Question

all but part a

2. (Population growth and technology growth) Consider an economy that is described by the production function Y depreciation rate of capital is 6 n 0.05 and the technology growth rate is g = 0.1 K (LE). Moreover the 0.15, the population growth rate is (a) What is the per effective worker production function, that is y ? What is the marginal product of capital, that is ? (b) If the saving rate is s 0.3, find the steady state level of capital per effective worker k*. What is the steady state level of consumption per effective worker c ? What is the steady state level of investment per effective worker i*? What is the steady state level of output per effective worker y*? (c) Find the golden rule level of capital per effective worker k, i.e. the steady state level of capital per effective worker that yields the highest steady state consumption per effective worker. Find also the golden rule consumption per effective worker level c that corresponds to this capital per effective worker and compare it to the one in question b. higher than c*? LE Is (d) Find the savings rate so that guarantees that we will reach the golden rule capital per effective worker k. (e) What is the growth rate of GDP per effective worker in the long run? The growth rate of GDP per worker in the long run? The growth rate of aggregate GDP?

Answer 1

0 2) Giveni Y - KV2(LE)"2 ; 8- 0.15, an=0.05) 9-0.1 a) y = K V2 (LE) 2 Dividing betti wis and RHS by LE, - ()!! o tie per effective worker production not fuition. which is the per non Now, MPR = By = 2 angol n go not iven by: bawer national 0.3) 6 Now, change in capital DR is given by: kraves DR = & f(k) - (S+n+gk 1+1 = $0.361/2-(0.19 + 0.05+0.0) [ 0.3612 - 0.3k Setting Ak=0 0.3k/2=0.3k : Now, alt = f(KA) – (stntg kt a 2 teš 1 - (0.3). 1 spalat sor, et =0.7 ! y = f(RA) = D o Golden Rule level of capital per effective wonhar is the level of capital that maximises consumption per effective wonher, ie, the level of capital where

Houes et = **Y2 - 03R* Now, ou = 1 RX-1/2 - 0.3 Setting on = 0 Rx > **Y2 = 0.3 or, Kis k*12= 0.6 - b or, R 0.6 Now, ağ = re* (p*g) = 10,832) Clearly, eng = 0-834 710.7 zi* :) We have: Cristy), ang 0.3 **1/2 Il 0.3 or k 1/2 = e IM ov, Ag - (E9)120.3 -0.5 ý = k1/2 (fran (0) logaritham and diffenentiating wont. 't, alooh/y = 1 dloge Ik kan I which is the growth rate per effective tabour, and it of GDP effective depends on the capital per labour. Will

Ayalu, Y-K (10) ((5) or, y = k1/2012 . Vaving Wywill чу у " sat Diferentialing w.virt . por about re, Cor growth vale per latou depends on bolu, growth val of capital, & efficiency of labour. Ay Now), y = k12 (LL)/2012 Toning lopnitten logy - I logk & I logh te loge pily routaling w it. b) 1.0, aggregate GDP groudth y growth rate of growth rate of depends on: capital! bebouw, & growth rate of efficiency.