Unit 2: Solow Swan with technology

Question 1

What symbol denotes Technology?

Answer 1

A

Question 2

How does technology change over time?

Answer 2

exogenously, increasing at rate g

Question 3

True or false:

The process for technology is imposed from outside the model rather than being explained within it

Answer 3

True- its exogenous

Question 4

How does technology enter the model?

Answer 4

Through the production function:

Y (t) = K(t)^α(A(t)L(t))1−α

Question 5

When we say that technology is labour augmenting, what does this mean from the perspective of the production function?

Answer 5

It means that technology operates much like an increase in the amount of labour in the economy

Question 6

What is the term A(t)L(t) often referred to? Why?

Answer 6

Effective labour because technology operates like an increase in the amount of labour

Question 7

Does the presence of technology in the Solow Swan model change the accumulation equation?

Answer 7

No, the central equations remain the same

Question 8

Why is the model with technology necessary to look at, what did the one without not show?

Answer 8

The model without could not generate rising output-per-worker or rising capital-per-worker in steady state

Question 9

What must be the case in order for output-per-worker to grow at a constant rate in steady state?

Answer 9

Capital per-worker must also grow at a constant rate in steady state

Question 10

In the solow swan, sustained growth or long-run growth in capital per worker and output per worker are a consequence of….

Answer 10

Technological progress

Question 11

What must be the case if the model is to have a balanced growth path with constant growth in the capital-labour ratio?

Answer 11

It must be the case that on that balanced
growth path output-per-worker, y (t), and capital-per-worker, k(t), are growing at the same rate, so that y(t)/k(t) is a constant

Question 12

What must be the case for y(t) and k(t) to grow at that same rate?

Answer 12

Both must be growing at rate g

Question 13

How does the Solow-Swan model with technology explain sustained growth in output-per-worker and capital-per-worker?

Answer 13

Sustained growth in these variables is a consequence of technological progress, where both capital-per-worker and output-per-worker grow at the same rate (g) in the steady state, driven by technological advancement.

Question 14

Whats the first step in solving the Solow Swan model with technology?

Answer 14

Normalise (divide) all of the equations by effective labour, A(t)L(t)

Question 15

What is the main difference between the model with technological progress and without?

Answer 15

Break even investment (with technological progress) now includes a term for technology growth since some investment is needed to compensate for rinsing technology purely in order to keep capital-per-effective worker constant

Question 16

How do you solve for steady state?

Answer 16

Look for a value for k(t) where k(t) = 0

Question 17

What three variables affect the steady state of the SS with technology?

Answer 17

growth rate of technology (g), depreciation rate (δ), and the population growth rate, (n)

Question 18

True or false:

In the long run steady state, the SS model predicts that capital-per effective worker, output-per effective worker and consumption per-effective worker do not exhibit growth

Answer 18

True, they are stationary

Question 19

Do variables expressed in per capita terms grow over time?

Answer 19

Yes the capital-labour ratio and output-labour ratio grow over time due to technological progress

Question 20

At what rate does output-per-worker grow at?

Answer 20

the rate of technological progress (g) because it is the product of technology (A(t)) and output-per-effective-worker (y​(t)), which remains constant in steady state.

Question 21

At what rate do capital, consumption and output grow at on the balanced growth path?

Answer 21

Technological progress (g), so per-worker measures increase steadily because of technology improvements, not because of changes in the number of workers or the amount of capital.

Question 22

What is total output (Y(t)) the product of?

Answer 22

The number of workers (L(t)) and the output-per-worker (y(t))

Question 23

What is the growth rate of total output?

Answer 23

sum of growth rate of workers (n) and the growth rate of output per worker (g), so (n + g)

Question 24

What remains stationary on the long-run balanced growth path in the Solow-Swan model with technology?

Answer 24

Capital-per-effective-worker, output-per-effective-worker, and consumption-per-effective-worker remain stationary and non-trending.

Question 25

How is output-per-worker (y(t)) represented in the Solow-Swan model with technology, and what is its long-run growth rate?

Answer 25

By the product of technology (A(t)) and output per effective worker (y(t)). In the long run, (y(t)) grows at the rate of technological progress (g).

Question 26

What is the growth rate of output-per-worker (y(t)) on the balanced growth path, and how is it calculated?

Answer 26

On the balanced growth path, the growth rate of output-per-worker is equal to the growth rate of technology (g). It’s calculated by taking the log-derivative of y(t) with respect to time.

