Revisited Mark This note ill take another look at logical effort, first revieing the asic idea ehind logical effort, and then looking at some of the more sutle issues in sizing transistors..0

More information

Advanced Macroeconomics II The RBC model with Capital

Advanced Macroeconomics II The RBC model with Capital Advanced Macroeconomics II The RBC model with Capital Lorenza Rossi (Spring 2014) University of Pavia Part of these slides are based on Jordi Galì slides for Macroeconomia Avanzada II. Outline Real business

More information

Macroeconomics Qualifying Examination

Macroeconomics Qualifying Examination Macroeconomics Qualifying Examination August 2015 Department of Economics UNC Chapel Hill Instructions: This examination consists of 4 questions. Answer all questions. If you believe a question is ambiguously

More information

Simple New Keynesian Model without Capital

Simple New Keynesian Model without Capital Simple New Keynesian Model without Capital Lawrence J. Christiano January 5, 2018 Objective Review the foundations of the basic New Keynesian model without capital. Clarify the role of money supply/demand.

More information

Advanced Macroeconomics

Advanced Macroeconomics Advanced Macroeconomics Endogenous Growth Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 1 / 18 Introduction The Solow and Ramsey models are exogenous growth

More information

Capital-Labor Substitution, Equilibrium Indeterminacy, and the Cyclical Behavior of Labor Income

Capital-Labor Substitution, Equilibrium Indeterminacy, and the Cyclical Behavior of Labor Income Capital-Labor Substitution, Equilibrium Indeterminacy, and the Cyclical Behavior of Labor Income Jang-Ting Guo University of California, Riverside y Kevin J. Lansing Federal Reserve Bank of San Francisco

More information

ECON607 Fall 2010 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment 2

ECON607 Fall 2010 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment 2 ECON607 Fall 200 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment 2 The due date for this assignment is Tuesday, October 2. ( Total points = 50). (Two-sector growth model) Consider the

More information

Indeterminacy in a Matching Model of Money with Productive Government Expenditure

Indeterminacy in a Matching Model of Money with Productive Government Expenditure MPRA Munich Personal RePEc Archive Indeterminacy in a Matching Model of Money with Productive Government Expenditure Angus C. Chu and Chih-Hsing Liao and Xiangbo Liu and Mengbo Zhang Fudan University,

More information

1. Constant-elasticity-of-substitution (CES) or Dixit-Stiglitz aggregators. Consider the following function J: J(x) = a(j)x(j) ρ dj

1. Constant-elasticity-of-substitution (CES) or Dixit-Stiglitz aggregators. Consider the following function J: J(x) = a(j)x(j) ρ dj Macro II (UC3M, MA/PhD Econ) Professor: Matthias Kredler Problem Set 1 Due: 29 April 216 You are encouraged to work in groups; however, every student has to hand in his/her own version of the solution.

More information

Modelling Production

Modelling Production Modelling Production David N. DeJong University of Pittsburgh Econ. 1540, Spring 2010 DND () Production Econ. 1540, Spring 2010 1 / 23 Introduction The production function is the foundation upon which

More information

Constrained optimization.

Constrained optimization. ams/econ 11b supplementary notes ucsc Constrained optimization. c 2016, Yonatan Katznelson 1. Constraints In many of the optimization problems that arise in economics, there are restrictions on the values

More information

Lecture notes on modern growth theory

Lecture notes on modern growth theory Lecture notes on modern growth theory Part 2 Mario Tirelli Very preliminary material Not to be circulated without the permission of the author October 25, 2017 Contents 1. Introduction 1 2. Optimal economic

More information

Macroeconomics II. Dynamic AD-AS model

Macroeconomics II. Dynamic AD-AS model Macroeconomics II Dynamic AD-AS model Vahagn Jerbashian Ch. 14 from Mankiw (2010) Spring 2018 Where we are heading to We will incorporate dynamics into the standard AD-AS model This will offer another

More information

Dynamic AD-AS model vs. AD-AS model Notes. Dynamic AD-AS model in a few words Notes. Notation to incorporate time-dimension Notes

Dynamic AD-AS model vs. AD-AS model Notes. Dynamic AD-AS model in a few words Notes. Notation to incorporate time-dimension Notes Macroeconomics II Dynamic AD-AS model Vahagn Jerbashian Ch. 14 from Mankiw (2010) Spring 2018 Where we are heading to We will incorporate dynamics into the standard AD-AS model This will offer another

More information

Toulouse School of Economics, Macroeconomics II Franck Portier. Homework 1. Problem I An AD-AS Model

Toulouse School of Economics, Macroeconomics II Franck Portier. Homework 1. Problem I An AD-AS Model Toulouse School of Economics, 2009-2010 Macroeconomics II Franck Portier Homework 1 Problem I An AD-AS Model Let us consider an economy with three agents (a firm, a household and a government) and four

