Question

Describe

1. Should poor countries grow faster than rich in a Solow model? Explain

2. Explain how changes in i. population growth rate,

ii. saving rate,

iii. technology growth rate change the stationary state in a Solow growth model.

Answer 1

unological insule progress, golden sale criteria Progress criteria de for steady arth techno gets modified state ĉ z fco- s A* 2 f ( R*) - 3f ($* J 2 * = (ha) - Estate Inv = Breake Diff. Wogit lite ga dat = o MPR - (st ntg) * max = CS+n+q) Steaty State Output Pet ff berikan In. BE TW Stutg) 6* kt gold Steady state capital Stack Per Effective wake.kt

so we can lorite depreciated capital ESÊ. mus Suppose that technological progress growth rate is grow steady state equation as – (stntg) f (R* The term (stntg) Ŕ refers to break even investments and it even has investime 3 components - 1) Investment is req'd to replace depreciated capita 2 Investment is read to provide you workers withe capital (nk). 3) Due to improvement in efficiency, more capet req'd for effective (ga in efficiency, more capital is workers the minimum amount of Evestment which is reald to keep capital stock per effective worker Sine at steady state, there is we waker constant, will be (Stntg R constant, will per - there is no change in capital stock no change in ve worker, so it implies that I at steady state, arvestment is equal to break even investment: .. # Effects of Technological Progress Technological progress, solow Model explains sustained growth in standard of living (ber cahita GDP/ output per wakes even at abitat Steady state. This is because with stock technological progress, capital ste per effective worker remains constant but aggregate stock of capital increases @ Cntg), while capital stock per worker increases @ g. Similarly at steady state output per effective worker remains constant But, total output of the Clonomy Ci/upp) increases @ Entg), while output per worker (y) (per capita GDP) which determines standard of living increases @ g. - therefore, according to Solow Model, only technological progress can explain sustainable growth and permanently rising living standard

in in in gress wheuate technological h iate Production functit Solo Solow binukelat Model, we can write function as - YzFK, LXE) vartal new to the here estable called officiency of it broduction methods worken i It reflects know As auntable technis labour labour rises. i it takes a to knowledge about production He technology improves, efficieny a XE measures the no of effective key of in legekas And efficiency and but total output (7) defends on id effective workers. This lective workers and it takes into d each worker. This new production de nds on total capital stack (R) and form of technological progress is called it total output. This I technological into allout o function tein Gabon augmented progress because it increases is increases ker Bividing this prod" funtion by LXE , we can efficiency It means that output elective worker. Since ru growth t output per effective worker depends on capital ben worker. Since, technological progress is labour ! population grow alow so its effect is similar to augmented # Stady state with Technological Progress AR = Investment - (st nt g) kl - sk = sf (k) - (S + not a (stnta - (8tn olfbut bereff worker SPCR *) = (Stnt Stntg Stutg (Rt) - ----

de choose economy's with canomy a are that - Transition to golden rule steady state We have been asturning that the policy maker simply choose Steady state and d jumped then jumped then immediatel immadiately. In this case, would a b choose steady state with highest con But now suppose that, lunomy has reached a stead. golden rule. what happen to consumption inventou o the other 'eronomy makes the transition between a en steady states ? Case I starting with too much capital Steedy State authut for worker highest consumption le has reached a steady policymaker golden sule state other stene i investment to and ouped when Det Sk* Sy se syt esf(x) Time Pericord C ho Consider a case in which economy begins at steady state with more calibal as compared to golden nule steady state. In that case, gout will try to do saving rate in order to reduce capital stock. Suppose that, gout poliny succeeds in reduing saving rate at some point of time to. It means saviup nate decreases to the level that will lead to golden rule. The role in saving rate causes an immediate ine in cons and dee in inv. Since in and dep were equal in the initial steady state, so now in. will be Tess than dofn. It means that economy is no longer in a steady state Gradually capital stack deneases leading to reduction in output As a result, cons and in will also reduce. These variables will Continue to fall so that economy reaches new steady state Sime, we are assuming that new steady state is a golden nule steady state. so cons must be higher as compared to its previous value. Althason autput and in. I will be lower

