The Weekend Quiz – February 12-13, 2022 – answers and discussion

Here are the answers with discussion for this Weekend’s Quiz. The information provided should help you work out why you missed a question or three! If you haven’t already done the Quiz from yesterday then have a go at it before you read the answers. I hope this helps you develop an understanding of Modern Monetary Theory (MMT) and its application to macroeconomic thinking. Comments as usual welcome, especially if I have made an error.

Question 1:

A nation that issues its own currency and floats it on international foreign exchange markets faces no solvency risk with respect to the debt it issues.

The answer is False.

The answer would be true if the sentence had added (to the debt it issues) … in its own currency. The national government can always service its debts so long as these are denominated in domestic currency.

The answer would be false because such nations sometimes borrow in foreign currencies in addition to their own currency.

It makes no significant difference for solvency whether the debt is held domestically or by foreign holders because it is serviced in the same manner in either case – by crediting bank accounts.

The situation changes when the government issues debt in a foreign-currency. Given it does not issue that currency then it is in the same situation as a private holder of foreign-currency denominated debt.

Private sector debt obligations have to be serviced out of income, asset sales, or by further borrowing. This is why long-term servicing is enhanced by productive investments and by keeping the interest rate below the overall growth rate.

Private sector debts are always subject to default risk – and should they be used to fund unwise investments, or if the interest rate is too high, private bankruptcies are the “market solution”.

Only if the domestic government intervenes to take on the private sector debts does this then become a government problem. Again, however, so long as the debts are in domestic currency (and even if they are not, government can impose this condition before it takes over private debts), government can always service all domestic currency debt.

The solvency risk the private sector faces on all debt is inherited by the national government if it takes on foreign-currency denominated debt. In those circumstances it must have foreign exchange reserves to allow it to make the necessary repayments to the creditors. In times when the economy is strong and foreigners are demanding the exports of the nation, then getting access to foreign reserves is not an issue.

But when the external sector weakens the economy may find it hard accumulating foreign currency reserves and once it exhausts its stock, the risk of national government insolvency becomes real.

The following blog posts may be of further interest to you:

Question 2:

By investing fiscal surpluses in a sovereign fund a government creates more space for non-inflationary public spending in the future.

The answer is False.

The public finances of a country such as Australia – which issues its own currency and floats it on foreign exchange markets are not reliant at all on the dynamics of our industrial structure. To think otherwise reveals a basis misunderstanding which is sourced in the notion that such a government has to raise revenue before it can spend.

So it is often considered that a mining boom which drives strong growth in national income and generates considerable growth in tax revenue is a boost for the government and provides them with “savings” that can be stored away and used for the future when economic growth was not strong. Nothing could be further from the truth.

The fundamental principles that arise in a fiat monetary system are as follows:

  • The central bank sets the short-term interest rate based on its policy aspirations.
  • Government spending capacity is independent of taxation revenue. The non-government sector cannot pay taxes until the government has spent.
  • Government spending capacity is independent of borrowing which the latter best thought of as coming after spending.
  • Government spending provides the net financial assets (bank reserves) which ultimately represent the funds used by the non-government agents to purchase the debt.
  • Budget deficits put downward pressure on interest rates contrary to the myths that appear in macroeconomic textbooks about “crowding out”.
  • The “penalty for not borrowing” is that the interest rate will fall to the bottom of the “corridor” prevailing in the country which may be zero if the central bank does not offer a return on reserves.
  • Government debt-issuance is a “monetary policy” operation rather than being intrinsic to fiscal policy, although in a modern monetary paradigm the distinctions between monetary and fiscal policy as traditionally defined are moot.

These principles apply to all sovereign, currency-issuing governments irrespective of industry structure. Industry structure is important for some things (crucially so) but not in delineating “public finance regimes”.

The mistake lies in thinking that such a government is revenue-constrained and that a booming mining sector delivers more revenue and thus gives the government more spending capacity. Nothing could be further from the truth irrespective of the rhetoric that politicians use to relate their fiscal decisions to us and/or the institutional arrangements that they have put in place which make it look as if they are raising money to re-spend it! These things are veils to disguise the true capacity of a sovereign government in a fiat monetary system.

In the midst of the nonsensical intergenerational (ageing population) debate, which is being used by conservatives all around the world as a political tool to justify moving to fiscal surpluses, the notion arises that governments will not be able to honour their liabilities to pensions, health etc unless drastic action is taken.

Hence the hype and spin moved into overdrive to tell us how the establishment of sovereign funds. The financial markets love the creation of sovereign funds because they know there will be more largesse for them to speculate with at the expense of public spending. Corporate welfare is always attractive to the top end of town while they draft reports and lobby governments to get rid of the Welfare state, by which they mean the pitiful amounts we provide to sustain at minimal levels the most disadvantaged among us.

