Suppose Apple sells phones with 4-inch screens and Samsung sells those 5-inch ones. Consumers have their hands of different sizes. Their most preferred sizes, as a result (that might depend on the probability that they drop their phones), are distributed uniformly on [4, 5] inches. The preferred smart phone will give each consumer a benefit v when consuming it. Suppose for each unit of difference between their consumed size and their preferred screen sizes, the consumer will be disutilized by t. Suppose Apple and Samsung are charging prices Pa, Ps, respectively. The marginal cost for producing a phone is c for both the firms.
a) Please write down the utility for a consumer with preferred size, when he/she is consuming the 4-inch iphone. Also please write down the utility when he/she is consuming the 5-inch galaxy.
b) What is the theta for the consumer indifferent between iphone and galaxy?
c) Given Pa,Ps, what are the demand functions for Apple and Samsung? d) What are the equilibrium prices for iphone and Samsung?
e) Now suppose v = 700, t = 400, what is the price in the market?
f) Suppose a larger iphone is easy to get bent.. Consumers understand this and they are more tolerant to an iphone smaller than they like (for the rigidity purpose). As a result, the disutility parameter for an iphone ta = 400, smaller than that for Samsung, ts = 500. What are the prices in this market? Should Apple tries to make iphone less "flexible" (which means its disutility parameter becomes the same as Samsung)?