Week 3: Solow Growth Model

Question 1

Exogenous Variable

Answer 1

variable is given in model and is determined outside of the model

Question 2

Endogenous Variable

Answer 2

variable that is determined by the model

Question 3

Solow Growth Model

Answer 3

exogenous model of economic growth that analyses changes in the level of output in an economy over time

Question 4

How is Solow Growth Model Different to Production Function? (3)

Answer 4

Augments production model with capital accumulation
Capital stock if no longer exogenous (variable given)
capital stock now endogenised (variable determined in model)

Question 5

How do you set up the Solow Growth model?

Answer 5

Use old production function equation and add an equation for the accumulation of capital over time

Question 6

Key aspects of the Solow Growth Model equation? (4)

Answer 6

• cobb douglas method
• constant returns to scale in capital and labour
• assume exponent of one third on capital
• all variable are time subscribed by t

Question 7

What does a resource constraint assume?

Answer 7

Assumes no imports or exports and no gov spending

Question 8

Resource Constraint Equation

Answer 8

C(t) + I(t) = Y(t)
C = consumption
I = investment

Question 9

Capital Accumulation Equation

Answer 9

K(t+1) = K(t) + I(t) - dK(t) 
K(t+1) = next years capital 
K(t) = this years capital 
I(t) = this years investment 
d = depreciation rate

Question 10

Capital Accumulation

Answer 10

an increase in assets from investments or profits

Question 11

Change in Capital Stock Equation

Answer 11

△K(t=1) = K(t+1) - K(t)
Thus
△K(t=1) = I(t) - dK(t)

Question 12

Is labour supply an endogenous variable in Solow Growth Model?

Answer 12

No for simplicity - amount of labour in economy is given exogenously at a constant level
L(t) = L

Question 13

Consumption Equation in Solow Growth Model

Answer 13

I(t) = sY(t)
I = investment 
s = fraction of total output invested 

C(t) = (1-s)Y(t)

Question 14

Saving Equation in the Solow Growth Model

Answer 14

Difference between income and consumption
Y(t) - C(t) = I(t) is saving Y(t) - C(t)
saving = investment

Question 15

Two ways to solve Solow Growth model

Answer 15

1. Graphical solution

2. Solve model in the long run

Question 16

What happens at the rest point of the economy?

Answer 16

All endogenous variables are steady

Question 17

In the steady state what is investment equal to?

Answer 17

investment = depreciation

Question 18

Mathematical solution for the Steady State

Answer 18

Nul and void

Question 19

What is the steady state level of capital positively related to? (3)

Answer 19

• investment rate
• size of the workforce
• productivity of the economy

Question 20

What is the steady state level of capital negatively related to?

Answer 20

depreciation rate

Question 21

What is a higher steady state production caused by?

Answer 21

Higher productivity and investment rate (s and A)

Question 22

What is a lower steady state production caused by?

Answer 22

faster depreciation

Question 23

Why does an economy reach a steady state?

Answer 23

• investment has diminishing returns

Question 24

What is an important result from the Solow Growth Model?

Answer 24

No long-run growth

Question 25

Drawback in the model regarding long-run growth

Answer 25

- after we reach the steady state there is no long-run growth in output

Question 26

Can growth in the labour force lead to overall economic growth?

Answer 26

Yes - in the aggregate | No - cannot in output per person

Question 27

What happens to output in response to an increase investment rate? (2)

Answer 27

- capital accumulates over time | - Capital stock increases by transition dynamics to reach new steady state

Question 28

What happens to output in response to a rise in depreciation rate?

Answer 28

- decline in output which is rapid at first and then settles at a new lower steady state

Question 29

What happens if an economy is 1. below steady state 2. above steady state?

Answer 29

1. it will grow | 2. negative growth rate

Question 30

What is growth like in economy when far below steady state?

Answer 30

the further below the faster the growth

Question 31

What is growth like in economy when close to steady state?

Answer 31

slower the economy will grow

Question 32

Strengths of the Solow Model

Answer 32

- provides a theory that determines how rich a country is in the long run - allows us to understand difference in growth rates across countries

Question 33

Weaknesses of Solow Model (3)

Answer 33

- main focus on investment and capital TFP is much more important but is unexplained - does not explain why different countries have different investment and productivity rates - does not provide a theory of sustained long-run economic growth

Question 34

How do you solve the Solow growth model? (2 steps)

Answer 34

1. combine the investment allocation and capital accumulation equation 2. sub fixed amount of labour into production function

Question 35

Diagram that shows economy moving towards steady state

Answer 35

Question 36

What happens to solow growth model when investment > depreciation

Answer 36

- capital stock will increase until the amount of investment = amount of capital that wears out due to depreciation - hence change in capital = 0 - capital stock will stay at this value of capital forever - steady states

Question 37

Solow growth model diagram with output

Answer 37

Question 38

What happens if economy is below steady state?

Answer 38

economy will grow

Question 39

What happens if economy if above steady state?

Answer 39

the growth rate of the economy will be negative

Question 40

What does it mean when the economy is far below the steady state?

Answer 40

the further below, the faster the economy will grow

Question 41

What does it mean when an economy is close to the steady state?

Answer 41

the closer to the steady state, the slower the economy will grow

Question 42

Solow Growth Model - Diagram when there is an increase in investment rate

Answer 42

Question 43

Solow Growth Model - Diagram when there is an increase in depreciation rate

Answer 43

Question 44

How can you have a negative growth rate in the economy?

Answer 44

If GDP falls from one quarter to the next then growth is negative

Question 45

Short run results of foreign aid on the economy when k* > k0 (steady state > aid)

Answer 45

1. Amount of capital per worker will immediately increase to k0 + f - staying on the left of the steady state 2. Output per worker increases from Af(K0) to Af (K0 +f) 3. Growth rate will decrease as MPK is lower

Question 46

Long run results of foreign aid on the economy when k* > k0 | steady state > aid

Answer 46

Economy will converge to the same steady state as before

Question 47

Diagram for the results of foreign aid on the economy when k* > k0 (steady state > aid)

Answer 47

Question 48

Short run results of foreign aid on the economy when k* = k0 (steady state = aid)

Answer 48

1. Amount of capital per worker will immediately increase to k* + f - moving to the right of the SS 2. Output per worker increases from Af(K*) to Af (K* +f) 3. Growth rate will be negative

Question 49

Long run results of foreign aid on the economy when k* = k0 | steady state = aid

Answer 49

Economy will converge to the same steady state

Question 50

Diagram showing results of foreign aid on the economy when k* = k0 (steady state = aid)

Answer 50

Question 51

Is there a permanent effect of foreign aid?

Answer 51

no

Question 52

What needs to happen in order for their to be a permanent change to the steady state?

Answer 52

There needs to be a change in the parameters for their to be a change in the steady state for example s or A