Final answer:
For a firm with a production function characterized by constant returns to scale, doubling all inputs will result in a doubling of output without any change in productivity, corresponding to Option C.
Step-by-step explanation:
In the context of a firm with a production function that has constant returns to scale, doubling all inputs will result in a doubling of the firm's output. This scenario is described by the concept of constant returns to scale, indicating that when all inputs are increased by a certain proportion, the output will increase by the same proportion. Therefore, if a firm doubles all the inputs, its output should also double, maintaining the same level of productivity.
The correct answer to the student's question is Option C: double but productivity will not change. Since the proportionate increase in inputs leads to an equal proportionate increase in outputs, productivity, which is measured by the ratio of output to inputs, remains unchanged. It's important to contrast this with other kinds of returns to scale. In the case of increasing returns to scale, output would more than double when inputs are doubled, and in the case of decreasing returns to scale, output would less than double.