The Weekend Quiz – August 25-26, 2018 – 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:

For the US private domestic sector to reduce its overall overall debt levels, the government must run a fiscal deficit.

The answer is False.

This question requires an understanding of the sectoral balances that can be derived from the National Accounts. But it also requires some understanding of the behavioural relationships within and between these sectors which generate the outcomes that are captured in the National Accounts and summarised by the sectoral balances.

The first fact that is assumed by the question is that the US external sector is in deficit and will remain that way for the foreseeable future. If the external sector was in surplus then the answer may be different (depending on the relative size of the fiscal balance and the external balance).

Refreshing the balances (again) – we know that from an accounting sense, if the external sector overall is in deficit, then it is impossible for both the private domestic sector and government sector to run surpluses. One of those two has to also be in deficit to satisfy the accounting rules.

The important point is to understand what behaviour and economic adjustments drive these outcomes.

To refresh your memory the sectoral balances are derived as follows. The basic income-expenditure model in macroeconomics can be viewed in (at least) two ways: (a) from the perspective of the sources of spending; and (b) from the perspective of the uses of the income produced. Bringing these two perspectives (of the same thing) together generates the sectoral balances.

From the sources perspective we write:

GDP = C + I + G + (X – M)

which says that total national income (GDP) is the sum of total final consumption spending (C), total private investment (I), total government spending (G) and net exports (X – M).

Expression (1) tells us that total income in the economy per period will be exactly equal to total spending from all sources of expenditure.

We also have to acknowledge that financial balances of the sectors are impacted by net government taxes (T) which includes all taxes and transfer and interest payments (the latter are not counted independently in the expenditure Expression (1)).

Further, as noted above the trade account is only one aspect of the financial flows between the domestic economy and the external sector. we have to include net external income flows (FNI).

Adding in the net external income flows (FNI) to Expression (2) for GDP we get the familiar gross national product or gross national income measure (GNP):

(2) GNP = C + I + G + (X – M) + FNI

To render this approach into the sectoral balances form, we subtract total taxes and transfers (T) from both sides of Expression (3) to get:

(3) GNP – T = C + I + G + (X – M) + FNI – T

Now we can collect the terms by arranging them according to the three sectoral balances:

(4) (GNP – C – T) – I = (G – T) + (X – M + FNI)

The the terms in Expression (4) are relatively easy to understand now.

The term (GNP – C – T) represents total income less the amount consumed less the amount paid to government in taxes (taking into account transfers coming the other way). In other words, it represents private domestic saving.

The left-hand side of Equation (4), (GNP – C – T) – I, thus is the overall saving of the private domestic sector, which is distinct from total household saving denoted by the term (GNP – C – T).

In other words, the left-hand side of Equation (4) is the private domestic financial balance and if it is positive then the sector is spending less than its total income and if it is negative the sector is spending more than it total income.

The term (G – T) is the government financial balance and is in deficit if government spending (G) is greater than government tax revenue minus transfers (T), and in surplus if the balance is negative.

Finally, the other right-hand side term (X – M + FNI) is the external financial balance, commonly known as the current account balance (CAD). It is in surplus if positive and deficit if negative.

In English we could say that:

The private financial balance equals the sum of the government financial balance plus the current account balance.

We can re-write Expression (6) in this way to get the sectoral balances equation:

(5) (S – I) = (G – T) + CAD

which is interpreted as meaning that government sector deficits (G – T > 0) and current account surpluses (CAD > 0) generate national income and net financial assets for the private domestic sector.

Conversely, government surpluses (G – T < 0) and current account deficits (CAD < 0) reduce national income and undermine the capacity of the private domestic sector to add financial assets.

Expression (5) can also be written as:

(6) [(S – I) – CAD] = (G – T)

where the term on the left-hand side [(S – I) – CAD] is the non-government sector financial balance and is of equal and opposite sign to the government financial balance.

This is the familiar MMT statement that a government sector deficit (surplus) is equal dollar-for-dollar to the non-government sector surplus (deficit).

The sectoral balances equation says that total private savings (S) minus private investment (I) has to equal the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)) plus net income transfers.

All these relationships (equations) hold as a matter of accounting and not matters of opinion.

So what economic behaviour might lead to the outcome specified in the question?

