The rate of capital depreciation rises permanently. Given the saving rate, what are the effects on steady-state capital per worker and output per worker?

Increased capital depreciation leads to a reduction in the steady state levels of capital per worker and output per worker when the saving rate remains constant. This is due to the decreased net investment in capital as more savings are directed towards replacing depreciated capital, limiting economic growth.

Explanation:

When capital depreciation increases permanently, it negatively affects the amount of capital available per worker since a larger portion of the savings used to replace depreciated capital cannot be used for net investments. Given the saving rate is unchanged, the steady state capital per worker would decrease because less capital accumulation is happening, leading to a lower steady-state level of capital. Consequently, since output is a function of capital, the output per worker will also decrease, moving the economy to a new, lower steady state of output per worker.

According to the theory of diminishing marginal returns, initial investments in capital deepening, which means increasing the amount of capital per worker, can result in significant increases in per capita output. However, after certain levels of capital per worker, additional amounts of capital will yield smaller increases in output. Thus, with higher capital depreciation, the effect of these diminishing returns is compounded, further restraining the growth of both capital per worker and output per worker in the long run.