if an economy has achieved its desired capital stock and wishes to maintain it,should any investment occur?if?

Answer 1

Yes, investment would still have to occur, because of depreciation. As the capital stock wears out, it would have to be replaced to maintain the same level. This is investment. There would be no new net investment, since this is defined as gross investment less depreciation. But investment should still occur.

Answer 2

To add to the answer (investment spending is necessary to offset capital depreciation), consider that not all capital stock is homogenous. Technology updates sometimes require the mothballing of certain capital items. Of course, obsolescence can be viewed as hurried depreciation, and so the expenditure on new technology can be viewed as offsetting (more rapid) depreciation.

It may also be that maintaining the desired capital stock interferes with another economic goal (say growth rate), which would require a higher-than-optimal level of capital stock to produce. It all depends upon the decision framework of that economy.