Capital Accumulation and Steady State Equilibrium

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Questions and Answers

What is the relationship between investment and depreciation in the steady-state?

Investment is higher than depreciation.

Investment is equal to depreciation. (correct)

Investment is lower than depreciation.

Investment is not related to depreciation.

What happens to output per worker initially, when investment increases?

Output per worker immediately increases to a new steady-state level.

Output per worker temporarily increases and then gradually decreases. (correct)

Output per worker remains constant at the initial level.

Output per worker temporarily decreases and then gradually increases.

What is the lowest level of output per worker that the economy reaches?

The level of output per worker at point B.

The level of output per worker at point (*) (correct)

The initial level of output per worker.

The steady-state level of output per worker.

What happens to output per worker after reaching the lowest level?

Output per worker starts to increase. Signup and view all the answers

What does the term 'steady-state' refer to in this context?

A state of zero economic growth. Signup and view all the answers

What is the impact of the depreciation rate on output per worker?

Higher depreciation rate leads to lower output per worker. Signup and view all the answers

What happens to output per worker as the economy transitions from point A to point B?

Output per worker first increases and then decreases. Signup and view all the answers

What is the relationship between the depreciation rate and the steady-state output per worker?

Higher depreciation rate leads to lower steady-state output per worker. Signup and view all the answers

What is the formula for growth?

$\frac{change}{initial\ state}$ Signup and view all the answers

What does "ga" represent in the provided context?

Growth of aggregate capital Signup and view all the answers

The formula "$ga = Igr + ga$" implies that the growth of aggregate capital is equal to the sum of:

Growth rate of investment and the growth rate of aggregate capital Signup and view all the answers

The text mentions "effective worker." What does it mean by this term?

A worker who uses more capital per unit of labor. Signup and view all the answers

The text states that when investments per effective worker are higher than investments per worker, there is a change in capital per effective worker. What type of change is it?

A decrease Signup and view all the answers

What does the "CAE" refer to, as mentioned in the text?

Capital-augmenting efficiency Signup and view all the answers

What happens to the number of effective workers over time in the extensive model?

It increases over time. Signup and view all the answers

What is required to maintain the same ratio of capital to effective workers?

A proportional increase in capital stock. Signup and view all the answers

What happens to "a" when investments per effective worker are higher than investments per worker?

It decreases Signup and view all the answers

What is the concept of growth, as defined by the text?

The rate of change of a variable over time Signup and view all the answers

What is the implication of the capital stock increase in relation to effective workers?

Capital stock must increase proportionally to the increase in effective workers. Signup and view all the answers

What condition is implied when the economy operates at lower levels than optimal?

It demands increases in capital stock to reach optimum. Signup and view all the answers

The text mentions "$s x (d gatgn)$". What is the relationship between this value and the growth of aggregate capital?

It is inversely proportional Signup and view all the answers

The text mentions that there is "no growth...of...and." What is it referring to here? (Select all that apply)

Investment Signup and view all the answers

In the extensive model, what can be inferred about the relationship between effective workers and capital?

More effective workers require a proportional increase in capital. Signup and view all the answers

What happens to capital per worker when it is too high to be sustained?

It decreases until it reaches a sustainable level. Signup and view all the answers

What must occur for capital per worker to reach its steady state?

Investment must equal depreciation. Signup and view all the answers

What is the initial condition of capital per worker described in the content?

Too high to be sustained. Signup and view all the answers

What indicates that the economy has reached a steady state?

Capital per worker stabilizes. Signup and view all the answers

How does the saving rate influence capital per worker?

It determines how quickly capital decreases. Signup and view all the answers

What is the relationship between investment and capital per worker in the steady state?

Investment equals depreciation. Signup and view all the answers

What effect will continued high capital per worker have on the economy?

It will lead to eventual capital depletion. Signup and view all the answers

Which factor is not mentioned as influencing capital per worker?

Population size. Signup and view all the answers

What does a change in capital per worker equal when there is no growth?

Equal to zero Signup and view all the answers

What is included in the extended Solow Model that differentiates it from the basic model?

Technological progress Signup and view all the answers

In the extended Solow Model, what is the production function used?

y = F(k, A) Signup and view all the answers

What do the variables ga and gn represent in the extended Solow Model?

Growth rates of technology and population Signup and view all the answers

What is the implication of a positive growth rate in the context of capital per worker?

It shows improvement in productivity Signup and view all the answers

Which model assumes technology progress is labor-augmenting?

Extensive Solow Model Signup and view all the answers

How does an increase in savings affect the extended Solow Model?

It promotes capital accumulation Signup and view all the answers

What does point A represent in the context of steady-state equilibrium?

The steady-state equilibrium of capital per worker and output per worker Signup and view all the answers

What results from a zero change in capital per worker in the model described?

Economic growth stagnation Signup and view all the answers

What is required for the economy to be at steady-state equilibrium according to the information provided?

Investments per worker must be equal to necessary investments per worker Signup and view all the answers

At point A, what are the investments per worker characterized by?

Being equal to necessary investments plus steady state Signup and view all the answers

Which of the following is NOT a characteristic of steady-state equilibrium as depicted in the graphic?

Maintains increasing investments over time Signup and view all the answers

In the context of steady-state equilibrium, what does 'necessary investments per worker' refer to?

Basic investments required to prevent decline in output Signup and view all the answers

What does steady-state equilibrium imply for future economic growth?

Growth potential is limited unless investments change Signup and view all the answers

What outcome occurs if investments per worker fall below necessary investments?

The economy faces potential decline Signup and view all the answers

What signifies a shift away from point A in the steady-state equilibrium?

An increase in investments beyond necessary levels Signup and view all the answers

Study Notes

Capital Accumulation Equation (CAE)

The change in capital per worker is determined by the difference between investment per worker and depreciation per worker.
Investment per worker increases with capital per worker, but the effect diminishes with higher capital levels due to diminishing returns to capital.
When capital and output are low, investment exceeds depreciation, leading to capital increases.
When capital and output are high, investment is less than depreciation, causing capital to decrease.

Steady State Equilibrium

A steady state is a state where the change in capital per worker is zero.
Investment per worker equals necessary investment per worker in the steady state.
In the steady state, capital and output per worker remain constant.
The growth/decline of capital is determined by the difference between investment and depreciation.

Extensive Model

The model illustrates the relationship with capital in an economy that progresses without technological improvements.
The relationship in output per worker versus capital per worker is crucial.
The economy will move towards a steady state with constant quantities of output and capital per worker.

Savings Rate and Growth Effect

A higher savings rate leads to higher capital and output per worker in the short term.
However, this only results in higher levels of output, not growth.
With higher savings, the economy eventually reaches a new steady state with higher capital and output per worker, but the growth rate remains the same.

Depreciation and Growth

An increase in depreciation shifts the investment per worker function downwards, resulting in a temporary decrease in capital per worker.
The economy will then reach a new steady state with lower levels of capital and output per worker, but the growth rate remains the same.

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Description

This quiz covers concepts related to the Capital Accumulation Equation and steady state in economic models. You'll explore how investment and depreciation influence the change in capital per worker and what defines a steady state in economics. Test your understanding of these crucial concepts in economic growth.