If an increase in all factors of production results in an equal increase in output, what property does the production function have?

A production function exhibits constant returns to scale when an increase in all inputs leads to a proportional increase in output. In this case, if doubling all factors of production results in output also doubling, the function clearly demonstrates this property. It signifies that the production process is efficient and that scaling up inputs results in a directly proportional increase in output, reflecting the stable relationship between input and output.

In contrast, decreasing returns to scale would imply that output increases by a lesser proportion than the increase in input, suggesting inefficiencies in scaling. Increasing returns to scale would mean output increases by a greater proportion than input, indicating that growing factors lead to greater efficiencies. Variable returns to scale encompasses any scenario of scaling input where the relation is not consistent, but again, the lack of a proportional output increase does not apply in this case.

Thus, the characterization of the production function as exhibiting constant returns to scale is accurate because all inputs are increased simultaneously, resulting in an equal proportional increase in output.