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Capital deepening refers to an increase in the capital stock per worker in an economy. This can result from either an increase in the capital stock (physical capital) or a decrease in the number of workers (labor).

Improvements in technology refer to advancements in the techniques, methods, and tools used to produce goods and services. This can include the development of new machinery, software, processes, or even organizational structures that increase productivity and efficiency.

The law of diminishing returns states that as more units of a variable input (like labor or capital) are added to a fixed input (like land), the marginal returns from each additional unit will eventually decrease. It's important to note that this law applies when other factors are held constant. Regarding capital deepening, we can expect to see an initial increase in returns as more capital is added per worker because it allows the workers to work more efficiently. However, as the amount of capital per worker continues to increase, the additional capital will eventually yield diminishing returns. This is because the productivity gains from extra capital become smaller as workers already have a large amount of capital to work with. Thus, capital deepening can initially lead to increased returns, but will eventually result in diminished returns when other factors are held constant.

Technological improvements can increase the productivity of both labor and capital, allowing for the production of more output with the same inputs. Unlike capital deepening, advancements in technology generally do not result in diminished returns. Technology improvements can shift the production function upwards, indicating that the same level of inputs can now produce a higher level of output. Therefore, with technological innovations, the additional returns from each unit of capital or labor do not necessarily diminish over time. In fact, technology can overcome or push back the point at which diminishing returns set in, as the new production methods allow for more efficient use of the inputs. It's important to note, however, that some specific technologies' impacts might decrease in significance over time as they become widely adopted, but this doesn't represent a general rule for all technological improvements. In conclusion, we wouldn't expect improvements in technology to result in diminished returns in general, unlike capital deepening.