Unit 1: Solow Swan Model

Question 1

Increases in ____
Increases in _____ per person
Increases in _____
Are all connected to economic growth

Answer 1

a) Income
b) Income per person
c) Welfare

Question 2

Are any countries experiencing negative growth? What does negative growth mean?

Answer 2

Yes and it means their level of economic activity (their output) is diminishing over time

Question 3

Why can a countries growth not be fully explained by changes over time in factors such as capital and labour?

Answer 3

Differences in technology and technological progress

Question 4

Economic growth can help us answer all apart from:
1. Why are some countries rich and others poor
2. Why do countries grow at different rates
3. Should we expect poor countries to catch up to rich countries over time?
4. Why are some countries able to consume more than others?
5. Are there economic policies that governments can implement that can enable an economy to grow more rapidly?

Answer 4

4

Question 5

What are the important facts regarding the growth process (identified in the 1960s)

Answer 5

1. Output-per-capita grows over time and its growth rate does not tend to diminish.
2. Capital-per-capita grows over time.
3. The rate of return on capital is constant.
4. The capital-output ratio is constant.
5. The shares of labour and capital in national income are constant.
6. The growth rate of output-per-capita differs markedly across countries

Question 6

True or false:
Capital-per-capita grows over time

Answer 6

True

Question 7

True or false:
The rate of return on capital is constant.

Answer 7

False

Question 8

The shares of labour and capital in national income are constant.

Answer 8

False

Question 9

There is enormous variation in per capita income across economies.

Answer 9

True- The poorest countries have per capita incomes that are less than 5 percent of per capita incomes in the rich countries.

Question 10

Rates of economic growth vary substantially across countries

Answer 10

True

Question 11

Growth rates are generally constant over time.

Answer 11

False- For the world as
a whole, growth rates were close to zero over most of history, but have
increased sharply in the twentieth century. For individual countries,
growth rates also change over time.

Question 12

A country’s relative position in the world distribution of per capita
incomes is fixed.

Answer 12

False- Countries can move from being “poor” to being “rich” and vice versa.

Question 13

In the United States over the last century:

(a) The real rate of return to capital shows no trend upward or downward.

Answer 13

True

Question 14

In the United States over the last century:

(b) The shares of income devoted to capital and labour show an upward trend.

Answer 14

False- they show no trend

Question 15

In the United States over the last century:

(c) The average growth rate of output per person has been positive and relatively constant over time

Answer 15

True– the U.S. exhibits steady, sustained per capita income growth.

Question 16

True or false: Growth in output and growth in the volume of international trade are
closely related.

Answer 16

True

Question 17

True or False:
Skilled works tend to migrate from poor to rich countries or regions whereas Unskilled dont

Answer 17

False, they both tend to go from poor to rich

Question 18

Is capital a stock or flow variable?

Answer 18

A stock variable, so Kt refers to the stock of capital available at the beginning of period t, whereas for flow variables like output, Yt refers to the quantity of goods produced during period t

Question 19

How do you know when output is rising or falling at time t?

Answer 19

If the derivative of output (wrt time) > 0 then outputs rising
If the derivative of output (wrt time) < 0 then outputs falling

Question 20

How can we compute the growth rate of an economic variable- like output?

Answer 20

Take derivative wrt time of the natural log of output

Question 21

If the capital-labour ratio is not changing over time, it means that…

Answer 21

Capital and Labour are growing at the same rate

Question 22

The rate of output growth is a weighted average of…

Answer 22

the growth rate for capital and the growth rate for labour.

Question 23

What should we think of the economy being populated by?

Answer 23

Households, firms, and a government

Question 24

Goods are produced according to the production function:

Answer 24

Y (t) = F (K (t), L(t))
So the number of goods produced depends on the quantities of capital and labour available

Question 25

True or false for the production function: Y (t) = F (K (t), L(t))

Both capital and labour are essential inputs, without both no production is possible

Answer 25

True

Question 26

True or false for the production function: Y (t) = F (K (t), L(t))

The production function is decreasing in both capital and labour

Answer 26

False- its increasing

Holding labour constant, more capital allows more goods to be produced and, holding capital constant, more labour allows more goods to be produced

Question 27

True or false for the production function: Y (t) = F (K (t), L(t))

The production function has diminishing marginal productivity with respect to capital and labour

Answer 27

True

Keeping the number of workers constant, you get a higher level of extra goods produced when you add the first piece then the second and third and so on…

Question 28

What is another way to say the production function has diminishing marginal productivity?

