ECONOMIC GROWTH. Student Assessment. Macroeconomics II. Class 1

Transcription

1 Suden Assessmen You will be graded on he basis of In-class aciviies (quizzes worh 30 poins) which can be replaced wih he number of marks from he regular uorial IF i is >=30 (capped a 30, i.e. marks from he uorial in he range of are convered ino 30 poins from quizzes) A comprehensive final exam (worh 70 poins); you will choose 3 quesions ou of 4. A pass grade is a or above 50 poins. Macroeconomics II Class 1 ECONOMIC GROWTH 1

2 A Road Map ECONOMIC GROWTH 1. Growh Accouning 3. Exension of he Solow Model 4. New Growh Theory Moivaion: Convergence? ECONOMIC GROWTH 2

3 1. Growh Accouning For he quaniy of oupu o grow, eiher he quaniy of inpus mus grow or produciviy mus improve or boh. For fixed A, he increase in oupu can come from wo sources: more capial and more labor Y Y Y Y A F K, MPK MPK Y K K K K MPN N MPN Y N N N N 1. Growh Accouning The marginal produc of capial equals is renal price; he marginal produc of labor equals is real wage. Y K N 1 Y K N capial share labor share Oupu increases no only because of increases in capial and labor bu also because of increases in he level of echnology, A. Y Y A K N 1 A K N 3

4 The amoun of oupu per worker, yy/n depends on he amoun of capial per worker, k K/N. Properies of he producion funcion Consan reurns o scale imply ha we can rewrie he aggregae producion funcion in inensive form Y K N K y F, F, 1 N N N N The producion funcion exhibis posiive and diminishing marginal producs f k 0 and f k 0 Inada condiions: lim k 0 f k f k lim 0 k f k 4

5 Labor produciviy (consan 2005 USD, lef axis) and he share of working populaion (righ axis) in he US , , , , Y/N N/POP ,2 0,1 0 One-secor economy in which oupu Y is a good ha can be consumed C or invesed I o creae new unis of physical capial K The economy is closed The labor force N (and populaion) grows a a consan, exogenous rae n Capial and labor are used o produce he economy s oal oupu according o a neoclassical producion funcion The saving rae s=s /Y is given exogenously and is consan, 0<s<1 Capial depreciaes a he consan rae d 5

6 The increase in he sock of physical capial K dk The increase in he sock of physical capial per worker K N K sy dk k nk N N N N The fundamenal dynamic equaion for he per capia capial sock is given by k sf I k n d k In seady sae, he change in capial per worker is zero. sf k n d k Oupu per worker y f k Consumpion per worker c 1 s f k 6

7 Deermining he capial labor raio in he seady sae. Are developed counries converging o seady sae? 3-year (mean 1,, +1) growh raes over

8 Are developing counries converging o seady sae? 3-year (mean 1,, +1) growh raes over The effec of a higher populaion growh rae on he seady-sae capial labor raio 8

9 The effec of an increased saving rae on he seadysae capial labor raio According o he Solow model Higher saving rae implies higher living sandards because he saving rae deermines he level of oupu per worker in he long run The saving rae has no effec on he long-run growh rae of oupu per worker, which is equal o zero An increase in he saving rae will lead o higher growh of oupu per worker for some ime, bu no forever. This period of growh will end when he economy reaches is new seady sae. 9

10 An increase in he saving rae leads o an increase, hen o a decrease, in consumpion per worker in seady sae. This is due o he fac ha An increase in he saving rae always leads o an increase in he level of oupu per worker. This ends o rise consumpion. An increase in he saving rae always reduces he par of income spen on consumpion. This ends o decrease consumpion. The Effecs of he Saving Rae on Consumpion per Worker in Seady Sae Consumpion per worker Saving rae, s 10

11 The level of capial associaed wih he value of he saving rae ha yields he highes level of consumpion in seady sae is known as he golden-rule level of capial. For s larger han s G, increases in he saving rae sill lead o higher capial and oupu per worker, bu lower consumpion per worker. For s=1, capial and oupu per worker are high, bu all of he oupu is used o replace depreciaion, leaving nohing for consumpion. The relaionship of consumpion per worker o he capial labor raio in he seady sae k n d f G 11

12 An increase in he saving rae requires an iniial decrease in consumpion. In he long run, he increase in he saving rae may lead o an increase or o a decrease in consumpion. Consumpion per worker c 0(s 0) c1(s1), for s0<s1<sg c1(s1), for sg<s0<s1 Time Technological progress reduces he number of workers needed o achieve a given amoun of oupu. Technological progress increases AN, which we can hink of as he amoun of effecive labor. Y F K, A N Producion funcion in inensive form yˆ Y AN f kˆ 12

13 kˆ syˆ n d g kˆ sf kˆ n d g kˆ sf kˆ n d g kˆ Dynamics of Capial per Worker and Oupu per Effecive Worker Required invesmen Oupu per effecive worker, Y/AN (d+n+g)(k/an) Capial per effecive worker, K/AN 13

14 The Characerisic of Balanced Growh Rae of growh of: Capial per effecive worker 0 Oupu per effecive worker 0 Capial per worker Oupu per worker Labor Capial Oupu g g n n+g n+g An increase in he saving rae leads o an increase in he seady-sae levels of oupu and capial per effecive worker. Oupu per effecive worker, Y/AN (d+n+g)(k/an) Capial per effecive worker, K/AN 14

15 3. Exension of he Solow Model Absolue convergence: Consider a group of counries, all of which have access o he same echnology, he same populaion growh rae and he same savings propensiy, and only differ in erms of heir iniial capial-labor raio. Then, we should expec all counries o converge o he same seady-sae oupu per capia and he same growh rae. 3. Exension of he Solow Model Wih large differences in he qualiy of labor, using oal employmen o represen he labor force in he Solow growh model migh no meaningfully capure differences in he labor inpu. Oupu is hen produced according o Y F K, AH Where K = sock of physical capial H = amoun of human capial-augmened labor A = labor-augmening measure of produciviy 15