If the nation is running an external deficit it means that the contribution to aggregate demand from the external sector is negative – that is net drain of spending – dragging output down. The reference to a “small” external deficit was to place doubt in your mind. In fact, it doesn’t matter how large the external deficit is for this question.

Assume, now that the private domestic sector (households and firms) seeks to reduce its overall debt holdings. That requires it to save overall – spend less than it is earning as a sector. Consistent with this aspiration, households may cut back on consumption spending and save more out of disposable income. The immediate impact is that aggregate demand will fall and inventories will start to increase beyond the desired level of the firms.

The firms will soon react to the increased inventory holding costs and will start to cut back production. How quickly this happens depends on a number of factors including the pace and magnitude of the initial demand contraction. But if the households persist in trying to save more and consumption continues to lag, then soon enough the economy starts to contract – output, employment and income all fall.

The initial contraction in consumption multiplies through the expenditure system as workers who are laid off also lose income and their spending declines. This leads to further contractions.

The declining income leads to a number of consequences. Net exports improve as imports fall (less income) but the question clearly assumes that the external sector remains in deficit. Total saving actually starts to decline as income falls as does induced consumption.

So the initial discretionary decline in consumption is supplemented by the induced consumption falls driven by the multiplier process.

The decline in income then stifles firms’ investment plans – they become pessimistic of the chances of realising the output derived from augmented capacity and so aggregate demand plunges further. Both these effects push the private domestic balance further towards and eventually into surplus

With the economy in decline, tax revenue falls and welfare payments rise which push the public fiscal balance towards and eventually into deficit via the automatic stabilisers.

If the private sector persists in trying to increase its saving ratio then the contracting income will clearly push the fiscal balance into deficit.

So we would have an external deficit, a private domestic surplus and a fiscal deficit.

The general point is that the government would be far better supporting this saving strategy by running a discretionary deficit and ensuring income and employment levels are high.

The following blogs may be of further interest to you:

Question 2:

Larger fiscal deficits as a percentage of GDP reduce the local productive resources that are available to the private domestic sector.

The answer is True.

It is clear that at any point in time, there are finite real resources available for production. New resources can be discovered, produced and the old stock spread better via education and productivity growth. The aim of production is to use these real resources to produce goods and services that people want either via private or public provision.

So by definition any sectoral claim (via spending) on the real resources reduces the availability for other users. There is always an opportunity cost involved in real terms when one component of spending increases relative to another.

Unless you subscribe to the extreme end of mainstream economics which espouses concepts such as 100 per cent crowding out via financial markets and/or

Ricardian equivalence consumption effects, you will conclude that rising net public spending as percentage of GDP will add to aggregate demand and as long as the economy can produce more real goods and services in response, this increase in public demand will be met with increased public access to real goods and services.

You might also wonder whether it matters if the economy is already at full capacity. Under these conditions a rising public share of GDP must squeeze real usage by the non-government sector which might also drive inflation as the economy tries to siphon of the incompatible nominal demands on final real output.

You might say that the deficits might rise as a percentage of GDP as a result of a decline in private spending triggering the automatic stabilisers which would suggest many idle resources. That is clearly possible but doesn’t alter the fact that the public claims on the total resources available have risen.

Under these circumstances the opportunity costs involved are very low because of the excess capacity. The question really seeks to detect whether you have been able to distinguish between the financial crowding out myth that is found in all the mainstream macroeconomics textbooks and concepts of real crowding out.

The normal presentation of the crowding out hypothesis which is a central plank in the mainstream economics attack on government fiscal intervention is more accurately called “financial crowding out”.

At the heart of this conception is the theory of loanable funds, which is a aggregate construction of the way financial markets are meant to work in mainstream macroeconomic thinking. The original conception was designed to explain how aggregate demand could never fall short of aggregate supply because interest rate adjustments would always bring investment and saving into equality.

At the heart of this erroneous hypothesis is a flawed viewed of financial markets. The so-called loanable funds market is constructed by the mainstream economists as serving to mediate saving and investment via interest rate variations.

This is pre-Keynesian thinking and was a central part of the so-called classical model where perfectly flexible prices delivered self-adjusting, market-clearing aggregate markets at all times. If consumption fell, then saving would rise and this would not lead to an oversupply of goods because investment (capital goods production) would rise in proportion with saving. So while the composition of output might change (workers would be shifted between the consumption goods sector to the capital goods sector), a full employment equilibrium was always maintained as long as price flexibility was not impeded. The interest rate became the vehicle to mediate saving and investment to ensure that there was never any gluts.

