After buying a hut to raise peasant productivity I got this. (a good bit of time later)
"Now that your peasants live inside a hut, they like to sleep a lot. Your land will produce 15 gold per acre if you remove the hut. Remove the hut for 2,900 gold?"
After tearing down the hut for the workers, they get sick and you get to hire a docter, this will get productivity up by 0.5.
And some time later the docter tells you that you need a housing for him and the workers. this also gives a extra 0.5 productivity.