how can a rise in inflation decrease the country debt value?



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Inflation in general makes debts go down in value.

If, today, you have a debt that is listed as $10,000 and that debt is equivalent to 3,500 loaves of bread or 6,000 hours of labor, then inflation comes along and makes the price of everything double, now your $10,000 debt is the equivalent of 1,750 loaves of bread or 3,000 hours of labor.

Since the dollars got less valuable the debt, despite being the same number of dollars, is worth less.

This effect actually being enough to reduce the value of any given debt depends on a few things. One is that the inflation has to run faster than the debt accrues interest. Most private loans won’t fall into this category, but for example some mortgages that were set with ~2.5% APR are enjoying inflation right now. For an individual to enjoy this effect they also need to see their wages keep pace with inflation, though typically wages lag behind as workers have a harder, slower time at renegotiating wages than companies have with simply raising prices in stores.

National debt tends to come in at some of the lowest interest rates seen in the economy and often terms are in the tens of years. Also, a nation’s income comes from the income across the economy from individuals and businesses, so a nation’s income will tend to track inflation more readily than an individual’s. This makes it much easier for national debt to go down in value when there’s inflation than a private debt.

Because debt is denominated in nominal terms and does not change with inflation. If GDP goes up simply because of inflation, all things equal (they are never equal), then debt to GDP will be lower.

One wrinkle with this is that interest rates on NEW debt will generally be higher when inflation is higher.

It doesn’t decrease the absolute value of the debt, but it does decrease the relative value of the debt.

Let’s say that you pay $1,000 per month for your mortgage, and you have a monthly salary of $6,000 after taxes. Your mortgage payment is 1/6th if your monthly income.

Now, let’s say that 5 years pass. There has been some inflation, and you’ve gotten cost of living raises to keep up with that. You now make $8,000 per month after taxes. Your mortgage payment is still $1,000, though, so while the hard dollar value is the same it is now only 1/8th your income.

Same thing goes with countries and their debt. The tax base will increase during inflationary times, meaning that tax revenues will also increase. However, the debt instruments issued in the past still have the same payout schedule, so a smaller % of tax revenues will go towards the debt (assuming no new debt is issued).

Let’s say you have debt of $1000 and your income is $20,000. That debt is 5% of your income. Now, because of inflation, your pay rises to $30,000. But the debt is still only $1000. Now the debt is equivalent to only 3.33% of your income.

Inflation comes with a rise in other prices and, typically, an increase in income. Debt is generally has a fixed numerical value for its principle that is not touched (directly) by inflation.

If I have $100 in debt, make $1000/month, and a candy bar costs $1, I have 100 candy bars of debt or 1/10 of a month of debt.

If my debt stays at $100 but inflation increases my wages to increase to $2000 and the price of a candy bar to $2, I have 50 candy bars of debt or 1/20 of a month of debt.

While my debt stayed the same, I effectively owe less money thanks to the 100% inflation in that period.

Now, this can get more complicated due to debt generally having interest payments as well as the principle amount. Depending on how the interest is calculated, this may partially or fully counter the effect. Higher inflation generally means higher interest rates, which may be applied to existing debt or only to new debt, depending on the debt contracts. Higher interest rates makes debt less affordable.

Additionally, if I want or need to spend more money than I take in, my deficit will be larger meaning I will be taking on more debt than before. Going back to the example, if I wanted to borrow money for a candy bar, before inflation I’d only need to borrow $1, while afterwards I need to borrow $2. However, as the percentage related to income is the same in both cases, the *meaningful* amount of this new debt remains the same.