More information

ECON0702: Mathematical Methods in Economics

ECON0702: Mathematical Methods in Economics ECON0702: Mathematical Methods in Economics Yulei Luo SEF of HKU January 12, 2009 Luo, Y. (SEF of HKU) MME January 12, 2009 1 / 35 Course Outline Economics: The study of the choices people (consumers,

More information

Structural change in a multi-sector model of the climate and the economy

Structural change in a multi-sector model of the climate and the economy Structural change in a multi-sector model of the climate and the economy Gustav Engström The Beijer Institute of Environmental Economics Stockholm, December 2012 G. Engström (Beijer) Stockholm, December

More information

Advanced Macroeconomics

Advanced Macroeconomics Advanced Macroeconomics The Ramsey Model Micha l Brzoza-Brzezina/Marcin Kolasa Warsaw School of Economics Micha l Brzoza-Brzezina/Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 47 Introduction Authors:

More information

Lecture 3, November 30: The Basic New Keynesian Model (Galí, Chapter 3)

Lecture 3, November 30: The Basic New Keynesian Model (Galí, Chapter 3) MakØk3, Fall 2 (blok 2) Business cycles and monetary stabilization policies Henrik Jensen Department of Economics University of Copenhagen Lecture 3, November 3: The Basic New Keynesian Model (Galí, Chapter

More information

Graduate Macroeconomics - Econ 551

Graduate Macroeconomics - Econ 551 Graduate Macroeconomics - Econ 551 Tack Yun Indiana University Seoul National University Spring Semester January 2013 T. Yun (SNU) Macroeconomics 1/07/2013 1 / 32 Business Cycle Models for Emerging-Market

More information

Internation1al Trade

Internation1al Trade 4.58 International Trade Class notes on 4/8/203 The Armington Model. Equilibrium Labor endowments L i for i = ; :::n CES utility ) CES price index P = i= (w i ij ) P j n Bilateral trade ows follow gravity

More information

MA Macroeconomics 3. Introducing the IS-MP-PC Model

MA Macroeconomics 3. Introducing the IS-MP-PC Model MA Macroeconomics 3. Introducing the IS-MP-PC Model Karl Whelan School of Economics, UCD Autumn 2014 Karl Whelan (UCD) Introducing the IS-MP-PC Model Autumn 2014 1 / 38 Beyond IS-LM We have reviewed the

More information

SGZ Macro Week 3, Lecture 2: Suboptimal Equilibria. SGZ 2008 Macro Week 3, Day 1 Lecture 2

SGZ Macro Week 3, Lecture 2: Suboptimal Equilibria. SGZ 2008 Macro Week 3, Day 1 Lecture 2 SGZ Macro Week 3, : Suboptimal Equilibria 1 Basic Points Effects of shocks can be magnified (damped) in suboptimal economies Multiple equilibria (stationary states, dynamic paths) in suboptimal economies

More information

V. The Speed of adjustment of Endogenous Variables and Overshooting

V. The Speed of adjustment of Endogenous Variables and Overshooting V. The Speed of adjustment of Endogenous Variables and Overshooting The second section of Chapter 11 of Dornbusch (1980) draws on Dornbusch (1976) Expectations and Exchange Rate Dynamics, Journal of Political

More information

Advanced Economic Growth: Lecture 2, Review of Endogenous Growth: Expanding Variety Models

Advanced Economic Growth: Lecture 2, Review of Endogenous Growth: Expanding Variety Models Advanced Economic Growth: Lecture 2, Review of Endogenous Growth: Expanding Variety Models Daron Acemoglu MIT September 10, 2007 Daron Acemoglu (MIT) Advanced Growth Lecture 2 September 10, 2007 1 / 56

More information

A t = B A F (φ A t K t, N A t X t ) S t = B S F (φ S t K t, N S t X t ) M t + δk + K = B M F (φ M t K t, N M t X t )

A t = B A F (φ A t K t, N A t X t ) S t = B S F (φ S t K t, N S t X t ) M t + δk + K = B M F (φ M t K t, N M t X t ) Notes on Kongsamut et al. (2001) The goal of this model is to be consistent with the Kaldor facts (constancy of growth rates, capital shares, capital-output ratios) and the Kuznets facts (employment in

More information

Indivisible Labor and the Business Cycle

Indivisible Labor and the Business Cycle Indivisible Labor and the Business Cycle By Gary Hansen Zhe Li SUFE Fall 2010 Zhe Li (SUFE) Advanced Macroeconomics III Fall 2010 1 / 14 Motivation Kydland and Prescott (1982) Equilibrium theory of the

More information