Term 2 week 2 Solow Model Flashcards
How does the Solow model vary from the simple production model?
In the prior model capital was exogenous and fixed.
Solow model makes capital endogenous but keeps labour fixed.
What is the solow model?
What are the assumptions?
Solow model is a model of capital accumulation.
Yt = A bar . K^alpha . L bar ^1-alpha
TFP and labour are fixed.
What is the maximisation problem for firms in solow model?
Pi = A bar . K^ alpha . L bar ^1-alpha
F.O.C
dpi/dk = 0
alpha yt/kt = rt
(1-alpha) Yt/lbar= wt
How do households change in the solow model?
-households were exogenous in prior model supplying fixed capital and labour
What do households do in the Solow model?
households consume a constant fraction of output and invest the rest of their income
I = sbarYt
consumption is then given by
Ct = (1-sbar)Yt
How does saving happen in the solow model?
Household saving is endogenous and fixed
What does investment do in the solow model?
It creates capital for the next period
What is the capital accumulation equation
What is the next change in capital accululation?
Kt+1 = It + kt - gammakt
where gamma is depreciation rate between 0 and 1
Investment - depreciation
What is the resource constraint for households in the solow model?
What are the assumptions?
Ct + It = Yt
Closed economy and no government spending
What are the endogenous variables for solow model?
What are the exogenous variables for solow model?
How many equations in the solow model?
What is K bar 0 in the solow model?
The level of capital at which the economy starts.
What are the ways in which capital can grow in the solow model?
Positive change in net stock of capital
I > gammakt (capital is growing)
Negative change in net stock of capital
I < depreciation capital is getting smaller
I = depreciation capital is staying constant (STEADY STATE).
How do you show the solow model graphically?
Explain the diagram
x axis capital
Y axis investment / depreciation
depreciation is straight 45 degree line
investment is a concave function as it is a portion of output so as in solow output is made up of exogenous labour it has diminshing returns.
What is net investment in solow model graph?
difference between investment and depreciation can be negative or positive or = 0
Explain the dynamics of the solow model graph starting from different points
if you start below K* the the marginal output
What does the solow model conclude?
When labour and TFP is fixed capital accumulation is not enough an engine of long term growth.
what are the steady states in the solow model?
1 at 0 and 1 at K*
at 0 you have nothing to save and nothing to invest - but unstable as if you add a tiny bit of capital
Why is investment a concave function in the solow model?
Becuause output is a concave function and investment is a fraction of
What is next change in capital per worker?
What is the relationship between capital and capital per worker
delta kt+1 = investment per worker - depreciation per worker
it is just a scaled down version
What is transition dynamics?
The process that takes the economy away from initial point of capital to steady state
What happens to endogenous variables in the steady state?
All endogenous variables are fixed
How can you model the solow model as a dynamical system using a graph
What does the capital per worker graph look like?
X axis capital per worker
Y axis investment depreciation per worker
Same shape as normal but scaled down
What is the solow model graph including output?
-Output is above all starting from origin
-Investment is curve below
-depreciation is straight line
Difference between output and investment is consumption
Difference between depreciation and investment is net change in capital.
How do we move from an initial level (below steady state) of capital eg K1 to steady state
What about if you start at a point beyond the steady state.
-You go to K1 and work out the net investment.
You add this net investment to K1 to get K2 which is an increase of capital.
You then go back to x axis at K2 and compute the net investment and keep going until steady state.
-At K3 for example you work out there is a negative net investment so you subtract this from the capital.
-You then go to this new point of capital and it keeps subtracting until you get to K*
- How can we present the solow model as a dynamical system?
- How do we solve the dynamical system graphically?
- Express kt +1 as a function of kt
Start by kt + 1 = kt + I - gammadep
sub in Sbar . Output
then sub in production function for output.
This gives
kt+1 = kt + sbar . output - gamma dep
This makes the whole function a function of kt
- Start at K0 go to kt(phi) line and then read off K1 then keep doing this
Explain the convergence of the dynamical system
At K0 the additional product of the output is high but as capital keeps increasing the additional product is decreasing, and depreciation stays constant and hence erodes the investment so it converges.
Works vice versa as well
What is the long run condition in the steady state?
sbar output = gamma investment
What happens when you solve for K* in the steady state
How do you solve for steady state in solow model?
In steady state investment = depreciation
INvestment = Sbar . output
Output = production function so sub it in
Then divide by (K*)alpha
Then divide by gamma
Then square root by 1-gamma
K* = L bar . (sbar . a bar / gamma bar)^1/1-alpha
What does the steady state in solow model say about it?
K* = L bar . (sbar . a bar / gamma bar)^1/1-alpha
K* is increasing in L bar, S bar and A bar and decreasing in the depreciation rate
How do we solve for the output in the solow model?
Try computing this
Then try computing per capita
You plug in the K* found in the steady state into the production function
When you sub K* in remember to the power of all the whole of K* to alpha.
Then simplify down
Y* = A^1/1-alpha (Sbar / gamma bar)^alpha/ 1-alpha . L bar . L bar
For per capita divide by L bar
What does the solution to the steady state output in the solow model show?
The exponent on TFP is A^1/1-alpha which is greater than one
TFP has effect greater than 1
TFP direct and indirect effect of TFP
direct effect the higher TFP the higher output
The higher output the more investment and more capital accumulation
What does the solow model conclude about long-term economic growth?
-With fixed labour capital accumulation alone is not enough to create long term growth due to diminshing returns.
This is because diminshing returns to output and depreciation causes it to converge to a steady state.
Can increase growth in the short term
What is the impact graphically of an increase in the savings rate?
What happens to output?
An increase in the savings rate causes the investment curve to rotate upwards
Investment temporarily exceeds depreciation
creating a new steady state.
The new steady state has higher output and capital per worker.
Show graphically the output time impulse function
X axis time
Y axis output
X starts constant and then curves up then constant again
Rapid after shock but slows down.
What are the effect of policies that increase savings?
But what could be the negative of this?
- They create short term economic growth but not in the long term
-An increase in saving also decreases consumption however as
What is the impact graphically of an increase in depreciation on Solow model?
Depreciation rotates upwards so depreciation is greater than investment.
This causes the steady state to decrease
What is the impact on impulse response function of an increase in depreciation
Constant than rapid decine then constant again
How does the Solow model predict that poor and rich countries will grow?
What do we see in the data?
It only predicts conditional convergence
That poorer countries will grow faster than richer countries but ONLY if they have the same steady state?
In the data we see that there is no conditional convergence.
How does the Solow model predict output per capita?
Solow model suggests that savings rate increases GDP and depreciation decreases GDP
yet data shows savings rate has noo correlation with GDP and higher depreciation aligns with higher GDP.
It backs up that TFP can explain growth
What does the steady state in the long run depend on?
-increasing in the savings rate
-decreasing in depreciation
What is the growth rate of GDP per capita
y2019-y2018/y2018
What is the level of income next period?
yt+1 = yt(1+g)
How do you work out the level of something after t year?
Constant growth rule
Lt = L0(1+gr)^t
What is the rule of 70?
t = 70/ g%
number of years it takes for something to double
Why is the ratio scale useful?
It can help to differentiate between constant and non-constant growth
How can you compute average growth rate?
