Suppose the Province wants to encourage more competition in sales of beer and now will allow certain supermarkets to sell a limited number of brands : Molson, Keith, Stella, Corona, and Heineken. The store's marketing policy is to sell only one brand to each customer. The store manager has decided to install a fancy digital board in the store that shows how many bottles of each brand is sold during a day. Whenever, a customer buys her beer, the digital board immediately gets updated. After installation of this board, Jack noticed that the behaviour of some customers is changed and their purchases are inuenced by the volume sold for each brand.

(a) The manager observes that the demand distribution follows a power law. He also knows that a p portion of customers select their beer brand without looking at the board and select uniformly at random but the remaining 1p portion are inuenced by the board's statistics. Propose two models (i.e. what does the ith customer choose) that might explain the power law distribution for sales that the manager is observing. Briey indicate why you think each model might explain the observed power law behaviour.

(b) As is sometimes the case, some people see an opportunity to exploit the new system. Knowing how people make their decisions on selecting the brands, the manager wants to improve the prot margin. As different brands have various prot margins, he would like to manipulate the initialization of the digital board so as to sell more of high prot beer brands. Also, he doesn't want the manipulation to be easily detected, so he decides to put some constraints on his morning dishonest initializations: all brands have atleast the value of 1 and the sum of all initial values on the board is not more than 15. According to your two models of behaviour, which morning initialization do you think he is going to use and why?

(c) Asmartcustomerunderstandssomemanipulationistakingplaceandjustwhenthe store opens the next day, she takes a snapshot of the digital board. Then, she writes a review of the store on her blog informing the reader regarding the dishonestly in reporting statistics. The manager is moved to another location and the new manager immediately stops the dishonest manipulation. Suggest an honest business plan for for the new manager which helps her still make increased prots by selling more high prot brands? (You don't need to come up with specics of the plan just a high-level plan is enough).