The wholesale price of a widget is $p dollars. The widget sells for $r dollars at retail. The manufacturer incurs $c fixed cost (assume no variable cost) and the retailer incurs $z fixed cost. The quantity of units sold is q. Please answer the following questions to explain why there are misaligned incentives:

What is the profit equation for the manufacturer? (i.e. how much profits will the manufacturer make?)

What is the profit equation for the retailer? (i.e. how much profits will the retailer make?)

Does the retailer or the manufacturer prefer a lower retail price $r