January 20, 2016 at 10:22 am #18666
The greater productivity of the division of labor depends on a difference in the efficiency of the producers. If their efficiency differs, then specialization replaces a less efficient producer with a more efficient producer. With the same inputs, then, output will be greater.
In your example, the efficiency of Crusoe and Friday is the same. Each of them forgoes 2A to produce another unit of B. 40/20 = 20/10 = 2/1. If different persons are the same, then, they would be interchangeable in different production processes without a loss of productivity.