Transcription of Chapter 7: Solow Model I
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Chapter7:SolowMo delI11 TheSolow-SwanMo ductionfunction:Y=F(K,L) =K L1 Outputp erworker:y YL;capitalp erworker:k KL;consumptionp erworker:c CL;investmentp erworker:i L1 YL= (KL) y=k C= (1 s)Y CL= (1 s)YL c= (1 s)yI=sY IL=sYL i= :A= opulation/lab orforcegrowth:L= ,constantsavingsrate:s= ,constantdepreciationrate: = :G=T= :X=M= 0G=NX= 0 Y=C+ ck Capitalgain :investment,i=sf(k) =sk Capitalloss :depreciatedcapital, kLawofmotion(discretetime): k=i k=sk ki < k k <0i= k k= 0i > k k >01 Econ302,Week9,10/30/2009; (Equilibrium)Steady-stateintheSolowmodel :inlong-runequilibrium,capitalp erworker(thecapital-lab orratio) :thefollowingequationde nesasteady-stateintheSolowmo :sf(kss) = kss kssf(kss)=s (1)Cobb-Douglascase:sk ss= kss kss= (s )11 (2)Ifthissteady-stateconditionholds,the owsinto(investment)andoutof(depreciation ) < kss sf(k)> k k >0k=kss sf(k) = k k= 0k > kss sf(k)< k k <0 Steady-statequantitiesasso ciatedwithkss:yss,css,iss(k :y ,c ,i ).
The Solow model predicts that countries with higher rates of savings and investment will have higher levels of capital and output/income per worker in the long-run, eterisc aripbus . How to increase k ss, and therefore y ss? 1. Increase s: s")k ss")y ss" 2. Decrease : #)k ss")y ss" Golden rule apital-labc or atior : The level of capital per ...
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