A prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded the orchard. The troll demanded payment of one-half the apples plus two more. The prince gave him the apples and set off again. A little further down the road he was stopped by a second troll guard. The troll demanded payment of one-half the apples plus two more. The price paid him and set off again. Just before leaving the enchanted orchard, a third troll stopped him and demanded payment of one-half the apples plus two more. The prince paid him and went sadly home with his two remaining apples. How many apples had the prince picked

Suppose there are three types of consumers who attend concerts at your university’s performing arts center: students, staff, and faculty. each of these groups has a different willingness to pay for tickets; within each group, willingness to pay is identical. there is a fixed cost of $1,000 to put on a concert, but there are essentially no variable costs. for each concert: i. there are 140 students willing to pay $20. (ii) there are 200 staff members willing to pay $35. (iii) there are 100 faculty members willing to pay $50. a) if the performing arts center can charge only one price, what price should it charge? what are profits at this price? b) if the performing arts center can price discriminate and charge two prices, one for students and another for faculty/staff, what are its profits? c) if the performing arts center can perfectly price discriminate and charge students, staff, and faculty three separate prices, what are its profits?