Tending to one's land definitely requires more effort than tending to someone else's. If it were partitioned, it can be substantiated that the grain production in the public land area would absolutely be excellent.
Therefore, the income from the public land is calculated based on the average yield of all mountain areas. After deducting farming costs, the extra earnings are then divided amongst everyone.
This complex calculation method, obviously, is a bit difficult for the serfs. However, as the lowest rung of society, one thing they do understand is—getting more grain.
The most important thing is that this isn't a one-time deal. Every year at harvest time, aside from their daily rations, they could get a portion of grain.
Work hard for a year, receive grain for a lifetime. Such a good deal is rare to come by.