Do you believe there are any limits to price authority? Or do you believe can the last business standing charge whatever is needed to support the wage rate demanded by an American worker?
Yes. That is how a free market works. They will be able to charge what they want until they get a competitor. If they charge too much then demand will go down, if they charge too little the demand will go up. Regardless, they will have complete control of price until they get a competitor. This is called a "monopoly" by the way.