Answer 28

It is concave

Question 29

True or false for the production function: Y (t) = F (K (t), L(t))

It has negative returns to scale

Answer 29

False- It has constant returns to scale

Meaning doubling the amounts of capital and labour used for production leads to double the number of goods produced

Question 30

True or false for the production function: Y (t) = F (K (t), L(t))

As K (t) approaches zero the MPK approaches ∞
and as K (t) approaches ∞ the MPK approaches
zero. Similarly for labour.

Answer 30

True

Question 31

Which production function possesses all 5 characteristics:

1. No production occurs without both capital and labor.
2. More capital or labor increases output.
3. Diminishing Marginal Productivity: Additional units of capital or labor yield less extra output.
4. Constant Returns to Scale: Doubling inputs doubles output.
5. The marginal product of capital or labor approaches infinity as the input nears zero and approaches zero as the input becomes large.

Answer 31

The Cobb-Douglas production function:

Y(t)=K(t)^α L(t) ^(1−α)

Question 32

The income identity which says that all goods produced are either consumed or saved is given by…

Answer 32

Y(t) = C(t) + S(t)

Question 33

S(t) = sY(t) implies that the model assumes…

Answer 33

A constant fraction of goods are saved

Question 34

The savings rate is given as a value between __ and ___

Answer 34

0 and 1 (i.e 0-100% of output)

Question 35

True or False:

The savings rate is constant

Answer 35

True

Question 36

Given the constant savings rate, how can consumption be expressed:

Answer 36

C(t) = (1 - S)Yt

where (1 -S) represents the fraction of the economy’s output that is consumed

Question 37

What does the equation for consumption tell us:

C(t) = (1 - S)Yt

Answer 37

A constant share of income is consumed

Question 38

What happens to the goods that are not consumed and instead saved? What would the resource constraint look like?

Answer 38

They are not wasted and instead used for investment, as reflected by the resource constraint:

Y (t) = C (t) + I (t).

Question 39

What does depreciation mean in the solow swan?

Answer 39

Using capital causes it to deteriorate or get worn out

Question 40

Why is it not that detrimental that some capital depreciates through use?

Answer 40

Because investment adds to the economy’s stock

Question 41

What is the original dynamic capital accumulation equation?

And using the fact that saving and investment are equal, and a constant fraction of output is saved, how can we write it?

Answer 41

K` (t) = I (t) − δK (t),
Where δ is the depreciation rate

·
K (t) = sF (K (t), L(t)) − δK (t).

Question 42

What does the capital accumulation equation: K` (t) = I (t) − δK (t), tell us?

Answer 42

Capital will be increasing over time when investment in new capital exceeds the capital worn out through depreciation

Question 43

What is included in capital, and how does it change over time in the model?

Answer 43

Capital includes all machines and equipment used for production. It changes over time by the amount of new investment minus what’s lost through depreciation.

Question 44

How does the population growth rate ‘n’ affect the model?

Answer 44

The population growth rate ‘n’ affects the labor force size (L), influencing production and savings levels in the economy. It assumes labor grows at rate ‘n’, affecting how much can be produced and saved.

Question 45

Why is it convenient to normalise the model wrt labour by dividing all equations by labour

Answer 45

Since labour is growing over time and so by doing this we don’t have to worry about the trend introduced by population growth

Question 46

What does “normalising the model” mean?

Answer 46

Dividing all equations in the model by labour

Question 47

What is the equation for the capital-labour ratio?

Answer 47

k (t) = sk (t)^α − (δ + n) k (t).

Question 48

What does the capital-labour ratio:
k (t) = sk (t)^α − (δ + n) k (t). tell us?

Answer 48

How capital per worker evolves. Investment per worker sk(t)^α tries to increase it, while depreciation and labor growth (δ+n) try to decrease it.
The balance of these forces determines whether the capital per worker (and thus productivity and economic well-being) grows or shrinks.

Question 49

What is the point in normalising the model?

