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EC201 MACRO > Term 2 week 2 Solow Model > Flashcards

Term 2 week 2 Solow Model Flashcards

1
Q

How does the Solow model vary from the simple production model?

A

In the prior model capital was exogenous and fixed.

Solow model makes capital endogenous but keeps labour fixed.

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2
Q

What is the solow model?

What are the assumptions?

A

Solow model is a model of capital accumulation.

Yt = A bar . K^alpha . L bar ^1-alpha

TFP and labour are fixed.

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3
Q

What is the maximisation problem for firms in solow model?

A

Pi = A bar . K^ alpha . L bar ^1-alpha
F.O.C
dpi/dk = 0

alpha yt/kt = rt

(1-alpha) Yt/lbar= wt

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4
Q

How do households change in the solow model?

A

-households were exogenous in prior model supplying fixed capital and labour

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5
Q

What do households do in the Solow model?

A

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

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6
Q

How does saving happen in the solow model?

A

Household saving is endogenous and fixed

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7
Q

What does investment do in the solow model?

A

It creates capital for the next period

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8
Q

What is the capital accumulation equation

What is the next change in capital accululation?

A

Kt+1 = It + kt - gammakt

where gamma is depreciation rate between 0 and 1

Investment - depreciation

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9
Q

What is the resource constraint for households in the solow model?

What are the assumptions?

A

Ct + It = Yt

Closed economy and no government spending

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10
Q

What are the endogenous variables for solow model?

What are the exogenous variables for solow model?

How many equations in the solow model?

A
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11
Q

What is K bar 0 in the solow model?

A

The level of capital at which the economy starts.

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12
Q

What are the ways in which capital can grow in the solow model?

A

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).

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13
Q

How do you show the solow model graphically?

Explain the diagram

A

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.

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14
Q

What is net investment in solow model graph?

A

difference between investment and depreciation can be negative or positive or = 0

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15
Q

Explain the dynamics of the solow model graph starting from different points

A

if you start below K* the the marginal output

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16
Q

What does the solow model conclude?

A

When labour and TFP is fixed capital accumulation is not enough an engine of long term growth.

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17
Q

what are the steady states in the solow model?

A

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

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18
Q

Why is investment a concave function in the solow model?

A

Becuause output is a concave function and investment is a fraction of

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19
Q

What is next change in capital per worker?

What is the relationship between capital and capital per worker

A

delta kt+1 = investment per worker - depreciation per worker

it is just a scaled down version

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20
Q

What is transition dynamics?

A

The process that takes the economy away from initial point of capital to steady state

21
Q

What happens to endogenous variables in the steady state?

A

All endogenous variables are fixed

22
Q

How can you model the solow model as a dynamical system using a graph

A
23
Q

What does the capital per worker graph look like?

A

X axis capital per worker
Y axis investment depreciation per worker

Same shape as normal but scaled down

24
Q

What is the solow model graph including output?

A

-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.

25
Q

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.

A

-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*

26
Q
  1. How can we present the solow model as a dynamical system?
  2. How do we solve the dynamical system graphically?
A
  1. 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

  1. Start at K0 go to kt(phi) line and then read off K1 then keep doing this
27
Q

Explain the convergence of the dynamical system

A

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

28
Q

What is the long run condition in the steady state?

A

sbar output = gamma investment

29
Q

What happens when you solve for K* in the steady state

A
30
Q

How do you solve for steady state in solow model?

A

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

31
Q

What does the steady state in solow model say about it?

A

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

32
Q

How do we solve for the output in the solow model?

Try computing this

Then try computing per capita

A

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

33
Q

What does the solution to the steady state output in the solow model show?

A

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

34
Q

What does the solow model conclude about long-term economic growth?

A

-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

35
Q

What is the impact graphically of an increase in the savings rate?

What happens to output?

A

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.

36
Q

Show graphically the output time impulse function

A

X axis time
Y axis output

X starts constant and then curves up then constant again
Rapid after shock but slows down.

37
Q

What are the effect of policies that increase savings?

But what could be the negative of this?

A
  • They create short term economic growth but not in the long term

-An increase in saving also decreases consumption however as

37
Q

What is the impact graphically of an increase in depreciation on Solow model?

A

Depreciation rotates upwards so depreciation is greater than investment.

This causes the steady state to decrease

37
Q

What is the impact on impulse response function of an increase in depreciation

A

Constant than rapid decine then constant again

37
Q

How does the Solow model predict that poor and rich countries will grow?

What do we see in the data?

A

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.

37
Q

How does the Solow model predict output per capita?

A

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

37
Q

What does the steady state in the long run depend on?

A

-increasing in the savings rate
-decreasing in depreciation

37
Q

What is the growth rate of GDP per capita

A

y2019-y2018/y2018

38
Q

What is the level of income next period?

A

yt+1 = yt(1+g)

38
Q

How do you work out the level of something after t year?

A

Constant growth rule

Lt = L0(1+gr)^t

38
Q

What is the rule of 70?

A

t = 70/ g%

number of years it takes for something to double

38
Q

Why is the ratio scale useful?

A

It can help to differentiate between constant and non-constant growth

38
Q

How can you compute average growth rate?

A

EC201 MACRO (19 decks)

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