3. The town of Beanville consists of an old stone road which is 1 Kilometre long. The town has a proud coffee heritage, where there are two world-famous coffee-houses located on either side of the road. They are both known for their aromatic slow-roast coffee and are the only two places where Beanville's 100 citizens can buy their daily cup of coffee from: each person has a perfectly inelastic demand of 1 cup of coffee each day. These 100 citizens are evenly distributed between the two coffee-houses, so that most people would need to travel some distance to buy their coffee. All consumers face a travel cost of $2 per Kilometre travelled. The two coffeehouses, 1 and 2, each sets their respective coffee price, P, and P2. simultaneously. Coffeehouse 1 has a cost of production of TC, = 42q1 , while coffeehouse 2 has a cost of production of TC2 = 4892, where q; denotes the cups of coffee for firm i. (42 marks total) a. In the Hotelling price model, is it assumed that both firms produce a homogeneous or a differentiated product? Explain. (6 marks) b. Explain the concept of the marginal consumer. Why he is important in the Hotelling model? (4 marks) c. Derive the demand functions for both firms. Clearly explain the logic that you apply at each step. (8 marks) d. Find the best-response price functions for both firms. Draw these on axes of Pi and P2, with P2 on the vertical axis. Label your axes and curves. (12 marks) e. Solve the Hotelling equilibrium price for each firm. Calculate the output and profit for each firm. (6 marks) f. How far away is the marginal consumer away from firm 1? What is special about this particular location, and how does it relate to the market share of the two firms? (6 marks)