Now suppose they get themselves hurt while working on your property (by stepping in a hole and twisting their ankle, for example). Congratulations, you've now opened yourself up to personal liability in an injury lawsuit.
You seem to be neglecting the impact that insurance requirements (both personal, commercial, health, and otherwise as required by legislation) have had on this "free market for labor".
(Plus, not all markets for labor are equal in America. Try and translate your lawnmower example to the medical field, for example.)
If you settle on a rate of $40 for the one acre and it takes someone four hours to do the job, then you are already violating the minimum wage laws in at least 27 states plus the District of Columbia.
And if you pay someone $100 for this work and they do it a dozen times over the course of the summer, you have to file a 1099 form to report the money you've paid them. Otherwise, they are considered W-2 employees and you have to deduct (and pay) payroll taxes, make WCI payments, etc. for their work. How can it possibly be a "free market" for labor when you have so many conditions imposed by a third party that isn't the employer or the employee?