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?

<p>Output per worker starts to increase. (D)</p> Signup and view all the answers

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

<p>A state of zero economic growth. (D)</p> Signup and view all the answers

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

<p>Higher depreciation rate leads to lower output per worker. (B)</p> Signup and view all the answers

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

<p>Output per worker first increases and then decreases. (A)</p> Signup and view all the answers

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

<p>Higher depreciation rate leads to lower steady-state output per worker. (C)</p> Signup and view all the answers

What is the formula for growth?

<p>$\frac{change}{initial\ state}$ (A)</p> Signup and view all the answers

What does "ga" represent in the provided context?

<p>Growth of aggregate capital (B)</p> Signup and view all the answers

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

<p>Growth rate of investment and the growth rate of aggregate capital (D)</p> Signup and view all the answers

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

<p>A worker who uses more capital per unit of labor. (B)</p> 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?

<p>A decrease (A)</p> Signup and view all the answers

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

<p>Capital-augmenting efficiency (C)</p> Signup and view all the answers

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

<p>It increases over time. (D)</p> Signup and view all the answers

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

<p>A proportional increase in capital stock. (C)</p> Signup and view all the answers

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

<p>It decreases (A)</p> Signup and view all the answers

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

<p>The rate of change of a variable over time (B)</p> Signup and view all the answers

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

<p>Capital stock must increase proportionally to the increase in effective workers. (D)</p> Signup and view all the answers

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

<p>It demands increases in capital stock to reach optimum. (B)</p> 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?

<p>It is inversely proportional (C)</p> 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)

<p>Investment (B), Labor (D)</p> Signup and view all the answers

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

<p>More effective workers require a proportional increase in capital. (B)</p> Signup and view all the answers

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

<p>It decreases until it reaches a sustainable level. (D)</p> Signup and view all the answers

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

<p>Investment must equal depreciation. (B)</p> Signup and view all the answers

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

<p>Too high to be sustained. (A)</p> Signup and view all the answers

What indicates that the economy has reached a steady state?

<p>Capital per worker stabilizes. (B)</p> Signup and view all the answers

How does the saving rate influence capital per worker?

<p>It determines how quickly capital decreases. (C)</p> Signup and view all the answers

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

<p>Investment equals depreciation. (A)</p> Signup and view all the answers

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

<p>It will lead to eventual capital depletion. (D)</p> Signup and view all the answers

Which factor is not mentioned as influencing capital per worker?

<p>Population size. (A)</p> Signup and view all the answers

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

<p>Equal to zero (D)</p> Signup and view all the answers

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

<p>Technological progress (A)</p> Signup and view all the answers

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

<p>y = F(k, A) (C)</p> Signup and view all the answers

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

<p>Growth rates of technology and population (C)</p> Signup and view all the answers

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

<p>It shows improvement in productivity (D)</p> Signup and view all the answers

Which model assumes technology progress is labor-augmenting?

<p>Extensive Solow Model (D)</p> Signup and view all the answers

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

<p>It promotes capital accumulation (B)</p> Signup and view all the answers

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

<p>The steady-state equilibrium of capital per worker and output per worker (A)</p> Signup and view all the answers

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

<p>Economic growth stagnation (D)</p> Signup and view all the answers

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

<p>Investments per worker must be equal to necessary investments per worker (D)</p> Signup and view all the answers

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

<p>Being equal to necessary investments plus steady state (C)</p> Signup and view all the answers

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

<p>Maintains increasing investments over time (B)</p> Signup and view all the answers

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

<p>Basic investments required to prevent decline in output (A)</p> Signup and view all the answers

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

<p>Growth potential is limited unless investments change (A)</p> Signup and view all the answers

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

<p>The economy faces potential decline (C)</p> Signup and view all the answers

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

<p>An increase in investments beyond necessary levels (C)</p> Signup and view all the answers

Flashcards

Initial Capital per Worker

The initial amount of capital available to each worker in an economy.

Saving Rate

The rate at which savings are accumulated in an economy, expressed as a proportion of income.

Unsustainable Capital per Worker

The situation where the initial capital per worker is too high for the current saving rate to sustain. This leads to a decline in capital per worker over time.

