Endogenous Growth Model

Notes on Macroeconomics – 3Revised on September 21, 2007first order condition isIf we guess the dynamics of1tcctand kt + 1astA= β . (3.20)ct+1ct= α(3.21)Atktkt( α )= + 11 − Akt t, (3.22)where α is an undetermined constant with 0< α < 1, by using (3.20) we can have thefollowing policy functions:ct( 1 β )= − Akt t(3.23)ktβ Ak= . (3.24)+ 1 t tNote that on the balanced growth path, the growth rate of economy isg = g = g = β A − 1, (3.25)y c k tso the economy will grow at the rate of β A t− 1 under the condition β A t> 1. If A tisgrowing, the growth rate of the economy will be also increasing over time. ForA = A, i.e.tthe technology factor is time-invariant, then the economy will grow forever at the rate ofβ A − 1. In addition, the saving rate described by the impatience parameter β has theinfluence on the growth rate. Furthermore, under the assumption ofAt= A, repeatedsubstitution using (3.24) givesktt+( β A) 1+ = k1 0orktt= ( β A) k0. (3.26)Thus, initial capital stockk 0has a permanent level effect, so economies with different6/16