I can see from comments that people are very confused about the role of the medium of account. I am going to address two misconception in the post. First I will explain exactly the sense in which the MOA is more central to monetary economics than the medium of exchange, and which sense it is not. Then I will explain why nominal price levels differ between countries.
Obviously it’s going to be impossible to explain the difference between a MOA and a MOE if the same asset serves both purposes. We’d end up with an “angels on the head of a pin” debate. Who could say why money is important if it serves both roles? At a minimum we need a MOE than is not a MOA. So let’s assume that a gram of gold is the MOA and a gram of silver is the MOE. Prices (and wages) are denominated in terms of gold grams, but bills at the cash register are paid in silver coins. They have those modern cash registers with built in computers. The exchange rate is set each morning based on conditions in the gold and silver markets. An easy way to envision this process is to assume some countries use gold and some use silver. Then the store just looks up the foreign exchange rate each morning and programs the cash register.
Now for my claim that the MOA is more “fundamental” than the MOE. What do I mean by this? I mean one thing and one thing only. Here goes:
A discovery of a new process for easily turning lead into gold would have massive inflationary implications for the economy. NGDP would soars and debtors would gain while creditors lost.
A discovery of a new process for easily turning lead into silver would reduce the nominal price of silver, but otherwise have no important implications for the economy.
That’s the sense (and the only sense) in which I think the market for the MOA is “interesting” and the market for the MOE is “uninteresting.” Now I am quite aware of that fact that in the gold alchemy case, the value of the existing stock of (silver) MOE measured in terms of the MOA does soar, so one can also argue that the MOE is important for that reason. I understand that argument, but simply don’t find it persuasive. It still seems to me that gold is the dog and silver is the tail.
Now on to international price level differences. Imagine that Austria uses grams of gold as their MOA, and Argentina uses grams of silver as their MOA. A visitor from Austria notices that prices in Buenos Aires seem 40 times higher than in Vienna, or at least the price tags on goods in stores that would say “2 grams” in Vienna say “80 grams” in Buenos Aires. So the “nominal price” (nominal means number) is 40 times higher in Argentina. Real prices are fairly similar, perhaps slightly lower in Argentina. The real ratio of price levels is also called the “real exchange rate.”
The Austrian visitor wants to know why nominal prices are 40 times higher in Buenos Aires. Do you explain the difference with reference to:
1. The path of nominal interest rates in each country over time.
2. The path of real interest rates over time.
3. The path of market interest rates minus the Wicksellian interest rate over time.
4. Fiscal policy in each country.
5. Minimum wage laws.
6. The difference in MOA.
I say answer 6 is not just the right answer, it’s the only non-insane answer. The market for the MOA determines each price level. Period, end of story.
And logically, if the market for the MOA determines what sort of numbers you see on price tags in 2013, it will also explain what sort of numbers you see on price tags in the year 2023. And that means (purely as a matter of logic), that it explain the inflation rate between 2013 and 2023.
PS. In 1900 Japanese prices were only modestly higher than US prices (nominally), whereas now they are roughly 100 times higher. How did this happen? The Keynesian model can’t really tell you. If you instead focus on the MOA in each country (let’s say currency printed by each government), it’s easy to understand why Japanese prices are now 100 times higher than US prices. These price differences don’t just happen, there are reasons. And don’t say the reason is “the exchange rate.” The exchange rate is simply another price, it begs the questions. It’s the market for the MOA that determines nominal values.