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amazonprimeAmazon Prime is a great deal in the eyes of many Amazon customers, offering free two-day shipping for $79/year, among other benefits.

But the price of Prime hasn’t kept pace with the company’s shipping costs, Amazon CFO Tom Szkutak said on the company’s last earnings call that Amazon is planning on raising the price of an Amazon Prime annual subscription by $20 or $40. Considering that Amazon has more than 20 million Prime subscribers, that could translate to a whole lot of cash.

But there’s a catch. While a price hike makes a lot of fiscal sense, it seems like Amazon is going to have its work cut out for itself convincing consumers. Only 58 percent of Prime subscribers surveyed by Consumer Intelligence Research Partners said they would renew their memberships if Amazon raised the price to $99, according to a report by the Wall Street Journal. If Amazon raised the price to $119 a year, 40 percent of the people surveyed said they would definitely stop being Prime members.

That’s rough news for Amazon, which has shown that a Prime membership leads customers to buy more items from Amazon on a more frequent basis.

It’s possible that the survey isn’t predictive of consumers’ actual behavior in the event of a price increase. Because Prime memberships automatically renew, there’s a decent chance some people will stay members out of sheer inertia. Still others will probably decide that they can actually afford the increased price.

If Amazon does increase the price of Prime, analysts at UBS, which worked with CIRP on the study, said that an increase of fees would be best “accompanied by either a) a higher level of value in the service offering (additional media content, streaming music and/or Fresh (supermarket) offerings) and/or b) an increased level of marketing around the perceived value of Prime to the general public.”

In addition, the analysts downgraded Amazon from a “Buy” to a “Neutral” rating on the news, setting a lower price target for the company’s stock. Amazon’s stock closed today at $349.25 a share, down almost 3.5 percent from its opening price.

We’ve reached out to Amazon for comment on this piece, and will update it if we hear back.

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