Solow Growth Model (L4) Flashcards
Solow model
capital is not fixed anymore, looks at long run growth
dynamic model (changes over time)
savings St
savings rate x output/income
s x Yt = St = It (Investment)
consumption
(1-s)Yt
GDP/Yt =
consumption + saving assuming all savings are invested into capital
resource constraint
Yt= Ct+It
capital stock accumulates with…
increases with new investment
decreases when capital depreciates
change capital (delta Kt)
Kt+1 -Kt = It- depreciation of capital
how can we find W and R
using graphs dynamic solution
optimal point for economy
when delta k=0 check notes diagram
steady state
when K, you stay at that point of capital
when investment=depreciation
sY=sA(K)^a(L)^1-a=sK
when k=0 is another steady stat, but K is the only stable one
steady state formula
(sA/d)^1/1-a= steady state capital =K=k
Y=A(K)^a(L)^1-a, sub in formula above
golden rule level of capital
consumption is maximised
resource constraint C=Y-I
C= F(K,L)-dK*
dC/dK=0=MPK=d
when k0>k*
saving rate must decrease so consumption increases, investment decreases
formulas to memorise
Yt= Ct+ It
Kt+1- Kt= It-dKt
It=sYt
Steady state level of capital
(sA/d)^1/1-a
Steady state level of output per capita
y*=A^1/1-a x (s/d)^a/1-a
when labour is fixed, what is change in capital
I-dk when change is 0
I=S
S=dK
sY=dK
when savings rate increases what happens to consumption and output
consumption decreases
steady state output increases
how to maximise consumption
kgold maximises consumption
(Axa/d)^1/1-a x L
MPK=d
why are saving rates different across countries
taxes
retirement patterns
political stability
how to calculate savings rate
sgold= dK*gold/Y
how to figure out K0 before it gets to K*
(s0/d)^1/1-a
k0-k*= how much k must reduce to reach sgold
how to evaluate what consumption path consumers would want
sum of B^tlog(Ct)
B=discount factor for how impatient consumers are
when taking into consideration population growth, what is Lt+1
Lt+1-Lt=nLt
change in Lt/Lt=n
n being population growth rate
output per capita
yt=f(Kt/Lt)=f(kt)
change in capital when L growth is considered
i-(n+d)k
I/L-(change in L/L +d)K/L
break even investment
amount of investment needed to keep capital stock per worker constant
constant k* when labour growth is considered COBB DOUGLAS
sA(k)^a=(d+n)k
k*=(sA/d+n)^1/1-a
what happens when there is higher population growth (n increases)
steady state level of output per worker falls & steady state capital
maximising consumption with population growth
MPK=n+d
