(1) La Strada restaurant makes a market analysis to find out that the minimum willingness to pay (wtp) for the lunch is $2.5 and maximum wtp is $12.5. Suppose that the wtp is uniformly distributed between these limits, that there are 100 lunch customers considering to go to the La Strada restaurant and that the cost of the lunch is $5. The restaurant classifies anybody with wtp more than $8.5 as a high-paying customer; the rest are considered low-paying customers. The restaurant will offer à la cart service to high-paying customers and a lunch buffet to low-paying customers. Let dy and d, respectively denote the demand of high-paying and low-paying customers. It can be shown that dy(p)=125-10p for 8.55 p <12.5 d, (p) = 85-10p for 2.5< p <8.5. (a) (1.5 pts) Find the optimal prices P. and pi for high-paying and low-paying markets, respectively and report the total optimal profit from the both segments. (6) (0.5 pts) What is the total profit when La Strada charges pH = 9 and P2 = 6? (2) (2 pts) Consider the problem about La Strada restaurant above. Now assume that the restaurant classifies anybody with wtp more than $7.5 as a high-paying customer; the rest are considered low- paying customers. The restaurant will offer à la cart service to high-paying customers and a lunch buffet to low-paying customers. We again denote, by dy and d , respectively, the demand of high-paying and low-paying customers. It can be shown that dy(p)=125-10p for 7.55 p<12.5 d. (p) = 75-10p for 2.5 2. (3) (1 pt) When a seller offers a volume discount to a buyer, the seller should eliminate arbitrage and cannibalization.
a) Consider the CPA classes at a bank and their pricing based on volume discounts. Also consider CPA classes offered to general public. Explain if/how arbitrage happens. Explain if/how cannibalization happens.
b) Consider a software licensed to multiple users at a single company and the licensing fee per user has a volume discount. Explain if how arbitrage happens. Explain if/how cannibalization happens.
c) Consider a commercial building contractor who spends millions of dollars on buying galvanized pipe from a supplier. The supplier sells the galvanized pipes in high volumes to building contractors and in low volumes to repair companies. The contractor buys the pipes with a volume discount. Explain if/how arbitrage happens. Explain if/how cannibalization happens.
d) Consider the three contexts above. In which context arbitrage is more likely to happen? In which context cannibalization is more likely to happen?