Question 27

What happens to the growth rates of capital, consumption and output along the balanced growth path?

Answer 27

They all grow at the rate of technological progress (g) along the balanced growth path.

Question 28

What are the growth rates of the TOTAL output, capital, and consumption on the balanced growth path?

Answer 28

Total output, capital, and consumption grow at the combined rate of
n+g on the balanced growth path.

Question 29

How does the growth rate of capital-per-effective-worker behave away from the steady state?

Answer 29

If capital-per-effective-worker is below the steady state, it grows positively; if it is above, it grows negatively. This variable adjusts to reach the steady state.

Question 30

True or false:

Countries with higher saving/investment rates and lower rates of depreciation, population growth, and technical progress will tend to be poorer.

Answer 30

False, richer!

Question 31

True or False:

Rising output-per-worker over time is a consequence of technological
progress.

Answer 31

True!

Question 32

True or false:

Differences in growth rates across countries are not a consequence of
differences in saving rates.

Answer 32

True, they are due to differences in
population growth rates and (perhaps) to differences in technological progress rates. Transition dynamics also affect growth rates across
countries.

Question 33

True or False:

Policies affecting a country’s saving/investment rate or its population growth rate can have significant effects on the level of output per capita but only a transitional influence on its growth rate

Answer 33

True, since long-term growth rates are determined by exogenous technological progress, whereas savings and population growth rates only affect the levels of output per capita during transitional phases.

Question 34

What does growth accounting analyse in the production function?

Answer 34

Growth accounting decomposes changes in output into changes in the factors of production—capital and labor—and changes in technology, known as the Solow residual.

Question 35

How is the production function expressed in the Solow-Swan model for growth accounting purposes?

Answer 35

The production function is expressed as Y (t) = B (t) K (t)^α L(t)^1−α, where B(t) represents total-factor productivity related to technology.

Question 36

What does the variable B(t) represent in the Solow-Swan model’s production function, and how is it related to technology?

Answer 36

B(t) is called total-factor productivity or multi-factor productivity, represents the level of technology and is related to it by B (t) = A (t)^1−α

Question 37

How are the growth rates for output, capital, and labor expressed in the Solow-Swan model?

Answer 37

gY = gB + αgK + (1 − α) gL,
gB = (1 − α) gA.
where gY, gK and gL are the growth rates of output, capital, and labor, and gB is the growth rate of total-factor productivity.

Question 38

What is the total-factor productivity growth (Gb) in the context of the Solow-Swan model?

Answer 38

part of output growth not explained by the growth of inputs (capital and labor) and is calculated as gB = gY − αgK − (1 − α) gL.

Question 39

Why is an estimate of α important in constructing the total-factor productivity growth

Answer 39

Because α represents capital’s share of income, which influences how much of the growth in output is attributed to capital versus technology.

Question 40

What was the slow-down in growth that occurred between 1973 and 1995 due to?

Answer 40

Declines in total-factor productivity growth and (to a
lesser extent) in the accumulation of capital

Question 41

True or false:

There is considerable medium-run variation in the rate at which technology grows.

Answer 41

True

Question 42

The variation in total-factor productivity growth suggests a need to model technology exogenously rather than endogenously .

Answer 42

False other way round

Question 43

True or false:

Explaining the productivity slowdown is difficult without a theory for technological progress

Answer 43

True

Question 44

What is the name of the saving rate that maximises steady state consumption-per-worker?

Answer 44

The golden rule saving rate

Question 45

How can the golden savings rate be constructed?

Answer 45

From the Solow-Swan diagram by identifying the point where the slope of the production function (in per-worker terms) equals the slope of the break-even
investment line.

Question 46

What are economies where r < n said to be and what are the implications

Answer 46

dynamically inefficient and suggests that the economy has oversaved, leading to a marginal product of capital lower than what would be optimal.

Question 47

True or False:

The change in the saving rate has a permanent effect on the growth rate of output-per-worker but
a transitory effect on the level of output-per-worker.

Answer 47

No other way round

Question 48

Why in the model with technology do we use “per effective worker” instead of just “per worker” for steady state levels?

Answer 48

“per effective worker” takes into account the augmenting effect of technology on labor productivity, and this adjustment is necessary to analyse the economy’s growth dynamics accurately when technological progress is included in the model