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### finalf05sol

Course: AECO 601, Fall 2009
School: SUNY Albany
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Word Count: 555

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Macroeconomics AECO601 I Solution to Final Exam (1) The rst 3 parts were straight from class notes. The equations for the system are: ct = f (kt ) + (1 u (ct ) = f 0 (kt ) + (1 u0 (ct+1 ) 0 Fall 2005 )kt ) kt+1 In the 4th part of the question there is an unforeseen decline in the discount rate. Recall that is the discount factor and that if is used for the 1 discount rate then = 1+ and in steady-state the...

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Macroeconomics AECO601 I Solution to Final Exam (1) The rst 3 parts were straight from class notes. The equations for the system are: ct = f (kt ) + (1 u (ct ) = f 0 (kt ) + (1 u0 (ct+1 ) 0 Fall 2005 )kt ) kt+1 In the 4th part of the question there is an unforeseen decline in the discount rate. Recall that is the discount factor and that if is used for the 1 discount rate then = 1+ and in steady-state the second equation becomes f 0 (k ) = + A decline in therefore leads to an increase in k because f (:) is concave. (I did not penalize any one for mistaking the discount rate for the discount factor. If that mistake was made then k would fall.) The main diagram for part 4 is Figure 1. For simplicity we start from an initial steady-state, point A. We know that eventually the economy will reach point C. Other than that we must always be in equilibrium and there are no anticipated jumps in c: When the unanticipated fall in happens the economy jumps from A to B immediately (i.e. on Jan 1). After that the economy converges over time (asymptotically) to point C. Figure 2 shows at the case when the change in 1). In this case we know that we have to be on the saddle-path through point C on Jan 1 but only the news in Nov 1 can cause a jump in c: On Nov 1 the economy jumps to point B1 between Nov 1 and Jan 1 it is on the path from B1 to B2. The economy reaches B2 exactly on Jan 1. Thereafter it tracks toward point C. is anticipated (on Nov 1 c A C B k*c k*b k Figure 1: Unanticipated decrease in : 2 c A B1 B2 C k*c k*b k Figure Anticipated 2: decrease in : 3 (2.1)There are 3 employment states: unemployed, value Vu ; employed without promotion, Ve and promoted, Vp : (The wage is another dimension to the state.) Asset value equations. (Ignoring the possibility of both events happening in any period means that an employed worker gets promoted with probability ; laid-o with probability and remains employed with probability 1 :) rVu = b + Ew [max fVe (w) Vu ; 0g] rVe (w) = w + (Vu Ve (w)) + (Vp (w) Ve (w)) rVp (w) = w + (Vu Vp (w)) To show that promotion is always a good thing we evaluate Vp (w) r (Vp (w) So Vp (w) Ve (w) = Ve (w)) = ( 1)w (Vp (w) Ve (w)) (Vp (w) Ve (w): Ve (w)) ( 1)w >0 r+ + (2.2) The 3 unknowns in population are nu ; ne and np : Figure 3 shows the diagram. ow Equations: nu + ne + np ne + ne ne ne + np = 1 = (1 = np = (1 F (w ))nu F (w ))nu One of these linear equations is super uous. (2.3) This i...

