In a sense the value of currency is irrelevant.
Let’s say Texas declares independence and because everything is bigger in Texas, they create a new currency, the MegaDollar (M$). Citizens can exchange in their USD at a rate of 1 USD => 1 000 000 M$, meaning a M$ is worth 1E-6 dollars.
Now, the shops also update their prices to the new currency. A beer that cost 2.5$ yesterday? Today it’s 2 500 000M$. Milk now went from 4$ a gallon to 4 000 000M$ a gallon. What you can immediately see is that the cost of products is actually exactly the same as before. You want that gallon of milk? Just walk to the bank with your 4$ and you get the 4 000 000 M$. So despite the M$ being FAR less valuable than the USD, after taking into account the exchange rate, the price and services cost exactly the same and the economy will be exactly the same size as before the currency swap.
Now, obviously this is only true when the exchange rate is fixed and/or the prices follow the exchange rate.
Let’s say that 5 years after the Texas independence, everyone in the US noticed that they don’t really give a shit and replaced the products they used to buy from Texas with local ones, which are now cheaper than Texan ones, because Texans now need to pay tariffs for their exports to the remaining states of the USA. So now no one is buying M$ to buy Texan products, and the currency exchange rate plummets from the initial 1$ => 1 000 000 M$ to a new rate of 1$ => 2 000 000 M$. After this drop, the megadollar is extremely cheap, and suddenly that 4 000 000 megadollar milk gallon only costs 2$, so it’s cheaper than local stuff even after the tariffs!
On the receiving end though, the guy selling the milk gallon (probably) can’t just double the price to match the new exchange rate, because he’d just lose his customers who want the cheap milk only because the M$ dropped in value. So he’s still getting the same 4 000 000 M$. So, assuming the overall demand for megadollar priced milk remains the same, the Texan milk economy is making just as many megadollars per year as they did before the currency rate drop. However, now when you convert to USD, their *effective* economy has dropped by a factor of two – because the M$ is less valuable than before.
Now, what can we learn from this? You can use currency exchange rates to study how well an economy is doing, but what matters is not the value of the exchange rate, but rather how it changes relative to the prices of products bought and sold in that currency. If the exchange rate increases by a factor of 10 but all prices also increase by a factor of 10, the net change in economy is actually zero.
Now of course this is vastly simplified, the economy is a complex and hard to predict system, and does not always behave fully rationally or logically. But the main gist is, the number on your money doesn’t matter, only how much stuff that arbitrary number is worth.
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