Assignment task: Consider two companies (A and B) competing with each other on a product attribute. The market's and the companies' differentiation on this attribute is as follows:
- The market is represented by a straight line, with the left end at point 0 and the right end at point 10. This line shows the possible values of the attributes that the companies could choose for their own products.
- Company A is located at point 3. Its price is $10.
- Company B is located at point 7. Its price is $16.
- Each consumer has his or her own preference for this attribute. The preferences of all consumers are distributed uniformly along the line.
- The consumers use the following criterion to evaluate the total cost of purchasing from a company:
p + 3d, where p is the price of the company's product, and d is the "psychic cost" caused by the distance from the consumer to the company.
Answer the following questions:
(1) Is this horizontal differentiation or vertical differentiation between A and B?
(2) A consumer is located at 5, will she buy A or B? Show your calculation.
(3) A consumer is located at 8, will she buy A or B? Show your calculation.
(4) A consumer is located at 6, will she buy A or B? Show your calculation.
(5) There is a total of 5 million consumers. Each of them will buy only one product, either from A or B.
What are the sales volumes of A and B? Show your calculations.