Question

A 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.

Answer 1

According to the given question, a customer has the option of paying $ 16 per class or pay $100 upfront for 10 classes and get the option of paying $ 10 for the successive classes. It is also a given that the beginners have no additional value for taking more than 8 classes. This means that if they take more classes they are paying for decreasing utility( law of diminishing marginal utility). Hence, instead of paying $100 for 10 classes out of which two classes have no value. In other words, if they go for $100 deal,they would paying for 2 classes that is 20$ for zero utility. taking into consideration the utility factor they would simply pay for the number of classes that are of value to them (i.e) 8 classes. This means $16 per class. Whereas for the regular customers who take more number of classes paying 100$ in the beginning for 10 classes and then choosing to pay $10 for each successive class works out cheaper. This is called second degree price discrimination. Since the there is no additional value to the yoga beginners after attending 8 classes means that they would generally not pay for classes that they do not attend and it is not certain that they would attend all the 8 classes. If a beginner attends only 6 classes at 16$ per class the amount payable comes up to 96$ where as he would have to pay $100 for 10 classes which he would not be attending. This is the logic that the business uses to maximise profits. Customers who are not beginners would go for this package and the business would offset the revenue loss due to price reduction by more regular customers and beginners opting for the $16 deal.