Anyway, the claim is that the creation of these sovereign funds create the fiscal room to fund the so-called future liabilities. Clearly this is nonsense. A sovereign government’s ability to make timely payment of its own currency is never numerically constrained. So it would always be able to fund the pension liabilities, for example, when they arose without compromising its other spending ambitions.

The creation of sovereign funds basically involve the government becoming a financial asset speculator. So national governments start gambling in the World’s bourses usually at the same time as millions of their citizens do not have enough work.

The logic surrounding sovereign funds is also blurred. If one was to challenge a government which was building a sovereign fund but still had unmet social need (and perhaps persistent labour underutilisation) the conservative reaction would be that there was no fiscal room to do any more than they are doing. Yet when they create the sovereign fund the government spends in the form of purchases of financial assets.

So we have a situation where the elected national government prefers to buy financial assets instead of buying all the labour that is left idle by the private market. They prefer to hold bits of paper than putting all this labour to work to develop communities and restore our natural environment.

An understanding of modern monetary theory will tell you that all the efforts to create sovereign funds are totally unnecessary. Whether the fund gained or lost makes no fundamental difference to the underlying capacity of the national government to fund all of its future liabilities.

A sovereign government’s ability to make timely payment of its own currency is never numerically constrained by revenues from taxing and/or borrowing. Therefore the creation of a sovereign fund in no way enhances the government’s ability to meet future obligations. In fact, the entire concept of government pre-funding an unfunded liability in its currency of issue has no application whatsoever in the context of a flexible exchange rate and the modern monetary system.

The misconception that “public saving” is required to fund future public expenditure is often rehearsed in the financial media.

First, running fiscal surpluses does not create national savings. There is no meaning that can be applied to a sovereign government “saving its own currency”. It is one of those whacko mainstream macroeconomics ideas that appear to be intuitive but have no application to a fiat currency system.

In rejecting the notion that public surpluses create a cache of money that can be spent later we note that governments spend by crediting bank accounts. There is no revenue constraint. Government cheques don’t bounce! Additionally, taxation consists of debiting an account at an RBA member bank. The funds debited are “accounted for” but don’t actually “go anywhere” and “accumulate”.

The concept of pre-funding future liabilities does apply to fixed exchange rate regimes, as sufficient reserves must be held to facilitate guaranteed conversion features of the currency. It also applies to non-government users of a currency. Their ability to spend is a function of their revenues and reserves of that currency.

So at the heart of all this nonsense is the false analogy neo-liberals draw between private household budgets and the government fiscal balances. Households, the users of the currency, must finance their spending prior to the fact. However, government, as the issuer of the currency, must spend first (credit private bank accounts) before it can subsequently tax (debit private accounts). Government spending is the source of the funds the private sector requires to pay its taxes and to net save and is not inherently revenue constrained.

You might have thought the answer was maybe because it would depend on whether the economy was already at full employment and what the desired saving plans of the private domestic sector was. In the absence of the statement about creating more fiscal space in the future, maybe would have been the best answer.

The following blog posts may be of further interest to you:

Question 3:

Consider a government that increases spending by $100 billion in the each of the next three years. Economists estimate the spending multiplier (which is the multiple by which income increases for a given injection of spending) to be 1.5 and the impact is immediate and exhausted in each year. They also estimate that the import propensity is 0.2 (meaning that imports rise by 20 cents for every dollar generated in the economy). They also estimate the tax multiplier (impact of tax changes on income) to be equal to 1 and the current tax rate is equal to 30 per cent. So for every extra dollar produced, tax revenue rises by 30 cents. Which of the following statements is correct?

(a) The cumulative impact of this fiscal expansion on nominal GDP is $450 billion and the private sector saves 24 cents out of every extra dollar generated.

(b) The cumulative impact of this fiscal expansion on nominal GDP is $450 billion and the private sector saves 28 cents out of every extra dollar generated.

(c) The cumulative impact of this fiscal expansion on nominal GDP is $315 billion and the private sector saves 24 cents out of every extra dollar generated.

(d) The cumulative impact of this fiscal expansion on nominal GDP is $315 billion and the private sector saves 28 cents out of every extra dollar generated.

The answer was Option (a) $450 billion and 24 cents.

The question involves two parts: (a) working out what is relevant to the answer; and (b) reverse engineering some of the relevant data to get the marginal propensity to consume (and hence the saving propensity).

To work out the cumulative impact you need to understand the concept of the spending multiplier which is the easier part of the question.

In Year 1, government spending rises by $100 billion, which leads to a total increase in GDP of $150 billion via the spending multiplier. The multiplier process is explained in the following way. Government spending, say, on some equipment or construction, leads to firms in those areas responding by increasing real output. In doing so they pay out extra wages and other payments which then provide the workers (consumers) with extra disposable income (once taxes are paid).

