Question

2. Consider an economy which has the production function Y = AK03L07 The growth rate of the population is 0.01, the growth rate of productivity is 0.02, the capital depreciation rate is 0.06, and the saving rate is 0.24. In 2019, capital is 1500.0, labor is 10.0, and productivity is 15.0. In a yearly Solow growth model that allows for population and productivity growth), (a) What is the growth rate of output in the long run? (b) What is the growth rate of per-capita output in the long run? (c) What is the ratio of capital to output in the long run? (d) What is the growth rate of output between years 2019 and 2020? (e) What is the growth rate of output per-person between years 2019 and 2020? (f) What is the the ratio of capital to output in year 2019? (g) What is the the ratio of capital to output in year 2020?

Answer 1

The Solow growth model is designed to show how growth in the capital stock, growth in the labor force, and advances in technology interacts in an economy as well as how they affect a nation's total output of goods and services. In Solow model long run growth model is decided by the rate of capital accumulation and which itself is decided by the saving rate and depreciation rate in the economy. The higher the saving rate higher is the investment (Solow model assumes the economy is closed and ignores the government expenditure for this purpose).Below I have shown the calculation and basic Solow model's working.

(a) The growth rate of output in the long run in Solow model equals the growth rate of population and growth rate of productivity. Hence, it is equal to

0.01+0.02=0.03.

(b) The growth rate of per capita output equals the growth rate of productivity. Hence, It is equal to

=0.02.

Y = Topal Output I Investment ea consumption Y = I tu National Income Identify here, so savings rate I= SY So that the population part of Income and of Incorre which in Consumes some saves some part form becorres Investment lefit of stock and the growth in Il steady the state As mentored Above, Iis fikut Charge in lofifd stock Ak - Investorert - ($+m+ y ) k here u S = Debreciation rate of capital I nagrowth rate of population growth rate of broductivity

0.24x674.09 (0.06+0.01 +0.02) kn - 161.78 0.09 TK 1797.55 Output in the theation (3) in long run, Pest valine of election (2) 711.67 (c) retio of telifol to output in the long run = k* 19 1797.55 711 67 = 2.52 (1) growth rate of authut between Year 2019-20. L sY = KAK +12) DL + DA here, ao contribution of lelifel (1x) z lorfübution of Lober DA technological growth A V

12o. = 0ool 0.02 given Η SA Α 1 Dk from 2019-20 DK a SY - Sk -0.24 x 674.09 Dk z 161.78 sk = 71.78 1 - 0.06x 1500 -90 = 0.047 DK z K 71.78 1500 AY - 10:38 0.047) + (0-1) (0.01) + 0.02 = 0.014 +0007 +0.02 20.014 + 0.007 + 0.02 - DY = 0.041 2 4.1% growth rate from 2019-20

That is to say the more is the growth rate of population the more Glitch is releared for them to work with. And, the growth rate of productivity is incorporated is in the form of Lobor Augmenting tehnological progress. Hence the more is the growth rate of Population and technologice proqress the higher is the defriction of elifel. growth rate of duffunt in the long run Yp = Ap ko :3 Loo7 So 0.24 Kr 1500 f = 0.06 4 10 , n oor Aq = 15 9. 0.02 Speedy state Celital stock is such prel lepiped stock doesnt Change , Ak=0 AK = SY- migt 8 k 0: SY-mits SY = (n +gts) ka Y= 151500) C3 (10)07 Y? 15x8.97 x 5.0 Y = 674.09