Learn German: In Bezug auf den Preis habe ich eine Frage. - With regard to the price I have a question.

The fixed phrase in Bezug auf (with regard to) always requires the accusative case. Because Preis is a masculine noun (der Preis), it changes to den Preis. Even though auf is normally a two-way preposition, it strictly takes the accusative in this expression.

Why does the verb habe come before ich in this sentence?

This is because of the strict 'verb second' rule in German. The entire phrase In Bezug auf den Preis occupies the first position in the sentence. The verb habe must take the second position, which forces the subject ich into the third position.

What does the noun Bezug mean outside of this phrase?

Der Bezug means a reference or connection. It is closely related to the reflexive verb sich beziehen auf, which means to refer to something. When you say in Bezug auf, you are literally saying 'in reference to'.

Is there a shorter way to say 'with regard to' instead of using a long phrase?

Yes, you can use the single preposition bezüglich (regarding). However, bezüglich usually takes the genitive case. If you used it here, the sentence would become: Bezüglich des Preises habe ich eine Frage.