Final answer:
The correct trade theory is New Trade, which considers government's role in assisting home companies and accepts government involvement for national security reasons.
Step-by-step explanation:
The trade theory that indicates that government may play a role in assisting its home companies, and acknowledges government involvement in areas such as space exploration for national security reasons, is New Trade theory. This theory differs from classical theories like Comparative Advantage, which simply suggests that countries should specialize in producing and exporting goods in which they can produce at a lower opportunity cost than other countries.
Unlike New Trade theory, Comparative Advantage does not specifically account for government intervention in trade, although it is acknowledged that government policies can and do affect trade.
For instance, although nation Y may have a comparative advantage in producing missile defense systems, it may not export these to nation X if they are geopolitical rivals. Similarly, a country may place restrictions on imports of goods that are culturally significant, such as Japan's case with rice, despite other nations possibly having a comparative advantage in rice production.