16 3. Exension of he Solow Model Level of educaion is a commonly used measure of human capial Each uni of labor N has been rained wih E years of schooling (educaion). Human capial-augmened labor is given by: H E N where reflecs he efficiency of a uni of labor wih E years of schooling relaive o one wih no schooling 3. Exension of he Solow Model Suppose ha he rae of growh of human capial is equal o (n+) where The inclusion of human capial does no change he basic philosophy of he Solow growh model. To keep capial per human-capial-augmened efficiency uni consan invesmen mus no only replace capial los due o depreciaion. Bu also accommodae populaion, efficiency and human capial growh. E E 16

17 3. Exension of he Solow Model Seady-sae and ransiion pahs in he modified Solow growh model Oupu per human-capial augmened effecive worker, Y/AH Y AH Required invesmen (d+n++g)(k/ah) Producion f(k/ah) Invesmen sf(k/ah) (K/AH) 0 (K/AH) * Capial per human-capial augmened effecive worker, K/AH Problem 1 Problem 1 Consider he effecs of axes imposed on boh labor and capial income. The producion funcion akes he sandard Cobb-Douglas form: 1 Y K AN The ax rae equals, saving rae equals s, he rae of echnological progress = g, capial depreciaion rae = d, and populaion growh rae = n. a) Wrie down he producion funcion in he inensive form. Use he dynamic equaion for capial per unis of effecive labor o compue he value of consumpion per unis of effecive labor in he seady sae. b) Compue he golden rule saving rae in he Solow growh model exended o include axes. c) Use he Basic Solow growh graph wih he saving and producion funcions drawn agains kˆ, o illusrae he consequences of a rise in he ax rae. Wha is he rae of growh of per capia income in he seady sae? Does i depend on he ax rae? 17

18 Problem 2 A consan reurns o scale producion funcion can be wrien in he inensive form as: yˆ f kˆ kˆ where kˆ denoes capial per uni of effecive labor, and 1>>0. The pace of labor-augmening echnological progress is given by g. The rae of depreciaion and he rae of populaion growh are consan and equal o, respecively, d and n. The rae of saving is consan as well and equals s bu due o poor developmen of financial secor a fracion z of savings is seized by he financial inermediaries o cover heir operaional coss and he oal amoun of savings available o invesors is reduced by fracion z. Use he Solow growh model o a) Calculae he level of per capia income in period. Assume ha a he economy is in he seady-sae and he level of echnology and employmen is given by A=100 and N=2500. b) Compue he golden rule level of he saving rae. Problem 3 The producion funcion is given by AN K E Y, where Y is oupu, A echnology, K capial sock, N labor and E sands for energy inpus. Parameers,, are posiive. a) The rae of growh of GDP was equal o 4%, he rae of growh of labor was 2%, capial sock increased by 3% and he sock of energy inpus by 4%. We also know ha 1 3. Use he growh accouning equaion (ake logs of he producion funcion!) o compue he rae of echnological progress (he rae of growh of A). b) Now suppose ha he sock of energy inpus sops growing and he producion 1 funcion urns o be Y EAN K. Wrie he funcion in he inensive form, i.e. yˆ Ef kˆ and calculae he golden rule savings rae. The rae of populaion growh = n, echnological progress (rae of growh of A) = g, depreciaion rae = d and he value of is known. 18

19 Problem 4 Producion funcion is given by: 1 Y K N The rae of populaion growh is n. The saving rae is s, and he rae of depreciaion of physical capial equals d. (The level of echnology is consan, A=1). Use he Solow growh model o answer he following quesions. a) Migrans arrive in he counry and join he naive labor force. Explain and show on he basic Solow model graph (wih he producion, savings and depreciaion funcions) how oupu per worker will respond o he migrans enrance ino he counry, assuming ha he parameers n, s and d remain unchanged. Wha will be he rae of growh of oupu per person in he shor and long run afer immigrans inflow? b) The number of workers is now given by M+N, where M denoes he number of migrans. There is perfec subsiuion beween naive and foreign workers and he producion funcion now reads as follows: 1 Y K N M Migrans have he same rae of populaion growh, bu i urned ou ha hey do no inves in capial. Migrans send home he saved par of heir earnings. Assuming ha he percenage of migran workers in oal workforce is given by m (m=m/(m+n)), he new saving rae is equal o s(1 m). Derive he value of oupu per person in seady sae. Should naive workers welcome immigrans? How are he level and rae of growh of per capia income in seady sae dependen on m? c) Using he daa from iem (b), calculae he saving rae ha maximizes consumpion in he long-run. Problem 5 Consider he Solow growh model in an economy where human capial, measured by he qualiy of healh, is a facor of producion. The producion funcion akes he following form 1 Y K AHN, where K is physical capial, H is he level of healhiness, N is he number of hours worked, A denoes he level of echnology. The amoun of effecive unis of labor is equal o AHN. The medical care allows o improve he level of healh by h% per year, hus H H h. The pace of echnological progress equals g, he saving rae equals s, he depreciaion rae is equal o d. The number of hours worked N grows by n% per year, hus N N n. a) Use he basic Solow growh graph wih he saving and producion funcions drawn agains kˆ (capial per unis of effecive labor), o illusrae he consequences of a rise in parameer h. Explain how he rae of growh of oupu per uni of effecive labor responds o a rise in h. b) Using he definiion of kˆ and compue he rae of growh of aggregae income (Y) and per capia income (y) in he seady sae. 19