A certain restaurant in town is known for refusing to giveseparate bills to customers. After a group has ordered and eatentogether at this restaurant, the group is presented with a singlebill for the entire amount that the group has eaten. It has beensuggested that the restaurant does this because, with a singlebill, those who dine in groups will be more likely to simply dividethe charge equally, each person paying the same amount irrespectiveof who ordered the most, and that diners, knowing they willultimately divide the charge equally, will order more than theywould 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 autility function of the form ui (xi , ci) = ai ln (xi) - ti , wherexi represents the amount of food ordered and eaten by i and ti isthe amount that i has to pay. The price of food is px = 1. Assumethat a1 = 1, a2 = 2 and a3 = 3.

a. How much food will each individual order knowing that thebill will be shared and how much will they order intotal?  

b. How much food will each individual order if he or she has topay for her own order and how much will they order in total?

c. Provide an intuition for why the bill is larger in (a) thanin (b).

(this is edited w; variables now)