I think its the opposite, prices will likely plummet even more.
The only thing keeping prices as high as they are now are government subsidies, and the literal federal government purchase and destruction of large amounts of produce.
I say let the floor fall out from under them, and open up instantaneous food-trade agreements with countries that have less agriculture space, or quickly growing populations.
India, the Maghreb region, and Venezuela are all open, or should be.
Be a pseudo-humanitarian super-power and make it rain food internationally to garner support.