Problem: Consider the consumer’s optimal-search model analyzed.
Suppose that there are nine types of stores each selling at a different price drawn from a uniform distribution where p is a subset of (1,2,3,4,5,6,7,8,9). Answer the given questions:
1. Construct a table showing the consumer’s reservation price, and the expected number of store visits under different values of the search cost parameter. More precisely consider the cases in which s = 0,1,2,3,4,5.
2. What is the value of s that will cause the consumer to purchase the product at his or her first store visit?
3. What is the value of s that will cause the consumer never to buy the product unless the price is p=1.
4. Using the value of s that you found in question 3, calculate the probability that the consumer will search forever. Prove and explain your result.