The role of infinitive in this sentence

Edit Note

This answer was written before Original Question was edited. The sentence is not quite the same but this post should still provide the answer to the new question.

The answer

It is a profitable thing to seem foolish.

The infinitive clause here is the phrase:

• to seem foolish

Notice that this is best understood as a clause, not a verb.

The grammatical function of this phrase is often referred to as Extraposed Subject. It is functioning as a Complement of the verb BE. However, we understand this as meaning:

• [To seem foolish] is profitable.

The reason we don't like to use sentences like the one above is that it is difficult to process sentences when we have an infinitival clause as Subject. We prefer to transform the clause by using a meaningless dummy Subject, the pronoun IT, and then to move the infinitive clause to the end of the sentence/larger clause:

• It is profitable [to seem foolish].

We often also do this with finite clauses too:

• [That Mary punched Bob] surprised me.
• It surprised me [that Mary punched Bob].

Notice that although the original sentences had the infinitival and finite clauses as Subjects, the transformed sentences have the word it as a Subject. The Extraposed Subjects are not grammatical Subjects any more, they are Complements of the verb BE and SURPRISE respectively, and they occur within the Predicate - not as part of the Subject phrases.