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Which of these statements is NOT true about the steady state of the basic Solow model?

1. The capital per worker and output per worker are constant.

2. The investment per worker is always equal to the depreciation per worker.

3. The marginal product of capital is always equal to the depreciation rate.

4. The saving and consumption per worker are constant.

Answer :

The Solow Growth Model, also known as the Solow–Swan model, is an exogenous growth model that explains long-term economic growth based on capital accumulation, labor or population growth, and increases in productivity. It was developed in the 1950s by Robert Solow and Trevor Swan.

In the steady state of the Solow model:

  1. The capital per worker and output per worker are constant.

    • This is true as the steady state is defined where there is no further change in capital per worker and output per worker due to the balance between investment and depreciation.
  2. The investment per worker is always equal to the depreciation per worker.

    • This is true because in the steady state, the amount of investment generated from savings is exactly enough to cover the depreciation on existing capital, maintaining a constant capital per worker.
  3. The marginal product of capital always is equal to the depreciation rate.

    • This statement is NOT true. In the steady state, the marginal product of capital does not necessarily equal the depreciation rate. Instead, the marginal product of capital is equal to the depreciation rate plus the rate of population growth and technological progress combined.
  4. The saving and consumption per worker are constant.

    • This is true because, in the steady state, the economy grows at a constant rate, which means that both saving and consumption per worker remain constant.

Based on this analysis, statement 3, "The marginal product of capital always is equal to the depreciation rate," is NOT true in the context of the steady state of the Solow model.

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