More On Growth (L5)

Question 1

Growth rate of technology

Answer 1

At+1 = At(1+g) At+1 - At / At = g

Labour augmenting technological process

Question 2

Effective worker

Answer 2

A x L

Question 3

Capital per effective worker

Answer 3

K/ A x L

Question 4

Change in capital per effective worker (law of motion) delta k or K/AL

Answer 4

i-(n+s+g)k
I/AL K/AL
n= labour growth
g= tech growth
s=depreciation

Question 5

Output per effective worker

Answer 5

k^a
K/AL ^a

Question 6

In the steady state, what do we know about investment and depreciation for effective workers

Answer 6

sY = dK
sub in values
sk^a =(d+g+n)k

Question 7

Law of motion for capital per effective worker

Answer 7

kt+1 - kt = sf(kt) -(d+n+g)kt

Question 8

steady state level of capital per effective worker

Answer 8

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

Question 9

Steady state level of output

Answer 9

y* = (s/d+n+g)^a/1-a

Question 10

Capital per effective worker growth rate

Answer 10

0

Question 11

Output per effective worker growth rate

Answer 11

0

Question 12

Output per worker growth rate

Answer 12

g

Question 13

output growth rate

Answer 13

n+g

Question 14

when is consumption maximised

Answer 14

MPK= d +n +g
a(k* gold)^a-1= d +n+g

Question 15

k*gold per effective worker

Answer 15

(d+n+g/a)^1/1-a

Question 16

y*gold per effective worker

Answer 16

(d+n+g/a)^a/a-1

Question 17

c*gold

Answer 17

y-(d+n+g)k

Question 18

wage

Answer 18

MPL=(1-a)Axk^a

Question 19

growth rate of wages

Answer 19

g

Question 20

rental price of capital

Answer 20

MPK= a(k)^a-1

Question 21

growth rate of rental price

Answer 21

0

Question 22

capital growth rate

Answer 22

n+g

Question 23

capital per output growth rate

Answer 23

0

Question 24

labour share of income growth

Answer 24

g+n-(n+g)=0 (constant)

Question 25

wage growth rate at a steady state

Answer 25

g

Question 26

labour growth rate

Answer 26

n

Question 27

golden rule for k* with technology

Answer 27

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

Question 28

golden rule of consumption

Answer 28

Kgold ^a -(d+n+g)kgold