Model of production (L3)

Question 1

growth rate

Answer 1

g=final-initial/initial or Yt+1-Yt/Yt
Yt+1 (final)= Yt(1+g) (discrete growth)

Question 2

If the initial grows multiple times in a year, what is the equation

Answer 2

Yt=Y0(1+g/n)^nt

Question 3

growth rate for continuous growth

Answer 3

Y0e^gt

Question 4

calculate growth rate if
Zt= Xt x Yt
Zt= Xt/Yt
Zt= X^a t

Answer 4

gz= gx + gy
gz= gx-gy
gz= a x gx

Question 5

arithmetic growth rate for discrete

Answer 5

1+gz=(1+gy)(1+gx)
gz=gx+gy as gxgy would give such a small value we can ignore it

Question 6

Annual growth rate (discrete)

Answer 6

Yt= Y0(1+g)^t

Question 7

Rate of growth of GDP per capita

Answer 7

Y/L

Question 8

Capital per worker

Answer 8

K/L roughly 1-3%

Question 9

Capital to output ratio

Answer 9

K/Y roughly 3%

Question 10

Labours share of income

Answer 10

W x L / Y roughly 2/3

Question 11

Profit

Answer 11

Revenue-costs
Price x F(Kd,Ld) - WxL - RxK
If profit >0 hire more labour/capital
Y-(MPLxL)-(MPKxK)=Profit

Question 12

Growth rate X^at explained

Answer 12

t is the percentage growth, a is the power it has been raised to, eg a=0.24 and growth rate=7% 7x0.24=1.68

Question 13

How to find increasing, decreasing/ constant returns to scale

Answer 13

check working

Question 14

MPK

Answer 14

marginal product of capital extra amount of output for each unit of capital
a(Y/K)
R/P

Question 15

MPL

Answer 15

marginal product of labour
(1-a)(Y/L)
W/P (price you sell a good at)

Question 16

Capital income

Answer 16

MPK x K
a(Y/K) x K
aY

Question 17

Labour income

Answer 17

MPL x L
(1-a)(Y/L) x L
(1-a)Y

Question 18

What happens to MPK as you increase K

Answer 18

Decreases

Question 19

MPL>W/P

Answer 19

hire more labour until W/P=MPL

Question 20

what does economic profit= when using cobb douglas

Answer 20

0
capital+labour income=aY+(1-a)Y=Y

Question 21

per capita GDP

Answer 21

A(K/L)^a= Ak^a

Question 22

TFP

Answer 22

A(UK)/A(US) x k(UK)/k(US)^a
plug predicted capita into equation to find

Question 23

finding the difference in A

Answer 23

logA(US)/A(UK)/ log(yUK/yUS)
(log the capita equation and rearrange for A)

Question 24

finding the difference in K

Answer 24

1-difference in A

Question 25

factors affecting difference in A

Answer 25

human capital (skills needed)
tech
institutions
resources misallocations

Question 26

Growth rate approximation for output

Answer 26

gY = (1-a)gL

Question 27

How to calculate accurate growth of output

Answer 27

Growth to the power of whatever has increased (if labour increased by 15%, do 1.15^(1-a)

Question 28

Real wage

Answer 28

W/P (MPL) x (L/Y) = (1-a)
Check ps1 for working

Question 29

rental price of capital

Answer 29

R/P x (K/Y) = a

Question 30

Real wage approximate

Answer 30

gw/p = -a xgL