More On Growth (L5) Flashcards
Growth rate of technology
At+1 = At(1+g) At+1 - At / At = g
Labour augmenting technological process
Effective worker
A x L
Capital per effective worker
K/ A x L
Change in capital per effective worker (law of motion) delta k or K/AL
i-(n+s+g)k
I/AL K/AL
n= labour growth
g= tech growth
s=depreciation
Output per effective worker
k^a
K/AL ^a
In the steady state, what do we know about investment and depreciation for effective workers
sY = dK
sub in values
sk^a =(d+g+n)k
Law of motion for capital per effective worker
kt+1 - kt = sf(kt) -(d+n+g)kt
steady state level of capital per effective worker
k*=(s/d+n+g)^1/(1-a)
Steady state level of output
y* = (s/d+n+g)^a/1-a
Capital per effective worker growth rate
0
Output per effective worker growth rate
0
Output per worker growth rate
g
output growth rate
n+g
when is consumption maximised
MPK= d +n +g
a(k* gold)^a-1= d +n+g
k*gold per effective worker
(d+n+g/a)^1/1-a
y*gold per effective worker
(d+n+g/a)^a/a-1
c*gold
y-(d+n+g)k
wage
MPL=(1-a)Axk^a
growth rate of wages
g
rental price of capital
MPK= a(k)^a-1
growth rate of rental price
0
capital growth rate
n+g
capital per output growth rate
0
labour share of income growth
g+n-(n+g)=0 (constant)
wage growth rate at a steady state
g
labour growth rate
n
golden rule for k* with technology
k*=(d+n+g/a)^1/a-1
golden rule of consumption
Kgold ^a -(d+n+g)kgold