- Starting with too little cabital - Strady Fate Output fer worden w + (+) Time Perud Steady Luc Capital State less when clonomy begins with govt will try to increase save in stock order to inc. capital Inc. in investment. Since As a result, stock of capital Enge Will in. in capital stack, outbut I Since new steady state is with less capital as compared to golden rule t o increase saving rate undy state ano rate sarring rate Jincrease in Causes causes I stock. immediate immediate dech decline in cons and since, investment increases, so now inv. exceeds dedim.. It stock of capital Encreases over time due to higher investment ranited stock output, cons and ine gradually increases steady state is golden mile steady state, so consi as must be higher compared to its previous value. Step 2 - Population Growth dep". due to Rough work - L² Loo k = 10 Kz 1000 8- loy = 0.1 y = f(K) Y= 100 100+50 2150 Nz Pof growth 5% Le 105 k²10 Kz 1050 y=80) Ya105 a 15% ý los mst. E(Stnr 3 due ton Break-even Investments by inc at the rate of n.

model shows that capital accumulation by itself cannot sustavied economic growth Higher rate of savings lead to higher temporary Gonomy eventually atteins steady lett a capital per worker to explain siistained on of economic growth i.e. pop growth and technolo cannot explain higher growth, bukan outbut per worker and tuce two souris del i Prapon growt stock per worker sustained economic growth, we introducet growth and technological progress. of economice In this section, we add pop growth to the model. Plats with investment and depreciation influences capital stock ben ng with pep growth, Capital stock per worker decreases dusker two reasons - 1 Deph reduces capital stack (8R) 2) Ine in labour Force reduces capital stock ben walker (ne). the other hand, capital stock ine due to investments. Therefore, ch capital stack per worker can be written as a Ak = Investment - Sk - ne z asy - (Stnk Dk = f (E) - (Stnk where (Sta) k = Breaks Break - Even Juw is the amount of inv, reau'd to keep capital stock be Warker constant. It includes depn of existing capital and amount of in necessary to provide new walkers with capital. Therefore, at stand state, there is no change in capital stock per worker because in is equal to break even lnu. At steady state, Akzo. y-fley a sf (kt) = (8+ n) k* Stn (CR) But be worker BET - - - 0.04 + laxy of - utho.o +- 0:12+ 3n = 0.24 3n = 0.12 na 0624 300 25 tee 25 effect of Pof Growth Pas growth Changes basic solow model in 3 ways - It brings us closes to explain sustained economic growth In the steady the with pefn growth, capital per worker and suspect her worker are constant

me growing at the rate of n, total capital stock in must also be growup at the rade an al capital stock (k) As the no of workers (%) must and total output o are another explanation for why why one countries are some nsider the effect of change in pep some poor. Consider the countien countries 2 Pop" growk gives us sich and some con effect of cho are stock ben worked model shows that growth Due to this, steady state cah will change. Therefore, 80/ and output per worke colenties with higher u pop growth rate we must note that capital per worker a ate will have lower level of per capital as ute that change in pop growth rate will have level uker and output per worker just like chane note will have lust like change level effect on in Sairine rade. steady state output po. - 1 BE (8tnk - y = f(K) sy = 88 kB 3 pop grouth effects criteria for golden rule level of capital y = cti y = f (RM) tot nhaty et = f (k*) - sf (kit) (+= f(k*) - (Sth) k* Diff wirt k* MX-( - Syt e f (KM) MPR z8tn

Il Claas in Solow Model Technological Proglem Rough work om ( - > (st > K - 10 K-100 E-1 nə 5% Ez1.5 8 - 10% g = 50% Slysator +50 + 500 2 650 650 = 65% 10% 5% 50%. At steady State, î D R = Investments - (St ntg) k Break Even Jweatment DR - sý - (st ntg) k AK? Soll (Stn g3 RzK/E Ř - At steady state LXE L increases @n sg= (St utg) E inueason @ Stinty Stnto F (RA) Y = F (k, LXE) 2} = F (2K, 2L XE) z = // LXE Lincreases @n Y/LXE = F (A LE & in @ g 9/E² F (K/E,!) (LXE) ine @ (ntg) E in @ g yine @ (ntg) At steady state, S 2 * y ine@g Y sluk ine @ (tg) y Ar in @ g.

