Final answer:
To decide if Amazon Prime is worth it, one must see if the savings exceed the $25 annual fee. With a $2 discount per item, you need more than 12 purchases a year to break even. Considering other Prime benefits might also influence the decision.
Step-by-step explanation:
The question posed is whether purchasing an Amazon Prime membership would be cost-effective given the discount on the price of goods offered with the membership. To determine if the Amazon Prime membership is worth the cost, one must consider how often they purchase goods and whether the savings from the membership will exceed its cost over the course of a year.
If the price of good x is $10 without Amazon Prime and $8 with Prime, you save $2 for each purchase made with Prime. The Prime membership costs $25 per year. To break even, you must purchase enough goods to save at least $25 in discounts. Therefore, the number of purchases needed to offset the membership cost is $25 divided by the $2 saved per purchase, which is 12.5 purchases. This means that if you buy more than 12 items in a year, only then would the Prime membership result in savings.
Since an Amazon Prime membership offers additional benefits beyond just the discount on goods, such as free shipping, video streaming, and more, the overall value of the membership could be higher, depending on how much you utilize these additional services.