Question

pls solve parts f,g,h

Suppose Country X's initial capital per effective worker (K/AN) ratio is 16, while Country Z's initial capital per effective worker (KAN) ountries have the same production function: F(K, A,N) = 10K, 5(AN)05 (a) Derive the output per effective worker. The evolution of the capital stock is given by K +1 = (1 - 6)K, + I, where is the depreciation rate. (b) Derive and show that in the long-run growth model, the steady state capital per effective worker needs to satisfy: (6 +84 +8n)(KIAN) = $10(K/AN)05 where 8, is the technological growth rate, gn is the population growth rate and s is the saving rate. Country X has a 10% saving rate, 4% population growth rate, 5% technological growth rate and 11% depreciation rate, while Country Z has a 15% saving rate, 3% population rate, 7% technological growth rate and 20% depreciation rate. (c) Calculate the steady-state capital per effective worker (KIAN) for both countries. (d) Does the initial capital per effective worker value affect the steady-state capital per effective worker? (e) Calculate the steady-state output per effective worker (Y/AN)' and steady-state consumption per effective worker (CIAN) for each country (1) Which country has the highest steady-state output per effective worker (Y/AN)"? (g) Which country has the highest steady-state consumption per effective worker (CIAN)? (h) Using graphs and your values from parts (c) and (e), explain if Country Z's capital per effective worker will catch-up country X's capital per effective worker.

Answer 1

0.5 6) Y= lokte scaun. Jos X=015 X= 0.5 NO ive de calitate (output per effective workes) = 10kos (ANC) Ons - ANE => 10 KAOS AL NE-0.5 = lo k º's AiNeons = 10 ( hits jos HEN R = kt . AENE (Capital per effective worker) gjet lo t of laße) effective So, the steady steete level of output pesticostes depends upen steady state revel of capital per worker. We know that, in steady state level → → coepitel per effetive woskes in steady stated ģ * > Greepee pes, effectiv G* = lock thos * worker in steady e 7 state 1 - V Scanned with CamScanner

County x S= 101, Ja = 54 In=40% 8 = 114 0.5 Country z S = 15:1. ja = 71. X=0.5 Jn = 34. 8 = 1904 Ir 151 Id- 7.+37 + 20 = lor yo 5%+4% +114. > 10x1/2 = 5 = loxile = 5 Ji* = 5. Both county have highest same steady - State output -pee- etfective wrskes. consumption per effective nos kes ANt we know that es Y = 4+ It It = syt le Scanned witbex = (1-5)Yt camScanneft

level of consump Hos pel worker Steady-state will be de Cou E = (1-syge county x S=107, V = 5 a = (-1010.5 County z CX* s=154. = 5. av = (-154.). 100-15 - - XS 190 XS 100 XS Cu = 4.5 = 85xs = 4.25 100 = 4.25 consumption County X has highest steady - state pes - effective worker. which is 4.5 Scanned with CamScanner