Final answer:
Technological change shifts the per-worker production function upward (option A), allowing for increased output with the same level of inputs, and enables economies to avoid diminishing marginal returns of capital deepening. It improves labor productivity through invention and innovation, exemplified by developments like the transistor.
Step-by-step explanation:
Technological change affects the per-worker production function by shifting the function upward. This means that, for a given amount of capital per worker, a technological improvement can lead to an increased level of output. For instance, as illustrated in various figures, when technology moves from Technology 1 to Technology 2 or Technology 3, each amount of capital deepening on the horizontal axis will result in a higher level of output on the vertical axis.
In the context of the per-worker production function, the introduction of new technology does not simply move the economy along the existing curve; rather, it creates a new function that allows the economy to sidestep the issue of diminishing marginal returns of capital deepening. The new technology increases the efficiency of both human and physical capital, enabling increased per capita output even when the capital deepening is constant.
Overall, technological change plays a crucial role in increasing labor productivity. Through invention and innovation, such as the development of transistors, workers can perform tasks more efficiently and effectively, leading to technological advancements that boost the per-worker production function.