# Imperfect Competition

Consider the consumer's optimal-search model analyzed in section 16.2

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 following 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.

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#### Solution Preview

Solution-Table 16.1: Reservation price as a function of the search cost parameter

Please see the attached file for the table

2. (a) Using (16.13), we can make the table as follows:

s 0 1 2 3 4 5

p 1 4.77 6.52 7.86 9.00 10

Solution-Table 16.1: Reservation price ...

#### Solution Summary

The solution answers the question below in great detail.