Higher consumption is thus induced by the initial injection of government spending. Some of the higher income is saved and some is lost to the local economy via import spending. So when the workers spend their higher wages (which for some might be the difference between no wage as an unemployed person and a positive wage), broadly throughout the economy, this stimulates further induced spending and so on, with each successive round of spending being smaller than the last because of the leakages to taxation, saving and imports.

Eventually, the process exhausts and the total rise in GDP is the “multiplied” effect of the initial government injection. In this question we adopt the simplifying (and unrealistic) assumption that all induced effects are exhausted within the same year. In reality, multiplier effects of a given injection usually are estimated to go beyond 4 quarters.

So this process goes on for 3 years so the $300 billion cumulative injection leads to a cumulative increase in GDP of $450 billion.

It is true that total tax revenue rises by $135 billion but this is just an automatic stabiliser effect. There was no change in the tax structure (that is, tax rates) posited in the question.

That means that the tax multiplier, whatever value it might have been, is irrelevant to this example.

Some might have decided to subtract the $135 billion from the $450 billion to get answer (c) on the presumption that there was a tax effect. But the automatic stabiliser effect of the tax system is already built into the expenditure multiplier.

So answers (c) and (d) were there to lure you into thinking the tax parameters were important for the first part of the solution.

However, the second part of the question required you to reverse engineer the multiplier. In mathematics the general rule is that you can only solve for unknown parameters if you have as many equations as unknowns. So if you have y = 2x. You cannot solve for y because you don’t know what x is. If I tell you x = 2 then you have one equation (y = 2x) and one unknown (y) so it becomes trivial y = 4.

Similar reasoning applies in this question.

The expenditure multiplier is defined as the change in real income that results from a dollar change in exogenous aggregate demand (so one of G, I or X). We could complicate this by having autonomous consumption as well but the principle is not altered.

Consumption and Saving

So the starting point is to define the consumption relationship. The most simple is a proportional relationship to disposable income (Yd). So we might write it as C = c*Yd – where little c is the marginal propensity to consume (MPC) or the fraction of every dollar of disposable income consumed. The marginal propensity to consume is just equal to 1 minus the marginal propensity to save (which is the 24 cents or 28 cents in the dollar that we are seeking in the question).

The * sign denotes multiplication. You can do this example in an spreadsheet if you like.


Our tax relationship is already defined above – so T = tY. The little t is the marginal tax rate which in this case is the proportional rate – 0.3 in the question. Note here taxes are taken out of total income (Y) which then defines disposable income.

So Yd = (1-t) times Y or Yd = (1-0.3)*Y = 0.7*Y


If imports (M) are 20 per cent of total income (Y) then the relationship is M = m*Y where little m is the marginal propensity to import or the economy will increase imports by 20 cents for every real GDP dollar produced.


If you understand all that then the explanation of the multiplier follows logically. Imagine that government spending went up by $100 and the change in real national income is $150. Then the multiplier is the ratio (denoted k) of the

Change in Total Income to the Change in government spending.

Thus k = $150/$100 = 1.50

That is the value assumed in the question. This says that for every dollar the government spends total real GDP will rise by $1.50 after taking into account the leakages from taxation, saving and imports.

When we conduct this thought experiment we are assuming the other autonomous expenditure components (I and X) are unchanged.

But the important point is to understand why the process generates a multiplier value of 1.50.

The formula for the spending multiplier is given as:

k = 1/(1 – c*(1-t) + m)

where c is the MPC, t is the tax rate so c(1-t) is the extra spending per dollar of disposable income and m is the MPM. The * denotes multiplication as before.

This formula is derived as follows:

The national income identity outlined in Question 4 is:

GDP = Y = C + I + G + (X – M)

A simple model of these expenditure components taking the information above is:

GDP = Y = c*Yd + I + G + X – m*Y

Yd = (1 – t)*Y

We consider (in this model for simplicity) that the expenditure components I, G and X are autonomous and do not depend on the level of income (GDP) in any particular period. So we can aggregate them as all autonomous expenditure A.


GDP = Y = c*(1- t)*Y -m*Y + A

While I am not trying to test one’s ability to do algebra, and in that sense the answer can be worked out conceptually, to get the multiplier formula we re-arrange the previous equation as follows:

Y – c*(1-t)*Y + m*Y = A

Then collect the like terms and simplify:

Y[1- c*(1-t) + m] = A

So a change in A will generate a change in Y according to the this formula:

Change in Y = k = 1/(1 – c*(1-t) + m)*Change in A

or if k = 1/(1 – c*(1-t) + m)

Change in Y = k*Change in A.

