Hi. I think you're locked in a tautology. If "transactional utility is the price of money itself" then it can only be determined in relation to that which it prices itself by, i.e. its own unit of currency or an equivalent.
My opinion is he used the wrong words.
"transactional utility is the price of money itself" SHOULD BE "transactional utility is the value of money itself"
As money is always acquired to be exchanged later for something else, its value is in the ability it confer to obtain some other good and service in the future.
This, in exchange depend on its features and how many people use it and how often.
Menger explained money as the "more re-sellable commodity" available in the market.
Mises, explaining the Regression Theorem, state gold (or any form of money) INITIAL value is the value of direct use at the time it is used for the first time as a mean on indirect exchange.
As gold started to be used as a mean of indirect exchange, the price (the exchange rate of gold measure in other goods and services) raised. This can be understood as the same quantity of gold was used before only for direct use (jewelry, etc.) now must be used for indirect exchange and some direct use. So the less valuable direct use must be ceased to free some gold to be used as a mean of indirect exchange.
That's just another example of the numbers game though. Price, value, theorems, equations - they're just self-referential symbols. We have become 'numbed' by the 'numb-ers' game to the extent that we can't see past the numbers to the human considerations and needs the numbers represent.
Here's a scenario to think about: imagine you could create 'money' on demand as and when you need it. For example, you walk into a shop and pick up a carton of milk. Instead of being 'charged' to pay back an illusory 'debt' you are requested to make a donation (a gift of money) of 2 units of currency in return for the item. You then scan a QR code with your mobile phone and the 'money' (nothing more than a number) representing the gift is created (by you) and transferred to the recipient's account. Under such a system, price inflation becomes meaningless. Rather, we see that price inflation has always been meaningless and just a numbers game.
For example, next day you walk into the same shop and select the exact same item, only this time you are asked to make a donation (a gift of money) of 5 units of currency. Your 'spending power' has in no way been reduced because, once again, you simply need to scan the QR code, whereupon the 5 units are created and transferred to the recipient. Nothing of 'value' has been created or lost, just the illusion of it.
Under such a system, we would only need to pay attention to the numbers to the extent that they identify a real-world imbalance between supply and demand. Everyone (not just the rich) would have an equal opportunity to obtain what is available. If there is not enough to go around then the system permits the 'financial resources' required to address the imbalance to be created on demand. Also, because 'cost considerations' would no longer be a factor, the issue could be addressed using best practice, i.e. not merely paying lip service to ecological concerns.
If this sounds like madness to you then consider what happens when you walk into a bank and ask for a mortgage. The bank pushes a button, transfers a number to your account, then tells you that this number represents a 'debt' and that you must spend the next 20 years paying off that debt. Who would possibly accept such a system?
My system would be an illusion, just as the existing system is also an illusion. The difference is that my illusion works to everyone's advantage.
HS