Question

Your store sells an item desired by a consumer. The consumer is using an optimal search strategy; the accompanying graph shows the consumer’s expected benefits and costs of searching for a lower price.

a. What is the consumer’s reservation price?

b. If your price is $\text{(3}$and the consumer visits your store, will she purchase the item or continue to search? Explain.

c. Suppose the consumer’s cost of each search rises to $\text{)16}$. What is the highest price you can charge and still sell the item to the consumer if she visits your store?

d. Suppose the consumer’s cost of each search falls to $\text{(2}$. If the consumer finds a store charging $\text{)3}$, will she purchase at that price or continue to search?

Short answer

1. The consumer’s reservation price is $5.

1. If the price is $3 and the consumer visits the store, she will purchase the item.

1. If the consumer’s cost of each search rises to $16 then the highest price that can be charged and still sold the item to the consumer is $6.

1. If the consumer’s cost of each search falls to $2 and the consumer comes across the store charging $3, the consumer will not buy from that store and keep looking for other options.

Step-by-step solution

Concept Introduction

The consumer's optimal search strategy permits the searcher to select the number of observations to be made during any period based on the information at hand.

The Reservation Price

(a)

The reservation price consists of that quote of the price of a product in which the consumer will accept to pay since it indifferent to her to buy at that price or to continue looking for a lower price. Therefore, the following condition will be met where the expected benefit of the reservation prices equals the cost –

Therefore, the value for price is $5.

Consumer’s Point of View

The optimal search rule is such that she will rejects prices that are above the reservation price and will make the decisionto buy at a price that is equal to or below the reservation price.

Therefore, at a price of $3 (below the reservation price) the consumer will have incentives to buy the product and notkeep looking.

The Highest Price

If the consumer's cost of each search rises to $16, the horizontal line will move upwards, generating a new break-even point with a new reservation price.

Therefore, according to the graph, the maximum price that can be charged to the consumer if she decides to buy the product will be $6.

Consumer’s Point of View(d)

If the expected benefits and costs of finding the lowest price is reduced to $2,curve will shift down from its initial point, generating a new equilibriumwith at price of $2.

Therefore, if the buyer finds a store with a price of $3 for the product that she wants, she will prefer to keep looking until she findsthe product at a price of $2.