State and steady level of Capital & Growth In capital Stock at determines output a A these changes lead Lital stock i.e. inventar but and equipment and wearing out of ald charge in capital stock factor is an important that the At any moment, capital stock an economy But, capital stock time and those can change over economic growth In particular, two forces Enfluences capital stock and depreciation here Investment refers to expenditure. On new plant and it causes capital stock to rise Depreciation refers to Wearin equipment capital and it causes capital stack to decrease. Therefore, charre in to is determined by difference of investment and depreciation. AR ² Investment and Depreciation ů - Sk Ak sy - Sk - Sk At steady state, there is no change in capital stock because invest equal to depreciation. That is, Akzo oz sf (6) - Sk* of (ko) - Sk* le Ak = AR e ( Steady state is significant because it represents long sun equilibrium economy. It shows that regardless of level of capital with which economy begins, it ends up with steady state level of capital. y = f(K) - Sk - Deph A i nxga eft

Golden Rule Level of capital The steady state value of capital that worker is called golden rule level of by Regold. To find steady state national income arounting - maximises consum capital and it ? cons per worker, we u onsumption per and it is devoted y z ct N N czy- i C = f(K) -sy c = f(K) - & f(K) It means that cons per worker is difference of output per worker auto investment per worker Sime, we want to find steady state consun so we substitute steady state values of investment and output As we know that, at steady state investments must be equal to debreciation, so steady state Consben worker can be written as - c* = f (k*) - sf (k*) C* = f (k*) - Sk* Ale to this egin, steady state cons is what is left off steady state output after paying for steady state depreciation. This egin also shows that an increase in steady state capital has two opposite eller on steady state consumption. One on hand, more capital means more coutput and on other hand, more capital means that more sulfat must be used to replace depreciated capital. Therefore, cons per worked to maximised when Marginal Product of capital is equal to des

UML | Economic lyrowith Models - # Solow MODEL The accumulation of capital g- output / worker ko capital per worker so sairnp rate c - Consiunktion ow growth in capital stock, growth in o gy Interacts in an economy and how they economy. We will build solow model in It is designed to show how growth in capital labour hour and advancement stock, go in technology Enteracts in an economy a affect total output of the economy. We will series of steps. In the first step, we examine In subbly and demand of how supply goods determine accumulation accumulation of of une capital. cabital. In step, assume we this In the that lavour foue and technology are fixed. supply of goods and Production Function Supply of Goods in solow model is based on production function which on states that output depends capital stock and labour force 1.e. Y=f(k, L) The model assumes that production function has constant returns to scale which means that of all inputs are increased in a given fixed proportion, then output will also increase in the same proportion lie. Y = F (L,K) ZY F (2L, ZK) let z=/L Y/L z F (1,K/L) y = f (1,k) y z f(k) where yz output per walker k kapital per worker y = f(k) This means that output/ worker is a function of capital per worker and due to diminishing returns, proda huntion gets flatter as capital per worker increases. The slope of production function measures marginal product of capital per worker EMPH)

Diff wrtk ya 10 Rick MPR = rope of prodfrum" - > o f"(k) <0 Dimininishing Ret Demand for Goods and Consumption Function, In solow model, demand for goods comes from co atment. It means that autput per worker is divided hepher onsumption per worker and investment per worker i e The model assumes that a fraction of income is saved f remaining fraction is spent on consumption Thereton consumption function can be expressed as we Substitution of cons frume in eqr - ① o ugh syl It shows that investments are equal to savings. function and consumption function are two main • Salow model 4 Therefore, broduction elements a in sy a sf(x)
Answer,

Solow Growth Model

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