A costly tug of war has broken out over what is usually one of the Farm Belt’s most ubiquitous commodities: corn.

Agribusiness companies, including Cargill Inc., Archer Daniels Midland Co. ADM, +0.90% and Smithfield Foods Inc. are dangling hefty premiums to buy bushels of corn in places where unrelenting rain this spring prevented farmers from planting millions of acres.