So saving (supply of funds) is conceived of as a positive function of the real interest rate because rising rates increase the opportunity cost of current consumption and thus encourage saving. Investment (demand for funds) declines with the interest rate because the costs of funds to invest in (houses, factories, equipment etc) rises.

Changes in the interest rate thus create continuous equilibrium such that aggregate demand always equals aggregate supply and the composition of final demand (between consumption and investment) changes as interest rates adjust.

According to this theory, if there is a rising fiscal deficit then there is increased demand is placed on the scarce savings (via the alleged need to borrow by the government) and this pushes interest rates to “clear” the loanable funds market. This chokes off investment spending.

So allegedly, when the government borrows to “finance” its fiscal deficit, it crowds out private borrowers who are trying to finance investment. The mainstream economists conceive of this as the government reducing national saving (by running a fiscal deficit) and pushing up interest rates which damage private investment.

The analysis relies on layers of myths which have permeated the public space to become almost self-evident truths. This trilogy of blogs will help you understand this if you are new to my blog – Deficit spending 101 – Part 1Deficit spending 101 – Part 2Deficit spending 101 – Part 3.

The basic flaws in the mainstream story are that governments just borrow back the net financial assets that they create when they spend. Its a wash! It is true that the private sector might wish to spread these financial assets across different portfolios. But then the implication is that the private spending component of total demand will rise and there will be a reduced need for net public spending.

Further, they assume that savings are finite and the government spending is financially constrained which means it has to seek “funding” in order to progress their fiscal plans. But government spending by stimulating income also stimulates saving.

The flawed notion of financial crowding out has to be distinguished from other forms of crowding out which are possible. In particular, MMT recognises the need to avoid or manage real crowding out which arises from there being insufficient real resources being available to satisfy all the nominal demands for such resources at any point in time.

In these situation, the competing demands will drive inflation pressures and ultimately demand contraction is required to resolve the conflict and to bring the nominal demand growth into line with the growth in real output capacity.

The idea of real crowding out also invokes and emphasis on political issues. If there is full capacity utilisation and the government wants to increase its share of full employment output then it has to crowd the private sector out in real terms to accomplish that. It can achieve this aim via tax policy (as an example). But ultimately this trade-off would be a political choice – rather than financial.

The following blogs may be of further interest to you:

Question 3:

Assume the government increases spending by $100 billion from now and maintains that injection for three years. Economists estimate the spending multiplier to be 1.6 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) and the current tax rate is equal to 20 per cent. They also estimate that the tax multiplier (impact of tax changes on income) to be equal to 1.

The cumulative impact of this fiscal expansion on nominal GDP is:

(a) $480 billion and households save 24 cents out of every extra disposable dollar generated.

(b) $480 billion and households save 28 cents out of every extra disposable dollar generated.

(c) $384 billion and households save 24 cents out of every extra disposable dollar generated.

(d) $384 billion and households save 28 cents out of every extra disposable dollar generated.

The answer was Option (b) $480 billion and 28 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.

See the links at the bottom of this answer.

In Year 1, government spending rises by $100 billion, which leads to a total increase in GDP of $160 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 $480 billion.

It is true that total tax revenue rises by $96 billion over the three years 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 $96 billion from the $480 billion to get answer (c) or (d) 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.

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 – 0.2 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 = 0.2*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 $160. Then the multiplier is the ratio (denoted k) of the

Change in Total Income to the Change in government spending.

Thus k = $160/$100 = 1.60

That is the value assumed in the question. This says that for every dollar the government spends total real GDP will rise by $1.60 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 1.60.

The formula for the spending multiplier is given as (see blogs listed below for a complete explanation):

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 is:

GDP = Y = C + I + G + (X – M)

Where C = consumption, I is investment, G is government spending, X is exports and M is imports (so (X – M) is net exports).

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 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 = (1.6 + 0.32 – 1)/(1.6*0.8)

c = 0.92/1.28 = 0.71875

So the MPS (marginal propensity to save) = (1 – c) = approximately 28 cents.

You may wish to read the following blogs for more information:

That is enough for today!

(c) Copyright 2018 William Mitchell. All Rights Reserved.

