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Say an economy begins with an initial level of capital per worker, \( k_0 \), that is above its steady state level of capital per worker, \( k^* \). All else equal, what will happen to output per worker and capital per worker over time?

Answer :

In summary, when an economy begins with an initial level of capital per worker above its steady state level, there will be short-term gains in output per worker. When an economy begins with an initial level of capital per worker, k0, that is above its steady state level of capital per worker .

Output per worker: In the short run, the economy will experience higher output per worker compared to the steady state level. This is because the initial level of capital per worker is above the steady state level, leading to higher productivity and output. However, over time, as the economy adjusts towards the steady state, the output per worker will gradually decline until it reaches the steady state level. This is because the diminishing returns to capital will start to take effect, causing the additional capital to have a lesser impact on output. Capital: Initially, the economy has more capital per worker than the steady state level. As the economy adjusts towards the steady state, the additional capital will be gradually absorbed and used up, resulting in a decline in capital per worker. The adjustment process may involve investment in new capital, depreciation of existing capital, or both.

Eventually, the economy will reach the steady state level of capital per worker, where the amount of capital per worker remains constant. To better understand this concept, let's consider an example. Imagine an economy with an initial level of capital per worker that is above the steady state level. Initially, this excess capital will lead to increased productivity and output per worker. For instance, if there are more machines available for each worker, they can produce more goods or services. However, as the economy adjusts, the marginal returns from the additional capital will start to diminish. This means that the increase in output per worker will become smaller until it reaches the steady state level. Similarly, the excess capital will gradually be used up or absorbed by the economy, resulting in a decline in capital per worker. This adjustment process ensures that the economy eventually reaches the steady state level of capital per worker, where the amount of capital per worker remains constant and the economy achieves long-term equilibrium.

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