Time Inconsistency Overcome: What happens to your pets during the Rapture?

I wonder if Tyler Cowen realizes how right he is when he says that there are markets in everything. I'm sure you've been concerned about what will become of your pets during the Rapture. Sure you're saved and will ascend to heaven directly. But what about poor fluffy?

Fluffy doesn't ascend with you, but you still love her don't you. Don't you want her to spend the rest of her days in comfort? If only there was a company that promised to look after your pets after you ascend to heaven? There is at least one http://eternal-earthbound-pets.com/

It's easy to make fun of this, but it is impressive that people have apparently solved the time inconsistency problem. You pay up front but they take care of your pet after you die. They have every incentive to let your poor pooch suffer while they spend their money on wickedness.

Perhaps you think that this isn't so different from regular life insurance. You pay premiums year after year hoping that the life insurance company will pay your beneficiaries. (Companies don't always look very hard for your beneficiaries.). But life insurance before the Rapture is different than life insurance afterwards. Without the Rapture insurance companies want to pay claims so that they can build an honest reputation and continue to get business. And of course the beneficiaries of most insurance policies can sue. Poor fluffy can't sue, and who knows what will happen to the legal system after the Rapture.

Apparently the companies spend resources making believers believe that the non-raptured are actually moral enough to take care of the pets once you've ascended. I think that's a great private sector response to a market failure.

Externalities solved by bees, Private Lighthouses providing public goods, Rapture Insurance; what can't markets solve?