<p><strong>tl;dr:</strong>  No, repaying national debt does not assume population increase although depending on the parameters of economy population increase can sometimes help with repaying the debt and also help with reducing the ratio of debt to GDP, but it is neither required nor assumed. Moreover, depending on parameters population growth can even be a hindrance as well.</p>
<p><strong>Full Answer:</strong> No the statement in the question is not accurate for several reasons. It is true that GDP depends on population because if every person can produce <span class="math-container">$\\\$100$</span> worth of GDP then 10 people will be able to produce <span class="math-container">$\\\$1000$</span> of GDP. However, you are incorrect in saying:</p>
<blockquote>
<p>decreasing population would mean both a decrease in GDP per capita</p>
</blockquote>
<p>because GDP per capita is already calculated as GDP per person. If every person can produce <span class="math-container">$\\\$100$</span> then GDP <em>per capita</em> will be <span class="math-container">$\\\$100$</span> whether country's population would be ten people or thousands, because GDP per capita is by definition total GDP of a country divided by population.</p>
<p>Furthermore, you seem to be confusing concept of <em>repaying debt</em> with <em>growing out of debt</em>.</p>
<p>From economic perspective what matters the most is the size of debt relative to national income. If a poor person who earns <span class="math-container">$\\\$200$</span> a month has debt of <span class="math-container">$\\\$10000$</span> that is a problem, but if rich person who earns <span class="math-container">$\\\$2,000,000$</span> a month has <span class="math-container">$\\\$10000$</span> that is not a problem at all (at least not from economic perspective).</p>
<p>Hence there is a concept of growing out of the debt which says that provided that <span class="math-container">$GDP$</span> grows at faster rate than debt the debt to GDP ratio will become smaller and smaller over time. However, this has nothing to do with paying down that debt in principle as the debt is still there and just becomes less economically significant.</p>
<p>From this perspective what matters is what is total GDP and total debt not their per capita counterparts. GDP can grow thanks to population growth but population growth is only one of the factors that can cause GDP to grow. In fact most of GDP growth comes from advancement in technology which makes economies more productive (see Romer's Advanced Macroeconomics). However, at the same time debt can grow with population as well if government borrows to fund policies that depend on size of population (such as healthcare for example) rather ones that have mainly fixed cost such as many public goods like water filtration. Provided that total GDP increases at higher rate as a response to population (<span class="math-container">$Pop$</span>) growth than total debt <span class="math-container">$D$</span> (that is <span class="math-container">$\partial GDP/ \partial Pop &gt; \partial D /\partial Pop \quad |  \partial GDP/ \partial Pop &gt; 0$</span>) it can help to decrease the debt to GDP, but that is not the same as saying it helps to repay debt and even if it helps to reduce debt to GDP ratio it does not mean at all that this ratio cannot be reduced without any population increase. In fact empirically in recent years in developed countries most growth in total GDP comes just from technology/productivity increase as in many developed countries population more or less stagnates but most of them still experience some growth of GDP.  Furthermore,  note that if <span class="math-container">$\partial GDP/ \partial Pop &gt; \partial D /\partial Pop \quad |  \partial GDP/ \partial Pop &gt; 0$</span> does not hold population growth can even make the debt to GDP worse.</p>
<p>When we talk about repaying government debt we have to look at government budget constraint. The government budget constrain is given as:</p>
<p><span class="math-container">$$G-T=\theta + \beta$$</span></p>
<p>where <span class="math-container">$G$</span> is government spending, <span class="math-container">$T$</span> is the net tax revenue after transfers and interest payments, <span class="math-container">$\theta$</span> is government financing by high powered money and <span class="math-container">$\beta$</span> is government financing by bonds (see for example <a href="http://www.princeton.edu/%7Eerp/ERParchives/archivepdfs/M144.pdf" rel="nofollow noreferrer">Blinder &amp; Solow (1973)</a>; <a href="https://www.journals.uchicago.edu/doi/abs/10.1086/259381?journalCode=jpe" rel="nofollow noreferrer">Christ (1968)</a>; <a href="https://willembuiter.com/CFDP0384.pdf" rel="nofollow noreferrer">Tobin &amp; Buiter (1976)</a>.</p>
<p>Government debt is accrued when government issues bonds <span class="math-container">$\beta&gt;0$</span> and conversely government debt is repaid when  <span class="math-container">$\beta&lt;0$</span>. Hence in order to see what needs to happen to start repaying the debt we can just solve the budget constraint for <span class="math-container">$\beta$</span>:</p>
<p><span class="math-container">$$G - T- \theta = \beta$$</span></p>
<p>which tells us that <span class="math-container">$\beta&lt;0$</span> when government spending <span class="math-container">$G$</span> will be smaller than the amount of taxes <span class="math-container">$T$</span> and high powered money <span class="math-container">$\theta$</span> government issues (so when <span class="math-container">$G&lt;T+\theta$</span>). Hence population growth is not necessary for repayment of debt or even assumed. Government will start repaying its debt if its spending is lower than net taxes plus high powered money it issues. Sure if population growth can increase net tax revenue <span class="math-container">$T$</span> while not causing government spending <span class="math-container">$G$</span> to increase it can help with repaying the debt but it is in no way necessary to assume it will happen for debt to be repaid (and it is also possible that increase in population could lead to more government spending than the increase in tax revenue where population increase would make situation worse).</p>

