I am a novice and I’m trying to understand the division of labor principle. I understand the example in your powerpoint presentation (slides 4,5,6 of voluntary exchange and division of labor lecture). Does it work with all numbers? What if Crusoe could continually produce 40 A or 20 B per unit of work and Friday 20 A or 10 B? (Crusoe always is twice as productive). Is there any benefit to specialization? Thank you.
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.