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.