Steady State of the Economy

The point at which investment in new capital equals the depreciation of existing capital. This leads to a steady state where capital per worker remains constant.

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Capital Per Worker Decreasing

The process of capital per worker decreasing until it reaches the steady state. This occurs when the saving rate is insufficient to maintain the initial capital per worker.

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Investment

The total amount of investment made in new capital within an economy.

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Depreciation

The rate at which existing capital wears out or becomes obsolete.

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Investment = Depreciation

The process by which investment in new capital balances out depreciation, resulting in a constant level of capital per worker.

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Capital-to-Effective-Worker Ratio

As the number of effective workers increases over time, maintaining the same capital-to-effective-worker ratio requires an increase in the capital stock (k) proportional to the increase in the number of effective workers (AN).

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Constant Capital-to-Effective-Worker Ratio

The number of effective workers (AN) increases overtime, which leads to an increase in capital stock (k). Having a larger pool of effective workers demands more resources to maintain the same level of efficiency.

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Economic Growth and Capital-to-Effective-Worker Ratio

The ratio of capital stock to effective workers plays a crucial role in economic growth. To maintain sustained growth, the capital stock needs to increase proportionally as the number of effective workers increases.

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Capital-to-Effective-Worker Ratio and Economic Growth

The increase in effective workers requires an increase in capital stock to maintain the same ratio. This is essential for sustained economic growth and productivity.

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Effective Workers

Effective workers are those who contribute to economic output. They can be described as skilled, knowledgeable, and capable of utilizing available resources efficiently.

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Steady state equilibrium

The level of capital per worker where investment equals depreciation, resulting in a constant level of capital and output per worker.

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Capital per worker (k)

The amount of capital per worker in an economy. It represents the amount of tools and equipment available for each worker.

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Output per worker (y)

The amount of output produced by each worker in an economy.

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Depreciation rate (δ)

The rate at which capital stock depreciates or wears out over time.

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Investment per worker (i)

The amount of investment in new capital per worker in an economy.

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Necessary investment

The level of investment per worker required to maintain the steady state equilibrium.

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Point A

The point where the economy is at its steady state equilibrium, with constant capital and output per worker.

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Starting point

The point where the economy is not yet at its steady state equilibrium.

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Steady-state point

The point where the economy reaches a stable state, with investment in new capital matching the depreciation of existing capital. This results in a constant level of capital per worker.

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Capital per worker

The amount of capital available per worker in an economy. A higher capital per worker generally indicates more productive workers and a higher standard of living.

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Depreciation Rate

The rate at which existing capital wears out, becomes obsolete, or loses value. This is a natural process that reduces the effectiveness of capital over time.

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Long-Run Capital Per Worker

In the long run, with consistent technological progress, the amount of capital per worker remains stable, leading to no overall economic growth.

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Solow Model

The Solow Model focuses on economic growth by analyzing the relationship between capital, labor, and technological progress.

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Extended Solow Model

The extended version of the Solow Model incorporates technological progress, which is assumed to be labor-augmenting, leading to higher labor productivity.

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Growth Rate of Technology (ga)

The growth rate of technology, a key factor in the Extended Solow Model, affects how quickly productivity improves.

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Growth Rate of Population (gn)

The growth rate of population, another important aspect of the model, influences the demand for resources.

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Investment and Depreciation

Capital invested in new production contributes to economic growth by increasing overall output, but depreciation reduces the capital stock over time.

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Maintaining the Capital-to-Effective-Worker Ratio

The ratio of the capital stock to the number of effective workers must remain consistent to sustain steady economic growth.

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Growth Rate

The change in a quantity, such as capital per worker, divided by the initial state of that quantity.

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Necessary Investment per Effective Worker

The amount of capital available per worker that is needed to maintain a particular level of productivity and economic growth.

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Change in Capital per Effective Worker

The change in the capital per worker.

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Negative Change in Capital per Effective Worker

The decline in the capital per worker due to insufficient saving and investment.

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Change in Capital per Effective Worker with Increasing Effective Workers

The change in capital per effective worker when there is an increase in effective workers.

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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.

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