Our residential well is drying up due to surrounding irrigation, who fixes this, us or farmer?

I don't think you are going to get farmers to stop irrigating their crops. Sounds like you need to drill a deeper well.

Why do you say its surrounding irrigation? Contact the local health department/building department or the State of Michigan MDEQ/MDNR to ask them if there are regulations. groundwater issues are problematic wherever they occur.

I would need more information to answer your question. The rule in Michigan is a landowner who uses ground water for a beneficial purpose is not subject to liability for interference if certain conditions are met. The water withdrawal cannot cause unreasonable harm to a neighbor by lowering the water table or reducing artesian pressure, cannot exceed a reasonable share of the total store of ground water and cannot create a direct and substantial effect on a watercourse or lake.

Please consult a real estate attorney.