Answer 49

It simplifies the analysis by removing the complicating factor of population growth, allowing us to focus on per-worker measures that are more directly related to individual well-being and productivity

Question 50

True or false:

The capital-labour ratio will be unchanged if investment-per-worker precisely equals (δ + n) k (t)

Answer 50

True- can be seen by looking at the equation

Question 51

Why is this term (δ + n) k (t) called “Break even investment?”

Answer 51

because (in per-worker terms) at least this much investment must take place just to keep the capital-labour ratio constant.

Question 52

Why does an increase in “n” dilute the capital-per-worker ratio?

Answer 52

As more workers join the labor force, the existing capital stock is spread more thinly unless additional investment is made.

Question 53

True or False:

When (in per-worker terms) actual investment is higher than break-even investment the capital-labour ratio will be rising and when actual investment is less than break-even investment the capital-labour ratio
will be falling.

Answer 53

True

Question 54

What are the 3 key equations in per worker terms?

Answer 54

Capital accumulation per worker: k (t) = sk (t)^α − (δ + n) k (t),
Output per worker: y (t) = k (t)^α
Consumption per worker: c (t) = (1 − s) y (t).

Question 55

What does α represent in the normalised model?

Answer 55

A constant that represents output elasticity of capital

Question 56

What is a steady state?

Answer 56

A point of rest where variables are not changing over time

Question 57

What are the 2 main reasons why we are interested in a steady state?

Answer 57

1. if the model has a steady state, then it will be able to provide meaningful long-run predictions
2. if the model has a steady state, then the model should also offer some predictability or forecastability

Question 58

How is the steady state capital per worker (k*) calculated in the model?

Answer 58

k* = (s/δ+n) ^(1/1−α)

Question 59

What does the steady state tell us about the capital-labor ratio and the output-labor ratio?

Answer 59

In the steady state, both the capital-labor ratio and the output-labor ratio are constant.

Question 60

What affects the capital per worker and output per worker in the steady state?

Answer 60

Both capital per worker and output per worker depend positively on the saving rate (s) and negatively on the depreciation rate (δ) and population growth rate (n).

Question 61

How does consumption per worker behave in the steady state?

Answer 61

Consumption per worker depends negatively on the depreciation rate (δ) and population growth rate (n). The effect of the savings rate (s) on consumption is ambiguous since it raises output but also implies less consumption today for more capital accumulation.

Question 62

What are the implications of constant capital-labor, output-labor, and consumption-labor ratios in steady state?

Answer 62

In steady state, the constant ratios mean that the capital-output ratio is also constant, implying that while the ratios remain unchanged, the actual amounts of capital, output, and consumption are growing at the same rate as the labor force, maintaining the ratios.

Question 63

What do constant ratios mean for growth rates in steady state?

Answer 63

Even though the growth rate of per capita quantities (k, y and c*) is zero in steady state, the absolute quantities of capital, output, and consumption grow at the rate of labor force growth, meaning the economy as a whole is growing.

Question 64

Can the economy grow without changing the steady-state ratios?

Answer 64

Yes, the economy can grow even if the steady-state ratios remain constant. This growth occurs because the labor force is growing, which leads to increases in the total amounts of capital, output, and consumption.

Question 65

What is a balanced growth path in the context of the Solow growth model?

Answer 65

A balanced growth path is a situation where all the economy’s per capita quantities grow at the same rate, which is the rate of technological progress in the Solow model. The economy can still be on a balanced growth path even if the capital-labor ratio differs from the steady state value.

Question 66

What happens if the capital-labor ratio is above the steady state value?

Answer 66

If the capital-labor ratio is above the steady state, investment is below the break-even investment and the capital-labor ratio will fall over time.

Question 67

What happens if the capital-labor ratio is below its steady state value?

Answer 67

If it’s below, the capital-labor ratio will grow over time due to diminishing marginal productivity of capital.

Question 68

What are the consequences of a falling capital-labor ratio?

Answer 68

If the capital-labor ratio is falling, it indicates that the economy is growing due to a rate of investment lower than what is required to maintain the steady state, pointing to diminishing returns to capital and an eventual return to the steady-state growth path.

Question 69

What does comparative statics involve?

Answer 69

A comparative statics exercise involves changing some parameter in the model and seeing what happens.

Question 70

What happens when the savings rate (s) increases to s’ in the steady state of the model?

Answer 70

The increase in the savings rate leads to a new higher steady state of capital per worker (k) and output per worker (y), since these are increasing functions of the savings rate s

Question 71

How do the initial and new steady states compare when the savings rate increases?

