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The income-expenditure relationship in macroeconomics – graphic treatment

Summary:
We have been doing a lot of work developing the MOOC at the University of Newcastle which will also mark the first – MMTed material. We will follow up the MOOC with more detailed learning options in subsequent months. Tomorrow, we will be filming some more material for the MOOC and I think you will enjoy what we have planned when the MOOC begins on March 3, 2021. As part of the planning I have been thinking of simplified frameworks for teaching rather complicated concepts and relationships. Here is an example of that sort of thinking. MOOC Modern Monetary Theory: Economics for the 21st Century Over the last several months by way of advancing Modern Monetary Theory (MMT) education initiatives, we have been involved in development a MOOC that will be launched in March 2021. I am working

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We have been doing a lot of work developing the MOOC at the University of Newcastle which will also mark the first – MMTed material. We will follow up the MOOC with more detailed learning options in subsequent months. Tomorrow, we will be filming some more material for the MOOC and I think you will enjoy what we have planned when the MOOC begins on March 3, 2021. As part of the planning I have been thinking of simplified frameworks for teaching rather complicated concepts and relationships. Here is an example of that sort of thinking.

MOOC Modern Monetary Theory: Economics for the 21st Century

Over the last several months by way of advancing Modern Monetary Theory (MMT) education initiatives, we have been involved in development a MOOC that will be launched in March 2021.

I am working with – NewcastleX – which is my university’s digital team to create the course material which will be available all around the world for free.

Anyone can enrol and participate and the material is suitable for anyone who is keen to learn new things and discuss these things with others of a like mind.

That is the philosophy of a MOOC.

The course – Modern Monetary Theory: Economics for the 21st Century – will start on March 3, 2021 and you can get all the enrolment details (it is free) from the link.

This will mark the first stage of the – MMTed project – that I have been trying to get off the ground for a while now.

We have been hampered by lack of funds to date, but the partnership with the University on this MOOC has really been a massive first step. The digital learning team at the University is first-class and have really helped me understand how these new platforms work.

Understanding the importance of fiscal deficits

What follows is a teaching device I use in introductory programs on macroeconomics which allow students to understand the basic rule of macroeconomics – spending equals output equals income, which drives employment.

It helps us understand the concept of equilibrium in macroeconomics and disabuses us of any notion that equilibriums is equivalent to ‘market clearing’ or full employment, which is the way the mainstream economists think of it.

We learn that an equilibrium can persist at very high levels of unemployment indefinitely without some external influence, like a fiscal stimulus entering the picture.

It can also be used as an alternative form of pedagogy (to algebraic derivations) of the sectoral balances and makes the role of fiscal policy very obvious.

Some people prefer this form of elaboration to the more concise algebra.

We also can easily establish the principle that if there is mass (involuntary) unemployment then we know at least one other thing – the fiscal deficit is too small or the surplus too big.

So I thought I would share this exposition with you all on my blog to diversify the way I usually present things.

And those who have previously studied economics will identify that this sort of structure is based on the long-standing circular flow exposition, which I tailor to suit my Modern Monetary Theory (MMT) perspective.

So a series of pictures which start from a simple basis and then get increasingly complicated as we introduce more and more real world elements.

Households and Firms

We start with a simple representation of the economy where we have households and firms.

The government is there too but we will abstract from its role at first even though none of this could happen without currency injections from the government.

The income-expenditure relationship in macroeconomics – graphic treatment

Throughout this analysis, we assume that prices are stable so that all the dollar flows are effectively in real purchasing power terms.

Business firms form expectations of what total spending in the economy will be and then assemble working capital and workers to produce to that expected sales volume. They price according to their unit cost estimates and their desired markup, the latter which reflects their profit ambitions.

That deployment then pays incomes to the suppliers of productive inputs.

Household consumption expenditure is then driven by total income, which returns revenue to the firms and around we go.

Spending drives output and employment which equals income.

The income-expenditure relationship in macroeconomics – graphic treatment

If there are no leakages from this circular flow and/or external shocks, then the system would be stable and persist indefinitely.

This is what we call a macroeconomic equilibrium state.

Now there is no presumption that this steady-state will coincide with full employment. It might but it is highly unlikely.

And it was this sort of underemployment equilibrium state that Keynes said justified government stimulus to break it up and push the economy to a higher employment state.

Tax leakage

Now what happens if we disturb this state by forcing the non-government sector to pay taxes?

In this example, I am abstracting from corporate taxes (and, as you will see social transfers). Their inclusion doesn’t fundamentally alter the story.

Now if that is all the happened – the taxes draining income out of the non-government sector into the government sector then total income flow becomes a disposable income flow and the consumption spending flow would be less.

As a result, firms would respond to the rising unsold inventories and produce less and lay off workers.

The income-expenditure relationship in macroeconomics – graphic treatment

So, in a modern monetary system, the imposition of taxes creates the condition where idle resources increase.

To return the economy to the previous equilibrium (restore the level of GDP and national income), the flow of government spending must at least offset the leakage of purchasing power from the tax drain.

The income-expenditure relationship in macroeconomics – graphic treatment

Now, we stated before that the original steady state was probably one where involuntary unemployment existed even though firms’ expectations of sales volumes were being continually met.

So even if the government spending injection offset the loss of consumption spending arising from the tax leakage, the economy would still be at below full employment.

In other words, the only way the economy could move towards full employment in this context (noting that households consume 100 per cent of their disposable income), would be for the government deficit to rise.

