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 suffer 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 firm has a profit of $115,200. This market is best modelled as Hotelling competition. You should neglect fixed costs throughout your analysis. Note: For the purposes of this assignment you should treat this market as a one- shot game. Do not consider repetition or associated phenomena such as collusion or predatory pricing. Step 1: Derive an expression for the location of the indifferent consumer. Use PA to represent the price of admission at Alfonso's Wonderland, and P5 to represent the price of admission at Bernice's Wild Rides. (2 marks) Step 2: Find the profit function for Bernice's Wild Rides. You should assume that Ber nice's marginal cost is $12. (4 marks) Step 3: Find Bernice's bestresponse function. (4 marks) Step 4: Find the profit function for Alfonso's Wonderland for the case in which their marginal cost is $6. (4 marks) Step 5: Find the bestresponse function for Alfonso's Wonderland for the case in which their marginal cost is $6. (4 marks) Step 6: Find the equilibrium prices and profits for the case in which Alfonso's marginal cost is $6 and Bernice's marginal cost is $12. (7 marks) Step 7: Find the profit function for Alfonso's Wonderland for the case in which their marginal cost is $9. (4 marks) Step 8: Find the bestresponse function for Alfonso's Wonderland for the case in which their marginal cost is $9. (4 marks) Step 9: Find the equilibrium prices and profits for the case in which Alfonso's marginal cost is $9 and Bernice's marginal cost is $12. (7 marks) In the island nation ofAutarka 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 firm, VendorCorp, has developed a new automation technology which promises to improve the efficiency of amusement park rides. VendorCorp is offering 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