Macro Teste 3 Final PDF

Questions : What if we are above or below the steady state ? 1) Dynamics of Capital and Output...

Questions : What if we are above or below the steady state ? 1) Dynamics of Capital and Output 2) Changes in S 6-Solow Model ga : or Dynamics Extended Model without the or change. 3) Timelines (Total worker) 2 How to return to the initial state? - Basic and Extended Model. , per capita per effective , = f() This means that in the model in the long un, the depends only on Capital Accumulation Equation (CAE) Ak Sx] Ex ↳ = - N N - - the change of capital per investments necessary investments worker per worker per worker change in Capital and output per worker is On the growth rate is O. > - Dynamics of capital and output output per worker I N 5x necessary investments III N estment per worm lin 1 capital per worker A steady-state In A , investments per worker equal to necessary investments per worker equilibrium in are. A SX- Capital per worker s ne the = change of Graphic 1 : when capital and output are low , investment exceeds depreciation and capital increases. When capital and output are high, investment is less than depreciation and capital decreases. - Output per worker increases with capital per worker , but , because of decreasing returns to capital the effect , is smaller the higher the level of capital per worker. ( thepew than investmentsof caprit higher L necessary investments p. c. capitatatin D0 positivo &4/n - + -if the level of capital per worker is capital per worker but by less and less as capital per worker increases When capital per worker is already high, ,. the effect of a further increase in capital per worker on output per worker , and by implication on investment per worker is small. For the given level of capital per worker the investments plw are higher than necessary inv p W. ,.. So with CAE we can say & UN3O + positive change increasing /n and increasing /w as long as there is the difference , , The between investments & change in capital per worker is given by the difference between investment per worker and depreciation per worker At (E) the difference is positive : andWand necessari investment. 2 , per worker exceeds depreciation , so capital per worker increases. As we move to the right along the horizontal axis look at higher and higher levels of capital per worker investment , increases by less and less while depreci , atich keeps increasing in proportion to capital. For some leve of capital per worker (*) *, investment is just enough to cover depreciation and , , and capital per worker remains constant. To the left of (*) * investment exceeds depreciation and , capital per worker increases To the right of. (*) * depreciation exceeds investment and capital per worker decreases.  - Consider an economy that starts with a low level of capital per worker - / * II Because investment depreciation at this point capital per worker increases. And because exceeds n , output moves with capital output per worker increases as well. Capital per worker eventually reaches , (**, the lad at which investment is equal to depreciation. Once the economy has reached the level of capital per worker (* ) * sutput at (2) and (**, * worker and capital worker remain constant per per their long run equilibrium les. - If a country starts instead from a high level of capital per worker, right of then depreciation , will exceed investment and capital per worker and output per worker will decrease. The initial level of capital per worker is , too high to be sustained given the saving rate. This decrease in capital per ↑u - too to be sustained the rate. This decrease capital worker per worker will continue is high given saving in N until the reaches the point where investment is equal to capital per worker economy again depreciation and is equal to (**. Then it will remain constant- it reaches steady state of the economy & , a. EXTENSIVE MODEL alif( * if we are (the economyl , at lower leves of , lower than optimal > - > ( + gn + ga)x - A0 - A tenoiseases over time the number of effective , (AN) increases overtime Thus. , mainting the sameo of capital to effective workers ( requires an increase in the capital stocu (k) proportional to the increase in number of effective workers (AN). from the economy starting right o , moves to the , with the leve of capital per effective worker inar OvertimeThisgoesonw investmentpereffectivewheri just sufficient to maintain the existing leve o ae ur · · In steady-state output (Y) , is growning at the same rate as effective labor (AN) , so that I ratio of the two constant Because effective labor grows at rate (ga +gw) culput is. growth insteady , state must also equal (ga + gn) The same applies to capital.. By implication the growth rate ofoutput is independent of the sacing rate. ,. When the steady state output per worker grows at the rate of technological progress. economy is in L , ↳ balanced growth  · Dynamics -> Increase in savings ↑s We are with Solow Model the basic model for technological dealing , which is the long run , but without progress. It takes into consideration two equations : production function : = F() and the capital accumulation equation , where the change in capital per worker is equal to investments per worker minus necessary investment per worker. graphic investment per worker (sX In the has the same shape as the production function - however , it , ends up being lower by s(the saving rate between , Oana1). The investment per worker increases with UN , but by less and less as capital per worker , as there will be decreasing returns to capital. Steady state- graphic the point A represents where the economy In the , is starting at , and it represents the steady-state equilibrium which is where the capital per Worker (t) , and output per worker equal to (*) the In point A the investments per worker are , equal to necessary investments per worker + steady-state equilibrim. Therefore following the capital accumulation equation , , in the long run , a change in capital per worker is equal to zero , and there is no growth of /N and "N in the LR. AU = SX-d N / The 0. 