Answer 71

The new steady state after the savings rate increase to s’ is higher for both k2 and y2 due to the higher savings rate.

Question 72

How does the economy transition from the old to the new steady state after an increase in the savings rate?

Answer 72

1. Higher saving rate leads to increased actual savings and investment.
2. Investment surpasses the break-even level, causing the capital-labor ratio to rise.
3. A higher capital-labor ratio increases output per worker, so both capital and output ratios grow along the transition path.
4. The growth of the capital-labor ratio will slow down due to diminishing marginal returns.
5. Eventually, the economy approaches a new steady state where the ratios of growth slow down and stabilise at the new higher steady state levels.

Question 73

What happens to the economy’s growth as it transitions to the new steady state?

Answer 73

During the transition, the economy experiences growth in capital and output per worker. This growth is initially fast but slows down as it approaches the new steady state due to diminishing marginal returns to capital.

Question 74

How do diminishing marginal returns affect the transition to a new steady state?

Answer 74

Diminishing marginal returns imply that while each additional unit of investment increases output, the additional gain decreases. Hence, even as investment per worker continues, the growth of the capital-labor ratio and output per worker slows until the new steady state is reached.

Question 75

What happens to the steady state when the population growth rate n increases to n’ ?

Answer 75

An increase in the population growth rate results in a lower new steady state for the capital-labor ratio (k) and output-labor ratio (y), as these variables are decreasing functions of n.

Question 76

How do the initial and new steady states compare when the population growth rate increases?

Answer 76

The initial steady state has a higher capital-labor ratio k1* and output-labour ratio y1* compared to the new steady state k2* and y2* due to the lower population growth rate in the initial state.

Question 77

How does the economy transition to the new steady state after an increase in the population growth rate?

Answer 77

1. A higher population growth rate increases the break-even investment.
2. Actual investment becomes lower than the new break-even investment, leading to a decrease in the capital-labor ratio.
3. A falling capital-labor ratio reduces output per worker.
4. Diminishing returns cause the capital-labor ratio to continue falling, but at a decreasing rate.
5. Eventually, the economy reaches a new steady state with lower capital-labor and output-labor ratios.

Question 78

What are the economic implications of a falling capital-labor ratio during the transition?

Answer 78

As the capital-labor ratio declines, the economy experiences a negative growth in per-worker output and capital, aligning with the new higher population growth. The capital-labor ratio declines until it stabilises at the new lower steady state level.

Question 79

How do diminishing marginal returns to capital and break-even investment interact during the transition to steady state with higher population growth?

Answer 79

As the capital-labor ratio falls, the marginal product of capital diminishes, causing the investment per worker needed to keep capital per worker constant (break-even investment) to also fall, but less than the actual investment, facilitating the transition to the new steady state.

Question 80

What are the long-term effects of an increase in population growth on the economy’s steady state?

Answer 80

Long-term effects include a lower steady state level of capital per worker and output per worker, reflecting the more rapid dilution of capital due to a faster-growing labor force, before the economy stabilises at this new steady state.

Question 81

What does the model predict regarding countries with higher average saving/investment rates?

Answer 81

Countries with higher average saving/investment rates will have higher average per capita output as higher savings lead to greater investment in capital, which increases the capital-labour ratio and hence output per worker in the steady state

Question 82

What does the model say about the relationship between population growth rates and per-capita output?

Answer 82

Countries with higher population growth rates will have lower levels of per-capita output, because more rapid population growth dilutes capital more quickly, leading to a lower capital-labor ratio and thus lower output per worker at the steady state.

Question 83

Does the model predict growth in per-capita income?

Answer 83

This version of the model does not predict continuous growth in per-capita income in the steady state; however, it does indicate that countries will experience growth in per-capita output/income as they approach the steady state.

Question 84

How does the current capital-labor ratio of a country affect its growth rate in per-capita output/income?

Answer 84

The model predicts that the further a country’s current capital-labor ratio is below the steady state, the faster its per-capita output/income will grow as it catches up to the steady state.

Question 85

Why is the concept of the steady state important for the model’s predictions?

Answer 85

The steady state is crucial because it provides a benchmark for comparing actual economic performance. It allows the model to make predictions about the levels of per-capita output and the growth rates along the transition path towards the steady state.