Learn Turkish: Mükellefin asgari geliri olduğu için vergi muafiyeti var. - Because the taxpayer has a minimum income, they have a tax exemption.

Words that indicate existence, like var (there is) and yok (there isn't), are not verbs and cannot take verbal suffixes. To put them into a subordinate clause like because there is... or because they have..., you must substitute them with the verb olmak (to be). Therefore, var becomes olduğu when combined with the participle and için.

The current lesson is about -dIğI oranda (to the extent that). How does olduğu için in this sentence relate to that?

They use the exact same grammatical foundation! Both structures take a verb root, add the -dIk participle, and follow it with a possessive suffix (here, ol-duk-u). The only difference is the word that comes after it. Using için creates a reason (because they have), while using oranda or ölçüde creates a proportional clause (to the extent they have).

Why does mükellef (taxpayer) take the genitive suffix -in?

It pairs with the possessive suffix on geliri to form the phrase mükellefin geliri (the taxpayer's income). This entire possessive phrase acts as the subject of the subordinate clause olduğu için (because it exists).

How is the phrase tax exemption constructed here?