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I have written down an explanation to one of the famous questions "why can't government print money to pay its debt"? after researching for some time on google, I need opinions as to whether this is what happens in real-life world?

In a Country X, President thinks we have too much debt to be paid to USA ... let us print money and will pay the debt off ...

After printing money(assume country X currency is Y), since they have to pay to USA in dollars, they go to foreign exchange bank and try to catch some "fool". Supposing a telecom operator in USA say Verizon wants to expand business in country X, wanted to buy currency Y since they may need that money to construct office,hire people,bribe politicians etc ... So they buy it from X government in return for dollars. Now country X pays it debt off to USA in dollars and sleeps happily.

Now Verizon expanding business in country X, effectively return the money they got it from X government to the people of X, by paying to construction,employees,etc ...

So people of X have more money but the production of X remained same, classical case of inflation.

So countries tend not to print money to pay off debt!

Is my explanation correct and more importantly I am interested in, is this the similar situation which happens in real life? Is there really like foreign exchange bank and do companies like Verizon really buy other countries currencies?

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Your get the basic intuition, but real-life situation is a little bit different.

First, I didn't really understand what you meant by "try to catch some 'fool'", but what you are calling foreign exchange bank is actually called the Foreign Exchange (market), and consist of buyers and sellers that are basically ready to buy and sell any currencies (almost all currencies in fact) provided that the price is align with their expectations. Classic laws of market apply to this market, and if the government of country X (its central bank to be more precise) print a lot of money, it corresponds to an increase in the the supply. The result, as you might expect, is a decrease in the price of money relative to other money, which is the exchange rate.

Money may be hard to understand, but it is actually a right to future cash flow of a given country. It is a sort of perpetual debt with zero coupon issued by a given country. So, if the country issues more money, it means that it issues more debt, so as a dilution mechanism it yields less cash flow to each unit of money, and since the price of money (as the price of any debt) is the expectation of future cash flow, the price will decrease.

Then, this will indeed results in more inflation. I expose two ways of seeing that. First, you can think about the price of goods as the price of goods relative to the price of money. Indeed, you're going to pay $x$ for a particular good because the seller knows that it will receive $x$ and that $x$ will give him the right to a certain amount of GDP (cash flow of country). But if the amount of GDP that the money represents is lower, he will ask for a higher price. Second, traditional monetary research has derived, a long time ago, the following formula which represents what I explained in my first point, but more formally. The following is always true, it is an accounting relation : \begin{equation} M\cdot V = P\cdot Q \end{equation}

$M$ is the amount of money, $V$ is the speed of money, $P$ is the price level and $Q$ is the output or quantity of goods exchanged.

Without entering into too much details on this equation (there are extended information on Internet), you can see that increasing $M$, holding $V$ and $Q$ constant, results in inflation.

To come back to your question, country does not (only) print money to repay their debt, because they are afraid of inflation. There is a big debate on inflation (I'm sure you can read a lot of stuff on Internet also), but loosely speaking inflation seems hard to contain. So to avoid hyper-inflation situation, they try to maintain inflation (in general below 2%).

Your story does not need another company investing in country X because, as you said people will end-up with more money, but production of country X will effectively increase. But it is true that companies buy currencies for investment purpose in the country. Even local company may end-up buy their own currency if for instance they sell product in USA (exportations), and sell the USD they received against buying their own currency. This is why importation and exportation (worldwide) is a good indicator for fluctuations in exchange rates.

Printing money to pay debt is a complicated question, and I only tried to sketch up some insight here. For more information, read more on money creation and inflation (either in the academic literature or in economic textbook for instance).

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It probably could. But it would not be popular with savers. Printing money means all the currency is worth less. So it is essentially like a universal tax on people who have money (usually the middle class and rich).

How would you like it if your thousand pounds saving was suddenly worth half as much as the government had devalued it to pay off the debt.

And those people who are in debt are now more well off since their debt is worth less. Is that fair too?

So all in all, it's not a very good idea unless you really want to annoy your voters.

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Actually a country can feasibly create money to buy off debts. But first some clarifications.

There is foreign denominated debt and locally denominated debt.

Let's start with local debt (say the Fed creating dollars to reduce our debt). This happens all the time indirectly as the Fed is constantly created the monetary base to buy treasury securities. They key to this avoiding inflation is to make sure bank deposits are not multiplied off of this new money. If a central bank can control the multiplier, then inflation will not be a problem. This is important because most monetary inflation comes from private banks and not central banks.

Then there is foreign debt. If not anticipated by the market a central bank can make a tidy profit by buying foreign currency with newly created domestic currency. Say there is an exchange ratio of 1000 dollars to 100 pesos. The market assumes this price based on the current quantity of pesos and other factors. If a central banks say doubles the quantity of pesos and uses them to buy dollars before the market can react, they can make some good profit. They key though is that the market will react and punish the Peso as it is now an unpredictable currency. When the exchange rate for the Peso drops, this means foreigners can buy more domestic goods (like say farmland). Say because of the drop in the Peso, a country has to sell off half of its farmland...which now just sends its produce to another country. Less goods for consumption is another form of inflation. This is why exchange rates are important. On top of this, the banking system will multiply (if not controlled) the new base money many fold creating a fine mess. If serious this can cause a banking crisis. As scared foreigners use Peso denominated bank accounts to buy dollars, they will stop lending short term to Peso banks which will create a liquidity crisis.

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