Answer:
a. The demand curve facing a monopolistic competitor in a market where all producers charge different prices becomes less elastic when it engages in international trade - Disagree
This statement is not true. If a monopolistic competitor engages in international trade, it will meet more competition, meaning that the audience (demand) that it has is more sensitive to prices, because they have more options available.
b. According to the gravity equation, countries closer to each other trade more - Agree
The gravity equation tells us that the volume of international trade is correlated with geographical proximity and economic size. That is to say, the closer and larger two economies are, the more international trade they engage with each other.
c. The only gain from trade in monopolistic competition in trade is lower prices - Disagree
Gains are the most important in lower prices, but there are also gains in competitiveness and quality.
d. The closer to 1 the index of intra industry trade is, the greater the difference between exports and imports of the same goods. - Disagree
An index of intra industry trade of 1 indicates that the country imports and exports roughly the same amount for a particular type of goods (the goods that belong to that industry). Hence, the statement is not true.