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SUNY Albany - AECO - 755146
AECO601 Macroeconomics I Solution to Final Exam (1) The rst 3 parts were straight from class notes. The equations for the system are: ct = f (kt ) + (1 u (ct ) = f 0 (kt ) + (1 u0 (ct+1 )0Fall 2005)kt )kt+1In the 4th part of the question the
SUNY Albany - AM - 370
TOPICS IN LABOR SUPPLY Application of labor supply model: Earned income tax credit (EITC) What is it?: A scheme to encourage greater labor market participation among members of poor households. What is does: supplements income for people on low pay E
SUNY Albany - AECO - 370
TOPICS IN LABOR SUPPLY Application of labor supply model: Earned income tax credit (EITC) What is it?: A scheme to encourage greater labor market participation among members of poor households. What is does: supplements income for people on low pay E
SUNY Albany - AECO - 755146
TOPICS IN LABOR SUPPLY Application of labor supply model: Earned income tax credit (EITC) What is it?: A scheme to encourage greater labor market participation among members of poor households. What is does: supplements income for people on low pay E
SUNY Albany - AM - 755146
AECO 601: Macroeconomics I (Based on questions by Prof. S. Williamson) Assignment 1 1. Consider the following representative agent model. The representative consumer has preferences given by u(c; l) = c + l where c is consumption, l is leisure, and &gt;
SUNY Albany - AECO - 601
AECO 601: Macroeconomics I (Based on questions by Prof. S. Williamson) Assignment 1 1. Consider the following representative agent model. The representative consumer has preferences given by u(c; l) = c + l where c is consumption, l is leisure, and &gt;
SUNY Albany - AECO - 755146
AECO 601: Macroeconomics I (Based on questions by Prof. S. Williamson) Assignment 1 1. Consider the following representative agent model. The representative consumer has preferences given by u(c; l) = c + l where c is consumption, l is leisure, and &gt;
SUNY Albany - AM - 370
UNIVERSITY AT ALBANY Department of Economics Economics 370 - Economics of Labor (2045) Spring 2009: MWF 12:35PM-01:30PM Room BA130 Prof: Adrian Masters Phone: 437-4418 E-mail: amasters@albany.edu Web page: http:/albany.edu/econ/Faculty/AMasters.htm G
SUNY Albany - AECO - 370
UNIVERSITY AT ALBANY Department of Economics Economics 370 - Economics of Labor (2045) Spring 2009: MWF 12:35PM-01:30PM Room BA130 Prof: Adrian Masters Phone: 437-4418 E-mail: amasters@albany.edu Web page: http:/albany.edu/econ/Faculty/AMasters.htm G
SUNY Albany - AECO - 755146
UNIVERSITY AT ALBANY Department of Economics Economics 370 - Economics of Labor (2045) Spring 2009: MWF 12:35PM-01:30PM Room BA130 Prof: Adrian Masters Phone: 437-4418 E-mail: amasters@albany.edu Web page: http:/albany.edu/econ/Faculty/AMasters.htm G
SUNY Albany - AM - 370
LABOR DEMAND INTRODUCTION What it is: ability and willingness to pay for labor services Source: Its derived from peoples desire to purchase the services offered by rms Affected by: peoples preferences, income, available technologies, weather1THE
SUNY Albany - AECO - 370
LABOR DEMAND INTRODUCTION What it is: ability and willingness to pay for labor services Source: Its derived from peoples desire to purchase the services offered by rms Affected by: peoples preferences, income, available technologies, weather1THE
SUNY Albany - AECO - 755146
LABOR DEMAND INTRODUCTION What it is: ability and willingness to pay for labor services Source: Its derived from peoples desire to purchase the services offered by rms Affected by: peoples preferences, income, available technologies, weather1THE
SUNY Albany - AM - 755146
AECO601 Macroeconomics I Solution to Assignment 6Fall 2005(1) Write the reservation wage equations as Z w u(w ) u(b) u( ) u(w )dF ( ) = 0 r+ w Then @ dw @ = @ d @w where Z w u0 (w ) @ 0 u0 (w )dF ( ) = = u (w ) + [r + + (1 F (w )] @w r+ (r + ) w
SUNY Albany - AECO - 601
AECO601 Macroeconomics I Solution to Assignment 6Fall 2005(1) Write the reservation wage equations as Z w u(w ) u(b) u( ) u(w )dF ( ) = 0 r+ w Then @ dw @ = @ d @w where Z w u0 (w ) @ 0 u0 (w )dF ( ) = = u (w ) + [r + + (1 F (w )] @w r+ (r + ) w
SUNY Albany - AECO - 755146
