Learn Polish: Państwo płaci emerytury. - The state pays pensions.

The word państwo has two distinct meanings. When used as a polite pronoun for ladies and gentlemen or Mr. and Mrs., it takes a plural verb, like państwo płacą. However, in this sentence, it means the state or the country. In this meaning, it is a regular neuter singular noun, so it correctly takes the third-person singular verb płaci.

What case is emerytury in here?

It is in the accusative case because it is the direct object of the verb. The base singular word is the feminine noun emerytura. For feminine nouns ending in -a, the accusative plural ending is -y, making it emerytury, which happens to look exactly like the nominative plural form.

How would this sentence change if the state was only paying one single pension?

You would need to change emerytury to its singular accusative form. Since it is a feminine noun ending in -a, the ending changes to -ę in the accusative singular. The sentence would become Państwo płaci emeryturę.

Why use the imperfective verb płaci instead of the perfective zapłaci?