Which is a fine song, though not related to The Farmer's Cursed Wife. It appeared on broadsides as The Politick Wife, and three examples can be seen at Bodleian Library Broadside Ballads:

The politick wife. Or the Devil outwitted by a woman Harding B 4(58)- printer and date unknown.

The politick wife: or The devil out-witted by a woman Douce Ballads 2(175b) -printer and date unknown, presumed 18th century.

The politick wife: or, The devil outwitted by a woman Printed between 1736 and 1763 by W. and C. Dicey, the Printing-Office in Bow-Church-Yard, London.