CC BY-SA 4.0
2020-09-12T21:38:10.037Z
Thanks, not an economist (obviously), so I'll have to digest this. By "repaying" I did mean basically outgrowing and I shouldn't have mixed total with per capita. My interest is actually in productivity and population, and I'll try to frame some better questions on this.
Nelson Alexander
CC BY-SA 4.0
2020-09-12T21:41:13.400Z
@NelsonAlexander you are welcome. Yes I thought that’s what you meant so I covered that first but wasn’t totally sure so that’s why I covered the second part as well. If your interest is in how productivity and population are intertwined then that Romer book provides some solid answers- it’s a graduate book so it is technical but if you have good math background you would be able to follow it and even if not you could still get the point from chapter conclusions/text while ignoring the math stuff. The chapters you would want to read are the one on solow growth mode and endogenous growth theory
1muflon1
CC BY-SA 4.0
2020-09-13T09:23:19.737Z
A book with decent math (but not as technical as Romer) and with much more intuition and explanation than Romer is "Introducing Advanced Macroeconomics" by Peter Soerensen and Hans-Whitta Jacobsen.  As the title says it is meant to introduce the stuff called "advanced macro" in Romer. Check the reviews on amazon for what it worth https://www.amazon.com/INTRODUCING-ADVANCED-MACROECONOMICS-GROWTH-BUSINESS/dp/0077117867#customerReviews
Jesper Hybel
CC BY-SA 4.0
2020-09-12T20:56:51.810Z
2020-09-12T21:22:02.890Z
2020-09-12T21:22:02.890Z
1muflon1
<p>I assume that the repayment of an increasing national debt depends on an increasing GDP. And increasing GDP, in turn, depends <em>mutatis mutandis</em>  on increasing population. So an increase in national debt assumes increasing population and, likewise, a decreasing population would mean both a decrease in GDP per capita and an increase in national debt per capita. Is this, in general, correct?</p>

<gdp><government-debt><population-economics><demographics>
Does national debt and its repayment assume population increase?
Nelson Alexander
# Does national debt and its repayment assume population increase?

(Asked by: username_0 on 2020-09-12)

I assume that the repayment of an increasing national debt depends on an increasing GDP. And increasing GDP, in turn, depends *mutatis mutandis* on increasing population. So an increase in national debt assumes increasing population and, likewise, a decreasing population would mean both a decrease in GDP per capita and an increase in national debt per capita. Is this, in general, correct?

**Tags:** gdp, government-debt, population-economics, demographics


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## 1 answers

### Answer by username_1 on 2020-09-12. Score: 3

**tl;dr:** No, repaying national debt does not assume population increase although depending on the parameters of economy population increase can sometimes help with repaying the debt and also help with reducing the ratio of debt to GDP, but it is neither required nor assumed. Moreover, depending on parameters population growth can even be a hindrance as well.

**Full Answer:** No the statement in the question is not accurate for several reasons. It is true that GDP depends on population because if every person can produce $\\\$100$ worth of GDP then 10 people will be able to produce $\\\$1000$ of GDP. However, you are incorrect in saying:

> decreasing population would mean both a decrease in GDP per capita

because GDP per capita is already calculated as GDP per person. If every person can produce $\\\$100$ then GDP *per capita* will be $\\\$100$ whether country's population would be ten people or thousands, because GDP per capita is by definition total GDP of a country divided by population.

Furthermore, you seem to be confusing concept of *repaying debt* with *growing out of debt*.