1. saving rate has no effect on the long-run growth rate of output per worker , which is equal to eventually the economy converges to , a constant level of output per worker. In the long un , the growth rate of output is equal to zero , no matter what the saving rate is. The saving rate also determines the leve of output per worker in the LR I  ⑮ the function giving saving / investment per worker as a function of capital per worker shifts upward from sof() to sif(). At the initial level of capital per investment worker() , exceeds depreciation capital per , so worker increases. As capital per worker increases , so does output per worker Un economy goes through a period of the positive growth When and so. capital per worker eventually reachesIn investmentisagainevaltodepreciation, andgrowthendsFromthe,theeconomyremainsatt. Y/w is initially constant at level Yo with an increase in the saving rate , autput per worker increases temporarly , until it reaches the highest level of atput perworker (*) , which will lead growth to 0. Here there , is a level effect but , no growth rate , with " and Yn at a higher level , with point B being the new steady-state. Decrease of S We are with Solow Model the basic model for technological dealing , which is the long run , but without progress. It takes into consideration two equations : production function : F() = and the capital accumulation equation , where the change in capital per worker is equal to investments per worker minus necessary investment per worker. In the graphic , investment per worker (sX has the same shape as the production function-however , it ends up being lower by s(the saving rate between , Oana1). The investment per worker increases with UN , but by less and less as capital per worker , as there will be decreasing returns to capital. Steady state- the In the graphic the point A represents , where economy is starting at , and it represents the steady-state equilibrium which is where the , capital per Worker (t) and output per worker equal to (*) the In point A the investments per worker are , equal to necessary investments per worker - steady-state equilibrim. Therefore following the capital accumulation equation , , in the long run , a change in capital per worker is equal to zero , and there is no growth of /N and "N in the LR. AU = SX-d ↳ with decrease in the rate from So and S the investment per worker function shifts a saving - , Down from So (*) to Sn( * )  whereforo acertaincapitalperwother( atthatpointinvestmentislowerthandeprecatn e , per worker decrease consequently , output per worker/GDP will also decrease making the economy suffer - , a period of negative growth temporarly. ↑ r We are with Solow Model the basic model for technological dealing , which is the long run , but without progress. It takes into consideration two equations : production function : F() = and the capital accumulation equation , where the change in capital per worker is equal to investments per worker minus necessary investment per worker. In the graphic , investment per worker (sX has the same shape as the production function - however , it ends up being lower by s(the saving rate between , Oana1). The investment per worker increases with UN , but by less and less as capital per worker , as there will be decreasing returns to capital. Steady state- the In the graphic the point A represents , where economy is starting at , and it represents the steady-state equilibrium which is where the , capital per Worker (t) and output per worker equal to (*) the In point A the investments per worker are , equal to necessary investments per worker + steady-state equilibrim. Therefore following the capital accumulation equation , , in the long run , a change in capital per worker is equal to zero , and there is no growth of /N and "N in the LR. AU = SX-d At initial depreciation represented it's where investments per worker , in point A , are equal to necessary investm. perworker (Therefore,followingcapitalacumulation there in capitale equation , is no change as  up depreciation from G tor' there is a shift ↳ With a increase of , in the necessary investments per worker function ,. For E investments worker are lower than necessary investments (sx*** ) and it ends , per up , anegative change capital per worker. causing in The economy goes then through temporary period a of negative growth. /N o and eventually reaches investment is equal to depreciation - the period growth of ends. So now the economy stays t worker and the at new steddy-state point is at B with new atput per , Y/w is initially constant at level Yowith an increase of depreciation rate, , atput per worker decreases temporarly , until it reaches the lowest level of atput perworker (*) , which will lead growth to. 0 Here there , is a level effect but , no growth rate , with " and Y/N at Helowest level , with point B being the new steady-state. all lower leel. De to lower when there is an increase in depreciation rate , sizes go to investments are lower). capital /necessary ↑ O effect - no growth ↳ dk + timeline down udy Decrease in Depreciation &o We are with Sollow model the basic moded for lang m But without technological deaking , which is the progress # takes. inte consideration two equations : production function :) and the capital acumulation equation , where the change in capital per worker is equal to investments per worker minus necessary investment per worker. In the graphic , investment per worker (s has the same shape as the production fatio-hour , it being love by ) the rate between Dama) The investment worker increases with emds up saving ,. per W , but by less and less as capital per worder , as there wil be decreasing returns t capital.  