In the island nation of Autarka there are two amusement parks: Alfonso's Wonderland and Bernice's Wild Rides. The amusement parks are located at either end of the island, 1km apart. Recently, a third rm, VendorCorp, has developed a new automation technology which promises to improve the eciency of amusement park rides. VendorCorp is o ering to sell the exclusive rights to this technology, and has asked the two parks to submit bids. The new technology promises to reduce the marginal cost of operating rides for a customer by $6. However, experience in other countries has shown that, in about 30% of amusement parks, the technology encounters compatibility issues and only reduces the marginal cost by $3. Unfortunately, there is no way to know whether these issues will be encountered until the technology is installed. You have been hired by Alfonso's Wonderland to analyse the business case for purchasing the exclusive rights to the automation technology. You have been asked to determine: The maximum price Alfonso's Wonderland should be willing to pay for the technology. The price that Alfonso's Wonderland is likely to have to pay if it is successful. The consequences for Alfonso's Wonderland if Bernice's Wild Rides purchases the exclusive rights instead of Alfonso's Wonderland. 2.2 The Market In Autarka there are 9600 people who like to visit an amusement park. Each of these consumers wants to visit one park once. The consumers' homes are evenly spaced across the island, and they each su er a disutility of $24 for each kilometre they travel to reach an amusement park. With their current technology, it costs an amusement park $12 for each customer they host. At present, the equilibrium price for an amusement park ticket is $36, and each rm has a pro t of $115,200. This market is best modelled as Hotelling competition. You should neglect xed costs throughout your analysis.

In the analysis section you must complete each of the steps detailed below. When com- pleting the steps you must: Type all equations using the `Insert Equation' function (or equivalent). Show all of your working and include sucient written description for the reader to follow your process. Note that hand draw gures and equations are not acceptable. There is no word/page limit for the analysis section. Step 1: Derive an expression for the location of the indi erent consumer. Use PAto represent the price of admission at Alfonso's Wonderland, and PBto represent the price of admission at Bernice's Wild Rides. (2 marks) Step 2: Find the pro t function for Bernice's Wild Rides. You should assume that Ber- nice's marginal cost is $12. (4 marks) Step 3: Find Bernice's best-response function. (4 marks) Step 4: Find the pro t function for Alfonso's Wonderland for the case in which their marginal cost is $6. (4 marks) Step 5: Find the best-response function for Alfonso's Wonderland for the case in which their marginal cost is $6. (4 marks) Step 6: Find the equilibrium prices and pro ts for the case in which Alfonso's marginal cost is $6 and Bernice's marginal cost is $12. (7 marks)

Step 7: Find the pro t function for Alfonso's Wonderland for the case in which their marginal cost is $9. (4 marks) Step 8: Find the best-response function for Alfonso's Wonderland for the case in which their marginal cost is $9. (4 marks) Step 9: Find the equilibrium prices and pro ts for the case in which Alfonso's marginal cost is $9 and Bernice's marginal cost is $12. (7 marks)