Question 3 - Firms and markets (22 Points) Orange Theory is the only fancy gym in town. The population of the town consists of two type of individuals fitness enthusiasts and regular gym-goers. The manager at Orange Theory is currently trying to solve the following problems: i. How many classes should be offered in the elite and basic plans? ii. How much should Orange Theory charge for each plan? Assume that the marginal cost of a class is c = 5. Orange Theory knows that each group of individuals have the following demand functions: Fitness enthusiasts: q = 12 - 3p- Regular gym-goers: q = 9 - ;pc where qe and pc are one class and the price per class. 1. (6 points) Assume that only fitness enthusiasts can attend Orange Theory and that the gym can charge their whole willingness to pay for a plan. What is the price of the plan and how many classes does it include? 2. (6 points) Assume that only regular gym-goers can attend Orange Theory and that the gym can charge their whole willingness to pay for plan. What is the price of the plan and how many classes does it include? Assume that the Elite plan has the number of classes per month you found in question 1 and the basic plan has as many classes as you found in question 2. If both plans are available to every consumer and Orange Theory wants to make sure that fitness enthusiasts purchase the elite plan and regular gym-goers purchase the basic plan. 3. (5 points) What is the willingness to pay of fitness enthusiasts for the basic plan WTP! ? 4. (5 points) What are the prices of the elite plan Pelite and Pbasic that would generate the above self-selection pattern