Steady state- the graphic the pointA represents In the , where economy is starting at and it represents the stedy-State equilibrium which is where the , capital per Worker () and output per worker equal h) the In point A the investments per , worker are equal to necessary investments per worther stedy-state equilibrium. Therefre , following the capital amuation equation , in the langrun , a change in capital per worker is equal Ho zero , and there is no growth of/ and in theR. A ↳ trocar explicação ↳ positive growth Extensive Solow Model · Increase in Savings Ms B > - Here we have the extended Solow , A Model which is the basic model with the addition of technological progress Cletter Al. Extended model has 2 functions : the production function y F(k = , AN because we Eassume that tech ↓ progress is labor per effective worker(increasing labor productivity ( intensive and we also include the growth rate of technology (ga) and the growth rate of population (gn). making the new change in capital per effective worker being * =S X (d ga g) - + + Here change in capital per effective worker is equal to investments per effective worker minus , investments per effective worker. necessary In the investment per effective worker graphic , (s) has the same shape of the production function ( = F( *). However , the difference is that inv. per effective worker is lower due to the savings parameter (from To , 23). With 4/AN , investment increases , but with less and less increas K /AN-there returns to as is decreasing capital.  In point A in basic model we had A = 0 , but now it's D S that growth rate ga)x which means (G , SX( + 0 YAN of its not anymre = + gn = zero , AN > - g 0 = Point A it's no longer called steady-state , and it's because growth isn't 0 anymore It represents Balanced. Growth Rate with capital per effective , worker- and atput per effective waker ( · In steady state the , growth rate of output dependsay on the rate of population growth and the rate of technological progress. In point A , with the initial saving rate(s) , investments per effective the worker are equal to the necessary in necessary investments per effective worker (s(d + ga gr(x) + So , following CAE , the change in capital per effective worker is equal to 0. Defining growth Y/AN YAN. as the change divided by initial state , in the long n there is no growth of and I not the slope not gy and + s on - worried about growth = ga = ga gr no growth led effect higher savings capital moreEDP keeptheseeste : > - more - - ③ e with effective worker function shifts up to sext an increase in the saving rate from so to se , the investments per Therefore for now investments per effective worker higher than necessary investments are , , pereffectiwarkeThere is posigrothinAnanditincreasesConsequently,increasesA is represented by point B. Changes in the saving rate don't affect the steady-state growth rate. But changes in the saving rate do increase the steady-state level of cutput per effective worker An economy in which there is technological progress has positive growth rate a of atput per worker , even in the long run. This long-run growth rate is independent the saving of rate. ⑮ explain model investment effective wark. per shiftsup from so to 51... trocar palavras  m of 5/ga/gn - - Here have the extended Solow Model which the basic model with the addition of technological , we , is progre Cletter Al. Extended model has 2 functions : the production function y F(K = , AN because we -assume that tech is labor progress ↓ per effective worker intensive (increasing labor productivity ( growth rate of technology (ya) and the growthrate of population and we also include the making the change capital per effective worker being new in Here change in capital per effective worker is equal to investments , per effective worker minus investments per effective worker. necessary In the investment per effective worker graphic , (s) has the same shape of the production function ( = F( *). However , the difference is that inv. per effective worker is lower due to the savings parameter (from To 23) ,. With 4/AN , investment increases , but with less and less increase as Y/AN-there is decreasing returns to capital. Point A it's no longer called steady-state , and it's because growth isn't O anymore It represents Balanced. Growth Rate with capital per , effective worker- and atput per effective waker ( · In steady state the , growth rate of output dependsay on the rate of population growth and the rate of technological progress. with the initial dor ga orgn investments In pointA , , per effective the worker are equal to the necessary in necessary s not on the slope - not worried about growth per effective warker s (d gr(x) growth no investments' ga = + + leve effect higher savings the capital moreEDP keep slope : > - more - - (no growth ( So , following CAE , the change in capital per effective worker is equal to 0. Defining growth Y/AN YAN. as the change divided by initial state , in the long on there is no growth of and I and gy + = ga = ga gr ↑ & ga Igr with the increase d or investments effective worker unction shifts up ga o of you , necessary per (d g) (d ga) ande mica >from + ga + to + ga + - So , for the E and given necessary investments per effective worker are higher than investments per effective , worker (s x (d gatgn)So with the CAE there's , + change in capital per effective worker is , a , negative So a decreases. ,. With the increase of 6 or ga andgu capital per effective worker are higher than investments , per effective worker (s An An ③ B+ new equilibrim : Sx = ( g + + ynx = 0 D nogrowth rate After tec effect but. progr Ga. has leves no growth on GDP per effective worker. YgA has level and growth effect on GDP per capita and total  /ga/go ↳ of model above -- explaining E > With a decrease of S/ga/gn - the