AECO601 Macroeconomics I Solution to Assignment 6Fall 2005(1) Write the reservation wage equations as Z w u(w ) u(b) u( ) u(w )dF ( ) = 0 r+ w Then @ dw @ = @ d @w where Z w u0 (w ) @ 0 u0 (w )dF ( ) = = u (w ) + [r + + (1 F (w )] @w r+ (r + ) w
SUNY Albany - AECO - 601
Notes on dynamic stability of steady-states of Dierence equation systems In general we can have F (xt ; xt 1 ) = 0 where x is a k-dimensional vector, 0 is the k-dimensional nul-vector and F : Rk Rk ! Rk . A Steady state is an x such that F (x ; x ) =
SUNY Albany - AECO - 755146
Notes on dynamic stability of steady-states of Dierence equation systems In general we can have F (xt ; xt 1 ) = 0 where x is a k-dimensional vector, 0 is the k-dimensional nul-vector and F : Rk Rk ! Rk . A Steady state is an x such that F (x ; x ) =
SUNY Albany - AECO - 601
ECO 601 - Macroeconomics 1 Fall 2004 Prof. Kenneth Beauchemin Solutions to Problem Set 5 1. (a) The agent solves{ct ,at } X t=1max t1 (ln ct + ln a2,t1 )s.t. ct + p1t a1t + p2t a2t = (p1t + y1t ) a1,t1 + (p2t + y2t ) a2,t1 and non-negativity
SUNY Albany - AECO - 755146
ECO 601 - Macroeconomics 1 Fall 2004 Prof. Kenneth Beauchemin Solutions to Problem Set 5 1. (a) The agent solves{ct ,at } X t=1max t1 (ln ct + ln a2,t1 )s.t. ct + p1t a1t + p2t a2t = (p1t + y1t ) a1,t1 + (p2t + y2t ) a2,t1 and non-negativity
SUNY Albany - AM - 755146
AECO601 FINAL EXAM (1) Optimal Growth with a consumption externality. Consider the following Economy: Time: Discrete; innite horizonFall 2006Demography: Continuum of mass 1 of (representative) consumer/worker households, and a large number of pro
SUNY Albany - AECO - 601
AECO601 FINAL EXAM (1) Optimal Growth with a consumption externality. Consider the following Economy: Time: Discrete; innite horizonFall 2006Demography: Continuum of mass 1 of (representative) consumer/worker households, and a large number of pro
SUNY Albany - AECO - 755146
AECO601 FINAL EXAM (1) Optimal Growth with a consumption externality. Consider the following Economy: Time: Discrete; innite horizonFall 2006Demography: Continuum of mass 1 of (representative) consumer/worker households, and a large number of pro
SUNY Albany - AM - 803
University at Albany Economics 803 Spring 2008 Advanced Macroeconomics II M, W, 12:00-1:20; Room LC013 Prof: Adrian Masters Phone: 437-4418 Email: amasters@albany.eduDepartment of EconomicsOffice: Economics BA 109C Office Hours: W 2:45-4:45 Or b
SUNY Albany - AECO - 755146
University at Albany Economics 803 Spring 2008 Advanced Macroeconomics II M, W, 12:00-1:20; Room LC013 Prof: Adrian Masters Phone: 437-4418 Email: amasters@albany.eduDepartment of EconomicsOffice: Economics BA 109C Office Hours: W 2:45-4:45 Or b
SUNY Albany - AECO - 803
University at Albany Economics 803 Spring 2008 Advanced Macroeconomics II M, W, 12:00-1:20; Room LC013 Prof: Adrian Masters Phone: 437-4418 Email: amasters@albany.eduDepartment of EconomicsOffice: Economics BA 109C Office Hours: W 2:45-4:45 Or b
SUNY Albany - AM - 370
COMPENSATING DIFFERENTIALS AND DANGEROUS JOBS (Borjas section 6.1) COMPENSATING DIFFERENTIALS A source of deviations from the law-of-one-price Emerge because people take account of other aspects of a job when considering whether to take it. Some aspe
SUNY Albany - AECO - 370
COMPENSATING DIFFERENTIALS AND DANGEROUS JOBS (Borjas section 6.1) COMPENSATING DIFFERENTIALS A source of deviations from the law-of-one-price Emerge because people take account of other aspects of a job when considering whether to take it. Some aspe
SUNY Albany - AECO - 755146
COMPENSATING DIFFERENTIALS AND DANGEROUS JOBS (Borjas section 6.1) COMPENSATING DIFFERENTIALS A source of deviations from the law-of-one-price Emerge because people take account of other aspects of a job when considering whether to take it. Some aspe
SUNY Albany - AM - 370
LABOR MARKET DISCRIMINATION Terms: Black:people of African decent including those whose families arrived in the USA via the Caribbean White: people whose families came directly from Europe and Asia Hispanic: people whose families arrived here via Lat
SUNY Albany - AECO - 370