So in the question you have one equation (the multiplier) and one unknown (c). This is because of the 3 behaviorial parameters (c, t and m) two are known (t and m) and you also know the value of the left-hand side of the equation (1.5). So in effect you can solve for c:

k = 1/(1 – c*(1-t) + m)

Thus k*[1 – c*(1-t) + m] = 1

Thus k – c*k*(1-t) + k*m = 1

Thus k + k*m -1 = c*k*(1-t)

Thus c = (k + k*m – 1)/(k*(1-t))

Then you plug in the values of the knowns and the result is:

c = (1.5 + 0.3 – 1)/(1.5*0.7)

c = 0.8/1.05 = 0.761905

So the MPS (marginal propensity to save) = (1 – c) = approximately 24 cents.

You may wish to read the following blog posts for more information:

That is enough for today!

(c) Copyright 2022 William Mitchell. All Rights Reserved.

This Post Has 12 Comments

  1. I would like to point out that my consistently low scores in the weekend quiz are not because I “have neo-liberal tendencies…” but because after only one read of Bill et. al’s excellent text book ‘Macroeconomics’ I am not clever enough to have understood, absorbed and therefore be able to apply, all of the wisdom contained therein.

  2. In relation to the discourse around the answer to Q2, my way of thinking about it from following Bills blog (for about 7 years now…I still mainly get the answers wrong…and hopefully Im still learning…so hoping I’m not about to put my foot in it!) is that a government with its own sovereign currency neither has money in that currency nor does not have money in that currency BUT / YET that government has the capacity to spend unlimited money in that currency to buy as much of anything that is for sale in that currency. That is the government is resource constrained NOT money (own currency) constrained. I use this way of thinking about it and thought Id better clear it with Bill as being correct (or at least not incorrect)

  3. wondering if Kit Wareham-Norfolk’s comment is in answer to my 1st comment which doesn’t appear…maybe because I followed with a 2nd comment (Michael) just to correct that name with a stray extra letter on my surname. Hoping this is right and if poss show my 1st comment (before K W-Ms comment) and remove my 2nd comment and don’t post this (3rd) one.

  4. Even though I am bad at maths, I got Q3 right (in trying to figure out a “propensity to save” I had worked out the marginal propensity to consume without realising it, but it led me to 24c!). But yet again I fall for the trick question and get Q1 wrong.

    It’s infuriating but I love it. Bill has clearly been doing this to his students for long enough that he knows what works!

  5. Q3 wrong as this was just too hard and I don’t know the formula.
    Q2 wrong as this was my mistake, not reading the question as per.
    Q1 wrong Bill you have gone too far, that is a sin of omission and downright deceptive imho 🙂

    Doing this for years now, still getting zero.

  6. @ Michael Galvin
    Re your comment not appearing: If you included a link to somewhere else that would have sent the post to be moderated before it becomes public. At the time I posted there were no replies visible.

    I’ve been tempted to make this comment for some time but the general tone on this blog is more serious than most of what I have to say. That is not meant as a criticism, but I think it unfair of Bill to imply that less than 2 out of 3 means you have neo-liberal tendencies when one may be pure of heart but not sufficiently fleet of mind!

    I finally gave in having been peeved at getting the answer to Q1 wrong. I had interpreted the question as referring only to the local currency and was aware of the difference concerning foreign currencies, so the understanding is there, but the question is a bit sneaky as Korual implies. Q2 was as simple as I thought Q1 had been and Q3 is completely beyond me.

  7. Maybe the best way to take these quizzes is to just ignore the score — throw it away. Decide that bill’s crack about neoliberal tendencies is just a dumb joke.
    Go for the discussion afterwards — like here. Here is where we can really think about stuff and get our ideas sorted. Somebody who keeps getting caught forgetting about borrowing in foreign currencies should just note that down as something to watch for when they think. Me, I always forget that households are not the entire domestic sector, despite what I keep thinking “domestic” means.

  8. You must understand Oz humour when reading Bill. He’s a devious little prick (expressed with humour and affection). Taking advantage of our propensity for thinking fast.

  9. Q3.
    I did it this way which seemed to give correct answer.
    The income in any period is the income in the last period less leakages.
    Total leakages can be expressed as a fraction x of the income in a period.
    If 100 is the income in period 1 then 100-100x = 100(1-x) is the income in period 2 and 100(1-x)^2 in period 3.
    It’s a nice geometric progression which we are told sums to 150.
    150 = 100 +100(1-x) + 100(1-x)^2 + 100(1-x)^3 etc.
    Multiplying both sides of this equation by (1-x) and subtracting from the first equation yields:
    150(1-(1-x)) = 100
    x = 1/1.5
    x = .67
    Now x is the leakages fraction = tax + imports + savings = .3 +.2 + .7(s) where s= mps
    .3+.2+.7s = .67
    .7s = .67 – .5 = .17
    So s = .17/.7 = .24

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