The excess government spending over taxes (G > T) would stimulate sales and firms would hire more workers and pay out higher incomes, which would then lead to higher tax revenue (if the tax system was linked to incomes) and higher household consumption expenditure.

This adjustment process – to the increase in government spending into deficit is what is called the expenditure multiplier.

Please read my blog post – Spending multipliers (December 28, 2009)- for more discussion on this point.

So under these conditions it is easy to understand that if there is involuntary unemployment (which means that people would take a job at the current wages if one was offered to them), then we know the fiscal deficit is too low.

You may also wonder how this new deficit spending state would restore equilibrium.

Well in these simplified conditions, the initial government spending impulse (into deficit) would stimulate rising income, rising taxation, rising consumption, with each additional induced increase in taxes and consumption spending being smaller than the last (because of the tax leakage at each step).

A new equilibrium would be reached at a higher income level once the change in tax revenue reached zero and total tax revenue was equal to the new level of government spending – thus wiping out the fiscal deficit.

If households consume all their income (as is being assumed at present) then equilibrium can only occur with the government in balance once a tax leakage is created.

The general rule is that equilibrium occurs when the leakages equal the injections.

This doesn’t mean we support fiscal balance. It is just a condition that would have to apply in this highly simplified case.

So let’s complicate it further.

Saving leakage

Now what happens if we are at a new equilibrium and households decide to save a proportion of their disposable income.

So now the marginal propensity to consume (MPC), which is the proportion of every extra dollar of disposable income receive that households consume is less than one.

That means that the marginal propensity to save (MPS) would be equal to 1 minus MPC.

The income-expenditure relationship in macroeconomics – graphic treatment

We now have an additional leakage from the income-expenditure stream, which if nothing else happened would reduce output, income, employment and subsequent consumption expenditure.

So higher saving alone will create unemployment in the non-government sector at the current settings.

With the current institutional complexity, the unemployment could be mopped up if government went into deficit (remember under our simplistic conditions the government was in balance previously).

The rising fiscal deficit could offset the loss of household consumption expenditure arising from the saving leakage.

The adjustment process would see national income rising again (as government spending exceeded the current tax revenue), tax revenue rising, household consumption spending and saving flows rising and would reach a new national income level when the sum of the leakages (taxes plus saving) equal the injection of government spending (into deficit).

So now there is no requirement that the fiscal position remain in balance. It has to be in deficit under these conditions to maintain full employment when household saving propensity is greater than zero.

Introduce imports

Now we add the foreign sector and recognise that the domestic economy spends some of its income each period on goods and services produced abroad – imports.

The flow of spending on imports constitutes an additional leakage from the leakage from the income-expenditure stream, which if no other intervention occurred would reduce output, income, employment and subsequent consumption expenditure.

Leakages reduce spending on domestic production and reduce national income.

Injections add to spending on domestic production and increase national income.

The income-expenditure relationship in macroeconomics – graphic treatment

Again, the loss of national income could be avoided if the fiscal deficit rose again to counter the leakages of imports.

Introduce Business Investment and Exports

In this framework, there are two additional injections that can offset the saving, tax, and import leakages – business investment and exports expenditure from the rest of the world.

At the current fiscal deficit, the spending flow injections from investment and exports would drive the economy beyond the full employment income level.

In fact the government could cut its net spending as these other spending injections entered the expenditure stream in order to maintain the output level at full employment.

The income-expenditure relationship in macroeconomics – graphic treatment

There are, of course, many different scenarios that we could play with in this framework.

One could construct a situation where export revenue is so strong relative to the import leakage that the economy could sustain full employment with the government in fiscal surplus.

The condition for equilibrium is that the leakages have to equal the injections.

So:

Saving + Taxes + Imports = Investment + Government + Exports

That condition will hold in equilibrium, and, given that in this simple model the three leakages are also functions of income (they rise when national income rises according to the propensities to save and import and the tax rate), there is a unique sum of injections that are required to offset the sum of the leakages that would be forthcoming at a full employment level of national income (GDP).

That doesn’t necessarily mean a government deficit is required.

But it does mean that if the sum of business investment and exports, given current government spending is not sufficient to equal what the the sum of the leakages that would be forthcoming at a full employment level of national income (GDP), then the only way the economy can reach full employment is if government spending rises.

So the equilibrium condition will deliver a stable level of output, but that, however, does not guarantee full employment.

Accordingly, to sustain full employment the condition for stable national income above can be re-written more specifically in this way:

The income-expenditure relationship in macroeconomics – graphic treatment

G = Government spending
T = Tax revenue
S = Saving flow
M = Import spending
I = Investment spending
X = Export spending

The Yf qualifier refers to the value of the flow in question at full employment given that the S, T and M flows will be higher at full employment than if the economy is in recession.

If the non-government drains > the injections which would occur at full employment, then for national income to remain stable, there has to be a fiscal deficit (G – T) sufficient to offset that gap in aggregate demand.

Conclusion

We eventually reached the sectoral balance relationship.

But the graphical exposition might provide further understandings that evade those who dislike the algebraic exposition.

That is enough for today!

(c) Copyright 2021 William Mitchell. All Rights Reserved.

Bill Mitchell
Bill Mitchell is a Professor in Economics and Director of the Centre of Full Employment and Equity (CofFEE), at the University of Newcastle, NSW, Australia. He is also a professional musician and plays guitar with the Melbourne Reggae-Dub band – Pressure Drop. The band was popular around the live music scene in Melbourne in the late 1970s and early 1980s. The band reformed in late 2010.

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