Chapter 8 Economic growth I: Capital accumulation and population growth

Question 1

What is the supply of goods in the Solow model based on, and what are the assumptions?

Answer 1

Supply of goods in Solow model based on production function - K and L not fixed

Assumes production function has constant returns to scale

Question 2

What does constant returns to scale imply for supply in Solow production function?

Answer 2

As there are constant returns to scale, Y/L=F(K/L,1)
i.e. output per worker is a function of capital per worker

Constant returns to scale implies the size of the economy (measured by number of workers) does not affect the relationship between output per worker and capital per worker

y=Y/L and k=K/L hence, y=f(k)=F(k,1)

Question 3

What is the slope of the production function?

Answer 3

The slope of the production function is MPK

MPK=f(k+1)-f(k)

Question 4

What is the demand for goods in the Solow model? And what is saving equal to?

Answer 4

Demand comes from consumption and investment
y=c+i - per worker
c=(1-s)y

s - saving rate, between 0 and 1
As y=(1-s)y+i - > i=sy
Investment equals saving

Question 5

What is the capital stock influenced by?

Answer 5

Depreciation and investment

Question 6

How is depreciation, capital and investment related?

Answer 6

Investment per worker: i=sy

Substitute y for f(k)

First considering investment: i=sf(k)

Relates existing stock of capital, k, with accumulation of new, i

δ - depreciation rate

∆k=I-δk=sf(k)-δk

the Solow model’s central equation determines behaviour of capital over time…
…which, in turn, determines behaviour of all of the other endogenous variables because they all depend on k. E.g., income per person: y= f(k) consumption per person: c= (1–s)f(k)

Question 7

What is the steady-state level of capital?

Answer 7

If investment is just enough to cover depreciation, [sf(k)=δk], then capital per worker will remain constant: Δk= 0.

This constant value = k* = the steady-state level of capital, where investment equals depreciation, hence no change in capital stock

An economy not at steady state will go there - long-run equilibrium

If investment exceeds depreciation, new capital is added, and output grows

As long as k < k, investment will exceed depreciation, and k will continue to grow toward k

Question 8

What happens if there is an increase in saving rate (assuming the economy begins at steady-state)?

Answer 8

When saving rate increases, upward shift of sf(k)

Investment is higher, however, capital stock and depreciation are unchanged

Hence, investment exceeds depreciation

The capital stock will gradually rise until economy reaches a new steady state which has higher capital stock and higher output

Thus, if the saving rate is high, the economy will have a large capital stock and a high level of output in steady state

Question 9

What does the Solow model say about the relationship between saving and economic growth?

Answer 9

Higher saving leads to faster growth, however, temporarily

Positive relationship between fraction of output devoted to investment and level of income per person

Thus, the Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run.

Question 10

What are policies with growth effect and what does it mean that a higher saving rate has a level effect?

Answer 10

Policies with growth effect - policies that alter steady-state growth rate

Higher saving rate is said to have a level effect, because only the level of income per person, and not growth rate, is influenced by the saving rate in the steady state

Question 11

What is the Solow growth model?

Answer 11

3. Solow growth model: designed to show how growth in the capital stock, growth in labour force and advances in technology interact in an economy

Question 12

What is the golden rule level of capital?

Answer 12

Economic well-being depends on consumption - the steady-state value of k that maximizes consumption - the Golden Rule level of capital k_gold^*

Question 13

How can we tell if an economy is at the Golden Rule level?

Answer 13

Two methods: (1) compute steady state capital stock, this can be used to compute steady state capital stock for any saving rate

(2) or find capital stock where 0 = MPK - δ

MPK = 0 when saving rate is at golden rule value

MPK > 0 whenever economy saves less than golden rule value and vice versa

Question 14

If capital stock is below golden rule steady state, what happens if there is an increase in steady-state capital?

Answer 14

If capital stock is below golden rule steady state - increases in steady-state capital raise steady-state consumption (as output increases more than depreciation) and vice versa

Question 15

Does the economy gravitate toward golden rule of capital?

Answer 15

The economy does not gravitate towards golden rule, if we want a particular steady-state capital stock, we need the saving rate to support it

Question 16

What problems to policy makers have when they start with more capital than golden rule steady state?

Answer 16

Policy makers should pursue policies aimed at reducing rate of saving in order to reduce capital stock

Reduction in saving rate causes - immediate increase in c and fall in i

I is now less than δ, hence, economy no longer in steady state

Gradually, capital stock falls - reduction in output, consumption and investment - continue until steady state reached (as this is golden rule steady state, c is not higher before even though I and y are lower)

Question 17

What problems do policy makers have when they start with less capital than golden rule steady state?

Answer 17

Policy makers must increase saving rate

Immediate fall in c and increase in i

Over time, higher I makes capital stock rise

As capital accumulates, y, c and I gradually increase until steady state

Because new steady state is golden rule - higher c

Current consumers and future consumers are not necessarily the same people - current consumers’ welfare does not increase as c initially falls

Trade-off between welfare of different generations

Question 18

Can capital accumulation by itself explain sustained economic growth?

Answer 18

No - eventually a steady state is reached. Thus, we must expand Solow model to include technological progress and population growth

Question 19

How does an increase in the rate of saving have a level effect on income per person?

Answer 19

It causes a period of rapid growth, but eventually that growth slows to reach a new steady state.

Question 20

What do we assume when including population growth in the Solow model?

Answer 20

We suppose population and labour force grow at same constant rate of n per period

Question 21

How does population growth affect the steady state?

Answer 21

The growth in number of workers makes capital per worker fall

Change in capital stock per worker: ∆k=i-(δ+n)k

(δ+n)k - break-even investment = the amount of investment necessary to keep the capital stock per worker constant

nk - the amount of investment necessary to provide new workers with capital

δk - depreciation of existing capital

Substituting sf(k) for i - ∆k=sf(k)-(δ+n)k

Steady state of capital per worker if k is unchanging

If k is less than k* - investment is greater than break-even investment, hence k rises and vice versa

At steady state i=δk+nk*

Question 22

How does population growth bring us closer to explaining sustained economic growth?

Answer 22

In the steady state with population growth, k and y are constant, however, as the number of workers is growing at rate n, total capital and total output must be growing at rate n (however, does not explain sustained growth in standard of living as y is constant, only explains how Y increases)

Question 23

How does population growth give us another explanation for why some countries are rich and some are not?

Answer 23

Predicts countries with higher population growth will have lower GDP per capita

Question 24

How can we incorporate the population growth in the golden rule?

Answer 24

MPK = δ + n

Question 25

The Malthusian model

Answer 25

Allowing the poor to have more children places even greater strains on society’s productive capabilities - hence alleviating poverty is counterproductive

Predicted mankind would live in poverty forever

He failed to see that growth in humanity’s ingenuity would more than offset effects of population growth - technological advances

Birth control not expected

Question 26

The Kremerian model

Answer 26

Suggests world population growth is a key driver of advancing economic prosperity - more people means more bright minds to advance technology

Question 27

What does the Solow model state about population growth?

Answer 27

The higher the rate of population growth, the lower the steady-state levels of capital per worker and output per worker