Learn Farsi: دولت برای تصمیم گرفتن به اقتدار نیاز دارد. - The government needs authority to make a decision.

The root of اقتدار consists of the consonants q-d-r (ق-د-ر), which you likely know from the word قدرت (qodrat - power). By slotting these root letters into the e-C1-t-e-C2-â-C3 pattern, we get e-q-t-e-d-â-r (اقتدار). Form VIII often turns a root into a resultant abstract noun or a state of being, translating here perfectly as "authority" or "having power".

Why is the preposition به (be) placed right before اقتدار?

In Farsi, the compound verb for "to need" is نیاز داشتن (niyâz dâshtan). This verb requires the preposition به to introduce the thing that is needed. You can think of the literal translation as saying the government "has a need to authority".

The English translation says "to make a decision", but what does تصمیم گرفتن (tasmim gereftan) literally mean?

Literally, it translates to "taking a decision". While English speakers usually "make" decisions, Farsi speakers "take" (گرفتن) them. This is a very common compound verb pairing that B2 learners should have committed to memory.

Why is تصمیم گرفتن in the infinitive form here instead of the subjunctive, which we usually use for purpose?

After the preposition برای (barâye - for), you can use the full infinitive to quickly and cleanly express purpose ("for deciding" / "in order to decide"). If you wanted to use the subjunctive, you would have to expand the phrase to برای اینکه (barâye inke - for the reason that) and conjugate the verb: (so that it makes a decision). The infinitive form used in this sentence is much more concise.