Week 3: Solow Growth Model Flashcards
Exogenous Variable
variable is given in model and is determined outside of the model
Endogenous Variable
variable that is determined by the model
Solow Growth Model
exogenous model of economic growth that analyses changes in the level of output in an economy over time
How is Solow Growth Model Different to Production Function? (3)
Augments production model with capital accumulation
Capital stock if no longer exogenous (variable given)
capital stock now endogenised (variable determined in model)
How do you set up the Solow Growth model?
Use old production function equation and add an equation for the accumulation of capital over time
Key aspects of the Solow Growth Model equation? (4)
- 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
What does a resource constraint assume?
Assumes no imports or exports and no gov spending
Resource Constraint Equation
C(t) + I(t) = Y(t)
C = consumption
I = investment
Capital Accumulation Equation
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
Capital Accumulation
an increase in assets from investments or profits
Change in Capital Stock Equation
△K(t=1) = K(t+1) - K(t)
Thus
△K(t=1) = I(t) - dK(t)
Is labour supply an endogenous variable in Solow Growth Model?
No for simplicity - amount of labour in economy is given exogenously at a constant level
L(t) = L
Consumption Equation in Solow Growth Model
I(t) = sY(t) I = investment s = fraction of total output invested
C(t) = (1-s)Y(t)
Saving Equation in the Solow Growth Model
Difference between income and consumption
Y(t) - C(t) = I(t) is saving Y(t) - C(t)
saving = investment
Two ways to solve Solow Growth model
- Graphical solution
2. Solve model in the long run
What happens at the rest point of the economy?
All endogenous variables are steady
In the steady state what is investment equal to?
investment = depreciation
Mathematical solution for the Steady State
Nul and void
What is the steady state level of capital positively related to? (3)
- investment rate
- size of the workforce
- productivity of the economy
What is the steady state level of capital negatively related to?
depreciation rate
What is a higher steady state production caused by?
Higher productivity and investment rate (s and A)
What is a lower steady state production caused by?
faster depreciation
Why does an economy reach a steady state?
- investment has diminishing returns
What is an important result from the Solow Growth Model?
No long-run growth
Drawback in the model regarding long-run growth
- after we reach the steady state there is no long-run growth in output
Can growth in the labour force lead to overall economic growth?
Yes - in the aggregate
No - cannot in output per person
What happens to output in response to an increase investment rate? (2)
- capital accumulates over time
- Capital stock increases by transition dynamics to reach new steady state
What happens to output in response to a rise in depreciation rate?
- decline in output which is rapid at first and then settles at a new lower steady state
What happens if an economy is 1. below steady state 2. above steady state?
- it will grow
2. negative growth rate
What is growth like in economy when far below steady state?
the further below the faster the growth
What is growth like in economy when close to steady state?
slower the economy will grow
Strengths of the Solow Model
- provides a theory that determines how rich a country is in the long run
- allows us to understand difference in growth rates across countries
Weaknesses of Solow Model (3)
- 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
How do you solve the Solow growth model? (2 steps)
- combine the investment allocation and capital accumulation equation
- sub fixed amount of labour into production function
Diagram that shows economy moving towards steady state
What happens to solow growth model when investment > depreciation
- 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
Solow growth model diagram with output
What happens if economy is below steady state?
economy will grow
What happens if economy if above steady state?
the growth rate of the economy will be negative
What does it mean when the economy is far below the steady state?
the further below, the faster the economy will grow
What does it mean when an economy is close to the steady state?
the closer to the steady state, the slower the economy will grow
Solow Growth Model - Diagram when there is an increase in investment rate
Solow Growth Model - Diagram when there is an increase in depreciation rate
How can you have a negative growth rate in the economy?
If GDP falls from one quarter to the next then growth is negative
Short run results of foreign aid on the economy when k* > k0
(steady state > aid)
- Amount of capital per worker will immediately increase to k0 + f - staying on the left of the steady state
- Output per worker increases from Af(K0) to Af (K0 +f)
- Growth rate will decrease as MPK is lower
Long run results of foreign aid on the economy when k* > k0
steady state > aid
Economy will converge to the same steady state as before
Diagram for the results of foreign aid on the economy when k* > k0
(steady state > aid)
Short run results of foreign aid on the economy when k* = k0
(steady state = aid)
- Amount of capital per worker will immediately increase to k* + f - moving to the right of the SS
- Output per worker increases from Af(K) to Af (K +f)
- Growth rate will be negative
Long run results of foreign aid on the economy when k* = k0
steady state = aid
Economy will converge to the same steady state
Diagram showing results of foreign aid on the economy when k* = k0
(steady state = aid)
Is there a permanent effect of foreign aid?
no
What needs to happen in order for their to be a permanent change to the steady state?
There needs to be a change in the parameters for their to be a change in the steady state for example s or A