LABOR MARKET DISCRIMINATION Terms: Black:people of African decent including those whose families arrived in the USA via the Caribbean White: people whose families came directly from Europe and Asia Hispanic: people whose families arrived here via Lat
SUNY Albany - AECO - 755146
LABOR MARKET DISCRIMINATION Terms: Black:people of African decent including those whose families arrived in the USA via the Caribbean White: people whose families came directly from Europe and Asia Hispanic: people whose families arrived here via Lat
SUNY Albany - AM - 370
The Wage Structure What is is?(Histogram of what people earn) Previous sections have looked at how wages are formed and what inuences the difference between them. Here we take a macro view and ask what factors shape the measured distribution of wages
SUNY Albany - AECO - 370
The Wage Structure What is is?(Histogram of what people earn) Previous sections have looked at how wages are formed and what inuences the difference between them. Here we take a macro view and ask what factors shape the measured distribution of wages
SUNY Albany - AECO - 755146
The Wage Structure What is is?(Histogram of what people earn) Previous sections have looked at how wages are formed and what inuences the difference between them. Here we take a macro view and ask what factors shape the measured distribution of wages
SUNY Albany - AM - 370
HUMAN CAPITAL Even after taking account of compensating differentials there is a lot of variation in pay between people. Some of this is attributed to Human Capital: an acquired aptitude for certain tasks, e.g. education, skills There are also innate
SUNY Albany - AECO - 370
HUMAN CAPITAL Even after taking account of compensating differentials there is a lot of variation in pay between people. Some of this is attributed to Human Capital: an acquired aptitude for certain tasks, e.g. education, skills There are also innate
SUNY Albany - AECO - 755146
HUMAN CAPITAL Even after taking account of compensating differentials there is a lot of variation in pay between people. Some of this is attributed to Human Capital: an acquired aptitude for certain tasks, e.g. education, skills There are also innate
SUNY Albany - AM - 755146
Prelim Sept 06 (Adrian questions) s (1) Optimal Growth with a proportional wealth tax. Consider the following Economy: Time: Discrete innite horizon Demography: Continuum of mass 1 of (representative) consumer/worker households, a Government which ha
SUNY Albany - AECO - 601
Prelim Sept 06 (Adrian questions) s (1) Optimal Growth with a proportional wealth tax. Consider the following Economy: Time: Discrete innite horizon Demography: Continuum of mass 1 of (representative) consumer/worker households, a Government which ha
SUNY Albany - AECO - 755146
Prelim Sept 06 (Adrian questions) s (1) Optimal Growth with a proportional wealth tax. Consider the following Economy: Time: Discrete innite horizon Demography: Continuum of mass 1 of (representative) consumer/worker households, a Government which ha
SUNY Albany - AM - 755146
AECO601 Macroeconomics I Assignment 5Fall 2005where ct is consumption and lt is leisure. The consumer is endowed with one unit of time in each period which can be allocated between work and leisure. The representative rm has access to a productio
SUNY Albany - AECO - 601
AECO601 Macroeconomics I Assignment 5Fall 2005where ct is consumption and lt is leisure. The consumer is endowed with one unit of time in each period which can be allocated between work and leisure. The representative rm has access to a productio
SUNY Albany - AECO - 755146
AECO601 Macroeconomics I Assignment 5Fall 2005where ct is consumption and lt is leisure. The consumer is endowed with one unit of time in each period which can be allocated between work and leisure. The representative rm has access to a productio
SUNY Albany - AM - 755146
AECO601 Macroeconomics I Solution to Assignment 3Masters1a) The rst part asks if Money is neutral in the model. In the more general set up from class, the 2 key equations are Mtd pt = L pt pt+1 t d (1 + n) Mt = H where pt is the price level, Mtd
SUNY Albany - AECO - 601
AECO601 Macroeconomics I Solution to Assignment 3Masters1a) The rst part asks if Money is neutral in the model. In the more general set up from class, the 2 key equations are Mtd pt = L pt pt+1 t d (1 + n) Mt = H where pt is the price level, Mtd
