> Now the sheets really are identical, and the only difference is my reputation for quality.

The information I value isn't related to the product you are selling, however, unless you also run the lottery (which would lead me to be highly suspicious). I'd pay roughly the same price for the same information on any medium, and it would be directly related to your reliability and not your reputation. E.g. you may have a reputation as a soothsayer, wizard, Oracle, or be named Omega but I will not bid more than the value of the lottery times your predicted accuracy (assume you sell only one prediction per lottery at auction, and your accuracy is the ratio of correct predictions to total predictions sold, to ignore the effect of multiple buyers+winners). Your brand reputation is your accuracy, not pieces of paper.

The closest analog I can think of is paying for a subscription to Consumer Reports to determine which lightbulb lasts the longest, for example. The information is decoupled from both the products and the manufacturers; the MTTF of a particular run of lightbulbs is simply a property of the world to be discovered. Given that a Consumer Reports subscription is less costly than the price difference on a basket of goods from reputable brands vs. generic brands suggests that consumers are not reaping an accurately priced benefit from brand reputation.

My theory is that most customers/consumers don't have the time and energy to invest into microeconomics (or reading CR) and therefore can't achieve an efficient market in the same sense that you or I could, or that large organizations can. Microeconomics requires approximations of rational actors and most people are not, and therefore business strategies incorporate this information in their pricing and advertising.

Another example is Costco which has generous return policies, sells with lower margins than most retail stores, and still makes money. Clearly they must be incorporating more information than is available by brand reliability or they would lose money on returns or sales or both. Likewise, they are charging a nominal membership fee for the job of collecting and acting on information about product quality that is isolated from the actual pricing of the products they sell. In practice, they work with existing manufacturers to rebrand their products as Kirkland at a lower price than the brand name, directly exploiting the arbitrage. There's probably still a fairly moderate price spread but it becomes harder to exploit with the cost of additional research and risk of asking for prices that are too low from the Kirkland suppliers. To survive (and thrive) they only have to pick a price in the middle of the spread where their popularity still allows manufacturers to make a sufficient profit that they put up with the dilution.

Where the market fails is in the creation of new industries that are willing to invest in manufacturing and selling products in the spread between the lowest cost junk and Costco prices. There is still money to be made there but customers won't have enough information to know that it's the most efficient option for them. It's the difference between saving pennies or millipennies on production costs vs. additional months or years of reliability that people would pay an entire extra dollar for, but practically pay several more when trusting brand reliability.