The free banking era and the "multitude of dollars" problem
There's a precedent for this sort of dollar heterogeneity. During the U.S.'s so-called "free banking era" that lasted from the 1830s until 1863, hundreds of different types of banknotes circulated, each issued by a unique bank. Notes were universally redeemable in a certain quantity of gold. Varying physical distances between a note's final resting point and its birth at an issuing bank (often in another state) led to widely disparate redemption costs across note brands. A merchant in Philadelphia who was paid in local bank notes need only take a short walk in order to redeem the note. If that same merchant was paid in a note issued by a bank in Chicago, however, redemption was much more onerous due to the time and distance required to travel from Philadelphia to Chicago.
So in the same way that an American Express dollar is the most costly of the modern day dollars, a distant bank's notes were the most costly of the free banking era's dollars.
Here are two interesting problems. How can a merchant establish a single set of sticker prices while still accommodating a wide range of disparate dollar payments media? Second, consider the fact that shoppers paying with a premium card like American Express (or distant bank notes) enjoy the widest range of benefits, but should also face the highest costs. How can the system ensure that the person who enjoys the marginal benefits associated with a given payments medium also bears its marginal cost? Put differently, how is quid pro quo ensured?
The solution: surcharging
In the free-banking era, the "multitude of dollars" problem was solved by a form of discriminatory surcharging. To begin with, merchants displayed their sticker prices in terms of a single unit; standard U.S. dollars (defined as 1.5 grams of gold). When the customer arrived at the till, the merchant determined what sort of surcharge to apply to each of the banknotes proffered according to its distance-to-redemption. With hundreds of note-issuing banks in existence, this was a cumbersome task. In order to speed up the process, the merchant would consult what was called a "bank note reporter." This handy publication, which was compiled by professional bank note analysts, provided merchants of a certain location, say Philadelphia, with the rates for all bank notes that circulated in Philadelphia adjusted for their shipping costs.
The image below is a section from Van Court's Bank Note Reporter and Counterfeit Detector, which I've snipped from Gary Gorton's introduction to the subject. It shows the the recommended price at which a merchant in Philadelphia should accept notes from Vermont, Maine, Pennsylvania, and elsewhere.
After a merchant had consulted his bank note reporter and tacked on the appropriate surcharge, it was time to redeem the note. Merchants didn't actually ship the notes themselves but sold them to a local note broker at a discount to face value. In fact, the numbers that Van Court published would have been sourced from this broker market. The broker in turn shipped the note back to the issuer, getting full face value upon redemption. The gap between face value and the initial purchase price covered the broker's shipping costs.
Thus the "multitude of dollars" problem was solved. By surcharging relative to a benchmark dollar, merchants succeeded in setting a single array of prices while accommodating a much wider range of heterogeneous payments media. This also allowed them to efficiently pass the marginal cost of using distant notes onto those customers who chose to pay with them, while rewarding customers who used low-cost local notes by not applying such surcharges.
So why not implement this same technique of surcharging today?
Consider that in our modern era, credit card networks recoup much of the cost of the services they provide (which are many, but include perks like rewards and the right to dispute a transaction) by requiring that card accepting retailers collect a fee from customers on the network's behalf. This parallels the free banking era, in which banks required third-parties to bear the cost of transporting notes for redemption.
The best way for a modern retailer to establish prices in this heterogeneous dollar world would be to replicate the solution settled upon by their free banking ancestors: set sticker prices in terms of the most basic unit, paper dollars, and exact an appropriately-sized surcharge on each card transaction at the till.
Rather than an old-fashioned Van Court's Recorder, a merchant could go about this by installing card-reading software that would quickly determine both the card being used and the appropriate surcharge. Thus, consumers who paid with premium cards, those cards that offer the most bundled services per transaction (and therefore incur the highest costs), would have to bear the largest surcharge while those with bare bones cards would pay a minimal surcharge. Anyone paying in cash, much like those who payed with local banknotes during the free banking era, would not incur any surcharge whatsoever. This system would ensure that each customer bears the marginal cost of their chosen means of payment. The retailer, who routes all of the surcharges they collect back to the card network, doesn't eat any costs and therefore succeeds in preserving their margins.
