Problem 4 - Uniform pricing - Two-Part Tariff The Cliffs is a climbing gym. At the Cliffs, the larger share of production cost comes from rent, equipment maintenance, and the salaries paid to the administrative staff. Suppose that the Cliffs' monthly total cost is TC=FC+2Q where Q is the monthly number of visits to the gym. 1. What is the Cliffs' marginal cost of admitting an extra person? Suppose that all 200 patrons of the Cliffs' have similar preferences summarized by the individual monthly demand curve PD?=10?q/2. 2. If the Cliffs chose to charge a uniform entry fee (uniform pricing), how high would the gym set the fee? 3. How many times would a patron visit the gym each month? What would be his/her monthly consumer surplus? 4. Keeping in mind that the Cliffs has 200 patrons, what would be the Cliff's producer surplus? 5. Would this economic outcome be socially optimal? Why? Suppose instead that the Cliffs' decided to use a two-part tariff and charge each patron a monthly membership fee and a low entry fee for each visit. 6. What is the highest amount of money F(q)+Pq that a patron would be willing to pay to visit the Cliffs q times in a month? 7. Hence, what is the Cliffs' marginal revenue in this case? 8. What is the profit maximizing number of visits per patron? What is the profit maximizing entry fee? What is the profit maximizing monthly membership fee? 9. In this case, what is the consumer surplus of a patron? What is the Cliff's producer surplus? Last, suppose that if the gym decided to stop collecting entry fees it could lower the marginal cost of a patron's visit to MC' =1. 10. If after paying the membership fee patrons were not charged entry fees, how many times would they visit the gym each month? 11. What would be the highest monthly membership they would be willing to pay? 12. Would the Cliffs' producer surplus be higher or lower than in part 9.? 13. Would the number of monthly visits to the gym be more or less efficient than in part 8.? Problem 4 - Uniform pricing - Two-Part Tariff The Cliffs is a climbing gym. At the Cliffs, the larger share of production cost comes from rent, equipment maintenance, and the salaries paid to the administrative staff. Suppose that the Cliffs' monthly total cost is TC=FC+2Q where Q is the monthly number of visits to the gym. 1. What is the Cliffs' marginal cost of admitting an extra person? Suppose that all 200 patrons of the Cliffs' have similar preferences summarized by the individual monthly demand curve PD?=10?q/2. 2. If the Cliffs chose to charge a uniform entry fee (uniform pricing), how high would the gym set the fee? 3. How many times would a patron visit the gym each month? What would be his/her monthly consumer surplus? 4. Keeping in mind that the Cliffs has 200 patrons, what would be the Cliff's producer surplus? 5. Would this economic outcome be socially optimal? Why? Suppose instead that the Cliffs' decided to use a two-part tariff and charge each patron a monthly membership fee and a low entry fee for each visit. 6. What is the highest amount of money F(q)+Pq that a patron would be willing to pay to visit the Cliffs q times in a month? 7. Hence, what is the Cliffs' marginal revenue in this case? 8. What is the profit maximizing number of visits per patron? What is the profit maximizing entry fee? What is the profit maximizing monthly membership fee? 9. In this case, what is the consumer surplus of a patron? What is the Cliff's producer surplus? Last, suppose that if the gym decided to stop collecting entry fees it could lower the marginal cost of a patron's visit to MC' =1. 10. If after paying the membership fee patrons were not charged entry fees, how many times would they visit the gym each month? 11. What would be the highest monthly membership they would be willing to pay? 12. Would the Cliffs' producer surplus be higher or lower than in part 9.? 13. Would the number of monthly visits to the gym be more or less efficient than in part 8
