A state wishes to tax alcohol to raise revenue while at the same time protecting their local producers. They have settled on accomplishing this by prohibiting the sale of liquor in privately-owned stores while allowing the sale of liquor in government-owned outlets only.
They are able to do this under the 21st Amendment. However, constitutionally, taxing out-of-state alcohol while leaving in-state-alcohol exempt goes against the dormant commerce clause.
Are the state-run outlets safe from the Dormant Commerce Clause as a market participant even though they are a state-run monopoly? And if so, can they levy a "tax" by making in-state alcohol cheaper than out-of-state alcohol?
NOTE: I will not accept answers that rely on alternatives to the hypo like "why don't they just give subsidies to the local producers?"