If only things were that easy. Though surcharging would be a great way to deal with the "multitude of dollars" problem, card networks like Visa and Mastercard have typically "legislated" against surcharges.* The networks can successfully impose this no-surcharge obligation on retailers because as an oligopoly, Visa and Mastercard can banish offenders from the network, putting a huge dent in the offender's sales. Why prevent surcharges? One reason the card networks probably do this is because they don't want the card-paying public to feel that they are being penalized in any way. If the feel put off, consumers might choose alternatives like cash and debit that aren't subject to surcharge.
Another solution: discounting
The no surcharge rule puts retailers in a bind. They are obligated to collect fees on behalf of the card networks, but without the ability to surcharge they're left absorbing the costs imposed by the networks while the customer enjoys all the benefits.
There's a neat way that that retailers can get around this hurdle. All they need to do is to mark up all their sticker prices to the level of the highest cost credit card, and then offer discounts to everyone who uses lower cost credit cards, debit cards, or cash. Discounting allows the merchant to collect the appropriate fee from each customer, funneling these fees back to the networks. As before, a given set of prices can accommodate a wide range of dollar payments media. Each party who enjoys a given marginal benefit also bears its respective marginal cost.
So as not to leave our analogy hanging, if this solution had been chosen by free-banking era retailers (perhaps because the free banks insisted that merchants avoid bank note surcharges), then the price level in Philadelphia would have been marked up to the value of the most-distant bank notes in circulation, say those from Chicago. Those paying in less-distant bank notes, say New Jersey notes, would have received an appropriately-sized discount.
An anomaly: we don't see discounts
Having outlined how to solve the modern "multitude of dollars" problem without surcharging, what happens in the real world? An odd phenomena tends to play out. While retailers have certainly marked up prices to a premium card standard (or thereabouts) in order to cover their costs, for some reason they rarely offer their customers discounts on cheaper payment options. Try asking for a cash discount at Walmart the next time you visit. This means that anyone who purchases something with cash, debit, or a bare bones credit card is being forced to pay for a juicy set of benefits associated with usage of an American Express card, namely fancy rewards and dispute rights, without actually getting to enjoy those benefits. Put differently, the merchant is effectively overcharging their customers by collecting more network fees than the networks actually require, keeping this excess to pad their bottom line.
Why this predatory behavior? Briglevics and Shy note that merchants may be wary of discounting if it creates confusion and distrust among customers. Potential delays at checkout counters might impose an extra set of costs on all parties. They also point out that merchants may not find it profitable to offer a cash discount to consumers who would use low-cost payments anyway. Schuh, Shy, Stavins, and Triest report that merchants may lack complete information on the full and exact merchant discount fees for their customers’ credit cards, and therefore can't implement a policy of accurate discounting.
Could it be that the right set of tools to provide discounts hasn't yet been created? Perhaps we need a modern version of Van Court's Bank Note reporter. Such a technology would allow merchants to rapidly determine the proper discount to apply to each disparate dollar type and clearly inform customers about the saving they have enjoyed.
Lack of technology may explain why cheap credit cards don't receive discounts relative to expensive ones, but it doesn't explain why cash discounts has never been adopted by retailers. One theory is that even if certain retailers start to offer discounts, the public may be too overloaded with information to switch, thus allowing the practice of predatory pricing to remain the status quo. Supporting this view is the following observation: while discounting for cash and debit payments is rare in most sectors of the economy, it is quite common among gas stations, as the image below shows.
Other retailers, say department stores, sell a wider variety of things than gas stations, many of these items only being purchased from time to time. This makes comparison shopping more costly. Brand loyalty only increases the hassles of switching. Department stores may find that a policy of cash discounts is simply not worth the effort as discounts get lost in the morass of data that a consumer is bombarded with on an hourly basis.
That being said, the online world's ability to provide faster cross-retailer comparisons than are possible in a bricks & mortar world could shake things up. Surely some smart fintech entrepreneur can create a way for online merchants to rapidly measure the appropriate discount (or surcharge in those jurisdictions that allow it) to apply to each card before consummation. This same tool would provide a user-friendly format for online shoppers to "see" competing card discounts across a number of merchants prior to hitting the buy now button. Just like they'll cross the street to hit the cheapest gas station, they may divert their purchase to the lowest cost website. If this sort of thing caught on, we'd see long forgotten free banking customs replicated in our modern era.
*This is currently the case in Canada. In Australia, merchants have been allowed to surcharge since the early 2000s. US merchants recently won the right to surcharge, although it is probably too early to know what effect these rule changes will have.