Q. The Brazilian firm is charging its foreign (U.S.) customers one half the price it is charging its domestic customers. Is this bad or good for the real income or economic welfare of the United States? Is the Brazilian firm engaged in dumping? Is this predatory nature on the part of the Brazilian steel company?

Answers: Good yes if you define dumping as selling abroad at a price lower than domestically. No if by dumping you denote selling below marginal cost. No - this isn't being done in order to capture market shares other than rather is "mere" static profit maximization behaviour as is expected of any self-respecting monopolist.