Question: For Example, what value of the warranty period equates the full replacement warranty with no warranty? (That is, for what value of W1 is the consumer indifferent to purchasing from store A or store B?)

Example: You are considering purchasing a battery for your automobile. You find the same battery offered at three different stores. Store A sells the battery for $21 and offers no warranty or guarantee. Store B sells the battery for $40 and offers a free replacement if the battery fails to hold a charge for the first two years of operation. Store C sells the battery for $40 as well but offers a pro rata warranty for the anticipated lifetime of the battery, which is advertised to be five years. The failure rate of the battery depends on the usage and the conditions, but from past experience you estimate that the time between failure is about once every three years. We will determine the values of C*1 and C*2 for both warranties. For the full replacement warranty, we have that