A certain restaurant in town is known for refusing to give separate bills to customers. After a group has ordered and eaten together at this restaurant, the group is presented with a single bill for the entire amount that the group has eaten. It has been suggested that the restaurant does this because, with a single bill, those who dine in groups will be more likely to simply divide the charge equally, each person paying the same amount irrespective of who ordered the most, and that diners, knowing they will ultimately divide the charge equally, will order more than they would have ordered had each expected to pay only for his own order. Analyze this situation using the following model. There are 3 diners in a group, denoted i = 1, 2, 3. Each has a utility function of the form Ui (Xi, Ci) = a; In (Xi) ti, (1) where xi represents the amount of food ordered and eaten by i and ti is the amount that i has to pay. The price of food is p = 1. Assume that ay = 1, Q2 = 2 and a3 = 3. a) How much food will each individual order knowing that the bill will be shared and how much will they order in total? (20 Marks) b) How much food will each individual order if he or she has to pay for her own order and how much will they order in total? (20 Marks) c) Provide an intuition for why the bill is larger in (a) than in (b). (10 Marks)