Question

6. Individual Problems 14-6 At a student café, there are equal numbers of two types of customers with the following values. The café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate) Students without Early Classes 63 105 Students with Early Classes Coffee 73 Banana The marginal cost of coffee is 10 and the marginal cost of a banana is 40. The café owner is considering three pricing strategies 1. Mixed bundling: Price bundle of coffee and a banana for 168, or just a coffee for 73 2. Price separately: Offer coffee at 63, price a banana at 105 3. Bundle only: Coffee and a banana for 128. Do not offer goods separately. Assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle.

Answer 1

bundle only i.e. pricing strategy 3 yields the highest profit because in strategy 1----

there can be various cases

• if both students choose price bundle for 168 then revenue =2*168=336 . Thus total cost = 2*10 +2*40=100. profit = 336-100=236
• if both students choose coffee only then revenue = 2*73=146 and total cost =2*10=20 therefore profit= 156
• if onechooses the bundle and the other chooses coffee then revenue= 168+73=241 and total cost = 10+40=50 therefore profit = 191
• here the seller is unsure of the choices of the customers , hence averaging the profits in the three cases we get (236+156+191)/3=194.33

in startegy 2 price separately , if :---

• both chooses coffee total revenue =63*2=126 , cost =2*20=40, total profit =80
• if both chooses banana tatal revenue =105*2=210 , cost =2*40, total profit =130
• if one chooses coffee and one chooses banana the, revenue=105+63=168,cost=10+40=50,profit =118

in strategy 3 bundle only

revenue =2*128=256 ,cost=50 therefore profit =216

hence choice 3 is mos feasible and yields highest profit to the owner