Lets pretend you want to start a business. You take out a loan from the bank. Use the money to start a business and then with the profits you make you then pay off the loan. Over this time period your debt has resulted in you marking more profitable.
In general terms if you are able to borrow money in a way that causes a greater return on investment in the future then it makes rational economic sense to do so. The limit on how much you should borrow is basically set by a combination of the expected return on investment and the interest rate you are borrowing at.
A rich country can borrow at very low interest rates because it is expected that they will be able to pay it off in the future. It then can invest that money in infrastructure and education and other services that increases the productivity of its economy and so they are able to service those loans. Making the countries even richer.
Rich countries are able to take up large debts because they are rich and people feel safe lending them money.
Rich countries are rich because they have capital (from loans) to improve their economy.
An improved economy means that it is safer lending to them.
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