The Yoga Studio has two types of customers, yoga regulars and yoga beginners, who each have the following demand for yoga classes per month: yoga...

4. The Yoga Studio has two types of customers, yoga regulars and yoga beginners, who each have the following demand for yoga classes per month: 

yoga regulars: p = 20 - q 

yoga beginners: p = 32 - 4q 

There is zero marginal cost to the studio of adding an additional person into a class, and yoga beginners get no additional value from taking more than 8 classes in a month. Suppose that the studio cannot identify and explicitly charge customers from these groups different prices, but they decide to try to discriminate by offering two different pricing options. Customers can attend classes for $16 each, or if the customer comes to 10 or more classes per month they pay only $10 per class (for all the classes they attend). In other words, customers can either pay $16 each class or they can choose to pay $100 upfront for 10 classes that month after which they can continue to attend classes at $10 each. Show that this pricing scheme can successfully charge yoga regulars $10 per class while still getting yoga beginners to pay $16.