Question

4) Suppose that scientists are unable to reverse climate change such that a nation's physical capital depreciates at a faster rate. Use the Solow Model to show the likely outcome of this phenomenon on this nation's long-run steady state level of output. Include an explanation of the transition, if there is one. Is there a growth effect? Is there a level effect? (8 points)

Answer 1

Balanced Growth Path In terms of long pun Eqh, it means where all endogenous vartables grow at home constant rated This Growth rate could be 2010 for some variables when the growth rate is zero, it is called steady state Steady state is a special case of the balanced Growth fath ! Assumptions Closed economy with a single commodity used for both coniuumption ļ invest inenti At the beginning of tlore period t, endowment of lab N4 cap by Rt - There are 4 identical households. All labour and capital ownership u equally distributed across all households → Households are offering labour & capital to fins- These are offered in elastically 7 The fusing are perfectly competitive. They are producing goods & distributing oft Total oft or total income & distributed to the households at the ind 4 period . - -

Yt! _U FLNG, Kt) NE Nt :- . . 1 . As we know, yo = F (NO, KL) FINE, Kt)is. yt: Nt = Ntfert) _ Mp pat N4 • f'(RE) [NCO)- K41)) + f(R) (1). :- f'ckt) Ere) + f(t). oleh f (Red – Re f'Lee) the ? CRE_) - King + $(R$):10) == f'(ke). I fo):0 This indicates that capital is cesential ONE akt -- --- . input in production ---- - NE Prett Keti Ntri - 8F (Nt, Kt) + (1 - 8) Ke Net Robil s SE (Nt Kt)+(1-8) kt 14 ) N

sfikt) & 18 Rt- Citn itn nt Delta Itn BE SS (Non erial) Sf (Rt) +(1-8). ht: Citn). at steady state, ketti Re Reken g(0) = Sf (0) + (1-8300 gekt).: Ton [&f'1A) +(1-6)}-20 g". Cet) - 8f"(R2) <0.- Triviat Rib) to There are two posible steady states 9 R20 trivial s5 (ū) du k* Non trivial cs _ We can ignore the trivial es because the economy always has a positive amount of capital and labour at the starting we always lassume that economy will start at Ilome positive k ratio hence we can nou the thiocial SS: I L . Note that ke le globally stable. It means that we can start with any & latio and we will always reach. Implication : In the long run, per capda output; 4= f(Re) will be constant at filthy while the aggregate output Yo = Neflikt) will be growing at the same ral as Ne=n At the steady state, Rieti Re Reti EV SACRp) + (1-8) ktor hut = $fCkt) + U-SI RE In

tong i-felpe (1-5) At Itn 1.4.2** > 0 Ok som .. 1, 2, 3 ame level effects In the socowian economy, the percapita income does not grow in the long run. l. On the other hand, the long run growth rate of the aggregate output in the socowan iconomy & always equal to n . Hote. There is no role for the gent in influencing long run growth rate here. In particular, if the ... geht tries to manipulate the savings ratio for ex: through taxation, then such a poricy i would have no long run growth impact of what is happening in the transitional period? dus: When economy & out of the steady state, the of grouth of capital labour latio is giventy - R=Reri he Rale

asfert) + (1-8) Rtv-kt Itin off Cht) – (mtf) kt (Itn) kt Ret < R² kt? kt ke aka YR O RTO → MIN - .. - olis__ -siltn) L'fCk) - RAUL LO [altn) k]² During transitions, the lower å the capital laba ratio, higher " the short run growth rati! L ! Absolute convergence The transitional growth gate of 0 percapita income in poorer countrie Countries with low & ratio) will be higher than that of rich countries / highei k/ratio) and eventually tury will converge to the same level of per apita Reomet This proposition is strongly rejected by the dała bc I this is pre supposing that the under une para mas for all 'economis are the same conditional convergence Among a group of countries which are similare they win 7 sunilar values of in ands etc the elativeed poorer countries will grow faster and eventually, the ser cape income of all those countries will drurge. But this hypothesis is not neepful to ex eain the persistent difference in pod capita in one amon rich and poor countries 0