Solow Growth Model (L4)

Question 1

Solow model

Answer 1

capital is not fixed anymore, looks at long run growth
dynamic model (changes over time)

Question 2

savings St

Answer 2

savings rate x output/income
s x Yt = St = It (Investment)

Question 3

consumption

Answer 3

(1-s)Yt

Question 4

GDP/Yt =

Answer 4

consumption + saving assuming all savings are invested into capital

Question 5

resource constraint

Answer 5

Yt= Ct+It

Question 6

capital stock accumulates with…

Answer 6

increases with new investment
decreases when capital depreciates

Question 7

change capital (delta Kt)

Answer 7

Kt+1 -Kt = It- depreciation of capital

Question 8

how can we find W and R

Answer 8

using graphs dynamic solution

Question 9

optimal point for economy

Answer 9

when delta k=0 check notes diagram

Question 10

steady state

Answer 10

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

Question 11

steady state formula

Answer 11

(sA/d)^1/1-a= steady state capital =K=k
Y=A(K)^a(L)^1-a, sub in formula above

Question 12

golden rule level of capital

Answer 12

consumption is maximised
resource constraint C=Y-I
C= F(K,L)-dK*
dC/dK=0=MPK=d

Question 13

when k0>k*

Answer 13

saving rate must decrease so consumption increases, investment decreases

Question 14

formulas to memorise

Answer 14

Yt= Ct+ It
Kt+1- Kt= It-dKt
It=sYt

Question 15

Steady state level of capital

Answer 15

(sA/d)^1/1-a

Question 16

Steady state level of output per capita

Answer 16

y*=A^1/1-a x (s/d)^a/1-a

Question 17

when labour is fixed, what is change in capital

Answer 17

I-dk when change is 0
I=S
S=dK
sY=dK

Question 18

when savings rate increases what happens to consumption and output

Answer 18

consumption decreases
steady state output increases

Question 19

how to maximise consumption

Answer 19

kgold maximises consumption
(Axa/d)^1/1-a x L
MPK=d

Question 20

why are saving rates different across countries

Answer 20

taxes
retirement patterns
political stability

Question 21

how to calculate savings rate

Answer 21

sgold= dK*gold/Y

Question 22

how to figure out K0 before it gets to K*

Answer 22

(s0/d)^1/1-a
k0-k*= how much k must reduce to reach sgold

Question 23

how to evaluate what consumption path consumers would want

Answer 23

sum of B^tlog(Ct)
B=discount factor for how impatient consumers are

Question 24

when taking into consideration population growth, what is Lt+1

Answer 24

Lt+1-Lt=nLt
change in Lt/Lt=n
n being population growth rate

Question 25

output per capita

Answer 25

yt=f(Kt/Lt)=f(kt)

Question 26

change in capital when L growth is considered

Answer 26

i-(n+d)k
I/L-(change in L/L +d)K/L

Question 27

break even investment

Answer 27

amount of investment needed to keep capital stock per worker constant

Question 28

constant k* when labour growth is considered COBB DOUGLAS

Answer 28

sA(k)^a=(d+n)k
k*=(sA/d+n)^1/1-a

Question 29

what happens when there is higher population growth (n increases)

Answer 29

steady state level of output per worker falls & steady state capital

Question 30

maximising consumption with population growth

Answer 30

MPK=n+d