Final answer:
The change in the production function from Q = √KL to Q=K√L represents technological progress, as it suggests higher output for the same levels of labor and capital, indicating a more productive use of these inputs. The change is labor-saving because it increases the output elasticity of capital relative to labor.
Step-by-step explanation:
When evaluating a firm's production function, which initially is Q = √KL and later changes to Q=K√L, we can ascertain whether this change represents technological progress and what type of change it is in terms of labor and capital. In the initial function, both capital (K) and labor (L) are under the square root, indicating they are used in equal proportion to produce output. Over time, if the production function evolves to Q=K√L, it implies that capital has a greater direct impact on production, indicating technological progress. This is because each unit of capital K is now multiplied by the increase in production due to additional units of labor to the power of 0.5 (or square root of labor).
Technological progress is indicated by the increase in output resulting from the same or less input. In this case, for a given level of K and L, the new production function would generate a higher level of Q, assuming L is greater than 1 and K is greater than 1, which is in line with the student's assumptions.
The change can be considered labor-saving or capital-using since it increases the output elasticity for capital while keeping labor's contribution under the square root. Such changes mean that relatively less labor is needed for each unit of capital, as capital has become more productive with thanks to technological advancement.