I am assuming that the production function for the economy has constant returns to scale, and all other inputs stay the same.
These are the steps I have made to try to answer this question:
1) Y/L = Productivity
2) Therefore, if Y=3 and L=2 (There were 2 workers in the economy), so Productivity = 3/2
3) L doubled, so now L=4
4) Now Productivity is equal to 3/4.
5) Productivity has therefore fallen by half of its former value.
Am I right in stating this? If not, can you please explain to me where I am going wrong?