This Post Has 7 Comments

  1. Thanks for pointing out the two nuances of “crowding out” – I have to admit that I mechanically assumed that it would not hold in the real markets as well. Are there any “real life” examples where governments clearly crowded out the real goods market, when it should not have done so? It just seems hard to imagine, or requiring a really extreme case (e.g. in a situation similar to Zimbabwe during the hyperinflation).
    Tx in advance!

  2. The quiz gives ‘False’ as the correct answer for Question 1. But the answers says ‘True’. And I understand why ‘True’ is probably the case as far as the US, with the ongoing trade deficits, is concerned. That was the only question I had correct, and now even that has been taken away…

    But as for question 2, I am still confident that my improbable scenario for deficit spending would not reduce the ‘local productive resources available to the private domestic sector’.

    And question 3 was more an algebra test than an economics question. Flunked it miserably. But even so, I do not think deriving an estimate for the MPC from an estimate of the fiscal multiplier effect is the right way to go about it.

    Oh well, thanks for the quiz and answers. Learned a few things.

  3. It just shows how not reading properly can sent one astray…. I cheated(I guess) on reaching the MPC I simply changed numbers (in excel) until I got 1.603. That final MPC was 7.17 which I rounded to .72…. Then I took a “world tour” over eleven periods and came to the following:.

    GDP Disp. Inc Consumpt. Saving Imports Taxes Leakages

    Total Change 160.25 128.20 92.31 35.90 32.05 32.05 100.00
    Times 3 480.76 384.61 276.92 107.69 96.15 96.15 99.99

    I simply could not get at the .28 savings…It bugged me the whole night then; bam! comes the answer…. The question asked for cents saved out of every extra disposable dollar generated. MPS and not total savings .
    I read it a million times and still didn`t see it. I kept looking at the total over eleven periods, 35.9

  4. Dr. Mitchell, if the non-government sector cannot increase net financial assets without the cooperation of the government, then how should we think about equity shares issued by corporations? I understand that they have both an asset (the share) and a liability (an entry on the company’s balance sheet as a liability), but in reality, of what significance is the liability on the balance sheet?

    On a bank’s balance sheet, loan assets and deposit liabilities are regularly created and regularly extinguished. For a corporation, the share assets and balance sheet liabilities are created and rarely, if ever, extinguished. In addition, the obligations that the corporation has to honor for the liability created are practically non-existent, unlike a bank’s obligation to honor the deposit liability it created.

    So would you agree that shares are a way of the non-government sector to create net financial assets? I think the answer is ‘false’ but the logic escapes me.

    Thanks, Joel

  5. “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 – 0.2 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 = 0.2*Y”

    Shouldn’t it be Yd=(1-0.2)*Y=0.8Y ? Or am I way off…. 😉

    Oh my God Bill, you have really made my mind spin with number 3. It will take hours to dissect that. I know it is all logical, and my high school algebra was always pretty good but when it comes to applying it to economics I struggle….

  6. Further questions

    “Y – c*(1-t)*Y + m*Y – A”

    Should it be Y – c*(1-t)*Y + m*Y – A=0?

    “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:”

    Should it be (1.6)?

    I follow the algebra now but would struggle to do it myself! MMT university is required……

  7. would you agree that shares are a way of the non-government sector to create net financial assets?

    I would be interested to read Bill’s thoughts.

    My guess is no, shares make no net difference to the financial assets of the non-government sector.

    The founders of a privately held firm use one form of financial asset (demand deposits at retail banks) to create another (equity stakes in a privately held firm). It’s just an asset swap – no change to the net financial wealth of the sector as a whole.

    When the firm offers shares to the public, the firm swaps one one form of financial asset (equity stakes in a firm) for another (demand deposits at retail banks – the people purchasing the shares are using demand deposits to make the purchases). Again, just an asset swap.

    If the firm becomes very successful and efficient at producing output that people want to buy, but the the federal government does not net add spending into the non-government sector in proportion to the increase in the economy’s productive capacity, the firm and its shareholders can accumulate wealth but only to the detriment of other entities in the non-government sector. The firm’s additional wealth (reflected in its rising profits and rising share price) had to come from elsewhere in the non-government sector. So again, assets get reshuffled within the non-government sector, but there are no net changes to the sector’s financial assets.

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