> I assert, instead, that appropriate compensation is proportional to the productivity of the work.
Productivity puts a ceiling on the compensation (If the farm owner is only getting $10/hr of productivity out of the laborers, there's no way they're going to pay more than $10/hr in the long run because they lose money if they do.), but supply and demand in the labor market decides the rate. It'll generally below the value that employers get from the workers (meaning that the employer profits from the arrangement).
Now it's a little more complicated than that because of imperfect information (the farm owners don't know how many people are going to come around looking for work or how little pay they'll take) and imperfect competition (Even if a worker hears that he could make twice as much 500 miles away, he might have to take the job where he is if he has no good way to get to that area with better jobs.), but that's how it works in theory.