From economic perspective what matters the most is the size of debt relative to national income. If a poor person who earns $\\\$200$ a month has debt of $\\\$10000$ that is a problem, but if rich person who earns $\\\$2,000,000$ a month has $\\\$10000$ that is not a problem at all (at least not from economic perspective).

Hence there is a concept of growing out of the debt which says that provided that $GDP$ grows at faster rate than debt the debt to GDP ratio will become smaller and smaller over time. However, this has nothing to do with paying down that debt in principle as the debt is still there and just becomes less economically significant.

From this perspective what matters is what is total GDP and total debt not their per capita counterparts. GDP can grow thanks to population growth but population growth is only one of the factors that can cause GDP to grow. In fact most of GDP growth comes from advancement in technology which makes economies more productive (see Romer's Advanced Macroeconomics). However, at the same time debt can grow with population as well if government borrows to fund policies that depend on size of population (such as healthcare for example) rather ones that have mainly fixed cost such as many public goods like water filtration. Provided that total GDP increases at higher rate as a response to population ($Pop$) growth than total debt $D$ (that is $\partial GDP/ \partial Pop > \partial D /\partial Pop \quad | \partial GDP/ \partial Pop > 0$) it can help to decrease the debt to GDP, but that is not the same as saying it helps to repay debt and even if it helps to reduce debt to GDP ratio it does not mean at all that this ratio cannot be reduced without any population increase. In fact empirically in recent years in developed countries most growth in total GDP comes just from technology/productivity increase as in many developed countries population more or less stagnates but most of them still experience some growth of GDP. Furthermore, note that if $\partial GDP/ \partial Pop > \partial D /\partial Pop \quad | \partial GDP/ \partial Pop > 0$ does not hold population growth can even make the debt to GDP worse.

When we talk about repaying government debt we have to look at government budget constraint. The government budget constrain is given as:

$$G-T=\theta + \beta$$

where $G$ is government spending, $T$ is the net tax revenue after transfers and interest payments, $\theta$ is government financing by high powered money and $\beta$ is government financing by bonds (see for example [Blinder & Solow (1973)](http://www.princeton.edu/%7Eerp/ERParchives/archivepdfs/M144.pdf); [Christ (1968)](https://www.journals.uchicago.edu/doi/abs/10.1086/259381?journalCode=jpe); [Tobin & Buiter (1976)](https://willembuiter.com/CFDP0384.pdf).

Government debt is accrued when government issues bonds $\beta>0$ and conversely government debt is repaid when $\beta<0$. Hence in order to see what needs to happen to start repaying the debt we can just solve the budget constraint for $\beta$:

$$G - T- \theta = \beta$$

which tells us that $\beta<0$ when government spending $G$ will be smaller than the amount of taxes $T$ and high powered money $\theta$ government issues (so when $G<T+\theta$). Hence population growth is not necessary for repayment of debt or even assumed. Government will start repaying its debt if its spending is lower than net taxes plus high powered money it issues. Sure if population growth can increase net tax revenue $T$ while not causing government spending $G$ to increase it can help with repaying the debt but it is in no way necessary to assume it will happen for debt to be repaid (and it is also possible that increase in population could lead to more government spending than the increase in tax revenue where population increase would make situation worse).

> **Comments:**
> **username_0**: Thanks, not an economist (obviously), so I'll have to digest this. By "repaying" I did mean basically outgrowing and I shouldn't have mixed total with per capita. My interest is actually in productivity and population, and I'll try to frame some better questions on this.  
> **username_1**: @username_0 you are welcome. Yes I thought that’s what you meant so I covered that first but wasn’t totally sure so that’s why I covered the second part as well. If your interest is in how productivity and population are intertwined then that Romer book provides some solid answers- it’s a graduate book so it is technical but if you have good math background you would be able to follow it and even if not you could still get the point from chapter conclusions/text while ignoring the math stuff. The chapters you would want to read are the one on solow growth mode and endogenous growth theory  
> **username_2**: A book with decent math (but not as technical as Romer) and with much more intuition and explanation than Romer is "Introducing Advanced Macroeconomics" by Peter Soerensen and Hans-Whitta Jacobsen.  As the title says it is meant to introduce the stuff called "advanced macro" in Romer. Check the reviews on amazon for what it worth https://www.amazon.com/INTRODUCING-ADVANCED-MACROECONOMICS-GROWTH-BUSINESS/dp/0077117867#customerReviews  

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