SUNY Albany - AECO - 755146
AECO601 Macroeconomics I Solution to Assignment 3Masters1a) The rst part asks if Money is neutral in the model. In the more general set up from class, the 2 key equations are Mtd pt = L pt pt+1 t d (1 + n) Mt = H where pt is the price level, Mtd
SUNY Albany - AM - 755146
University at Albany Department of Economics Economics 601 - Macroeconomics I Fall 2008: T/TH 01:15PM-02:35PM Room BA 210 Prof: Adrian Masters Phone:437-4418 Email: amasters@albany.eduGA: Chen Cao E-mail: cc971113@albany.eduOffice: Economics BA 11
SUNY Albany - AECO - 601
University at Albany Department of Economics Economics 601 - Macroeconomics I Fall 2008: T/TH 01:15PM-02:35PM Room BA 210 Prof: Adrian Masters Phone:437-4418 Email: amasters@albany.eduGA: Chen Cao E-mail: cc971113@albany.eduOffice: Economics BA 11
SUNY Albany - AECO - 755146
University at Albany Department of Economics Economics 601 - Macroeconomics I Fall 2008: T/TH 01:15PM-02:35PM Room BA 210 Prof: Adrian Masters Phone:437-4418 Email: amasters@albany.eduGA: Chen Cao E-mail: cc971113@albany.eduOffice: Economics BA 11
SUNY Albany - AM - 370
LABOR MARKET EQUILIBRIUM Competitive Equilibrium Equilibrium as the intersection of supply and demand curve What does it look like to participants? workers and rms take wages and output prices as given1Worked Example Suppose the market for secret
SUNY Albany - AECO - 370
LABOR MARKET EQUILIBRIUM Competitive Equilibrium Equilibrium as the intersection of supply and demand curve What does it look like to participants? workers and rms take wages and output prices as given1Worked Example Suppose the market for secret
SUNY Albany - AECO - 755146
LABOR MARKET EQUILIBRIUM Competitive Equilibrium Equilibrium as the intersection of supply and demand curve What does it look like to participants? workers and rms take wages and output prices as given1Worked Example Suppose the market for secret
SUNY Albany - AM - 755146
06E:204 Macroeconomics Suggested solutions to Assignment 2 Problem 1. In this representative agent model we do not have any distortions (taxes are lump-sum) and thus, the First Welfare Theorem holds. The competitive equilibrium (C.E.) is Pareto optim
SUNY Albany - AECO - 601
06E:204 Macroeconomics Suggested solutions to Assignment 2 Problem 1. In this representative agent model we do not have any distortions (taxes are lump-sum) and thus, the First Welfare Theorem holds. The competitive equilibrium (C.E.) is Pareto optim
SUNY Albany - AECO - 755146
06E:204 Macroeconomics Suggested solutions to Assignment 2 Problem 1. In this representative agent model we do not have any distortions (taxes are lump-sum) and thus, the First Welfare Theorem holds. The competitive equilibrium (C.E.) is Pareto optim
SUNY Albany - AM - 755146
06E:204 Macroeconomics Suggested solutions to Assignment 5 Problem 1. (a) To nd the competitive equilibrium we have to set up a dynamic programming problem. In even periods t = 0, 2, 4, . Bellman equation for this problem is: ve (kt ) = max [ln ct +
SUNY Albany - AECO - 601
06E:204 Macroeconomics Suggested solutions to Assignment 5 Problem 1. (a) To nd the competitive equilibrium we have to set up a dynamic programming problem. In even periods t = 0, 2, 4, . Bellman equation for this problem is: ve (kt ) = max [ln ct +
SUNY Albany - AECO - 755146
06E:204 Macroeconomics Suggested solutions to Assignment 5 Problem 1. (a) To nd the competitive equilibrium we have to set up a dynamic programming problem. In even periods t = 0, 2, 4, . Bellman equation for this problem is: ve (kt ) = max [ln ct +
SUNY Albany - AM - 755146
Proportional income tax in simple dynamic model with a government. Consider the following economy: Time: Discrete; innite horizon Demography: Continuum of mass 1 of (representative) consumer/worker households, and a large number of prot maximizing rm
SUNY Albany - AECO - 601
Proportional income tax in simple dynamic model with a government. Consider the following economy: Time: Discrete; innite horizon Demography: Continuum of mass 1 of (representative) consumer/worker households, and a large number of prot maximizing rm