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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?

A. It depends on the depreciation rate
B. It depends on the population growth rate
C. The level of capital per worker will increase while the level of output per worker will stay the same
D. The level of capital per worker will stay the same while the level of output per worker will decrease
E. The level of capital per worker and output per worker will be negative
F. The level of capital per worker and output per worker will stay the same
G. The level of capital per worker and output per worker will increase
H. The level of capital per worker and output per worker will decrease
I. It depends on the saving rate

Answer :

The correct answer is D. The level of capital per worker will stay the same while the level of output per worker will decrease.

When an economy starts with an initial level of capital per worker (k0) above its steady-state level of capital per worker (k*), there will be adjustments that occur over time. All else being equal, the following will happen:

1. Output per worker: Initially, the level of output per worker will be higher than the steady-state level. However, over time, as the capital stock adjusts towards the steady-state level, the output per worker will decrease. This is because the diminishing returns to capital will lower the productivity of each worker as the capital per worker decreases.

2. Capital per worker: The level of capital per worker will gradually decrease towards the steady-state level. This adjustment occurs due to investment and depreciation. As the capital stock decreases, the capital per worker also decreases.

Therefore, the correct answer is D. The level of capital per worker will stay the same while the level of output per worker will decrease.

It is important to note that the outcome may also depend on factors such as the depreciation rate, population growth rate, and saving rate. However, in this scenario, all else is equal, so these factors do not come into play.

In summary, when an economy begins with an initial level of capital per worker above its steady-state level, there will be a decrease in output per worker while the level of capital per worker gradually adjusts towards the steady-state level.

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