I am now using Friday’s blog space to provide draft versions of the Modern Monetary Theory textbook that I am writing with my colleague and friend Randy Wray. We expect to complete the text by the end of this year. Comments are always welcome. Remember this is a textbook aimed at undergraduate students and so the writing will be different from my usual blog free-for-all. Note also that the text I post is just the work I am doing by way of the first draft so the material posted will not represent the complete text. Further it will change once the two of us have edited it.
[NOTE: The redux notation in the title refers to re-edits of earlier blogs with the same title. At present, the updated Chapter starts from Aggregate demand – Part 5 (redux) and continues today. Earlier Parts in the Aggregate Demand series are redundant and should be ignored].
From Part 5:
The formal expression for the expenditure multiplier is derived directly from the equilibrium national income and expenditure relationship.
The Aggregate Demand Function was given as E = A + [c(1 – t) – m]Y. The national income equilibrium condition is given as:
(8.15) Y = E
If we substitute the equilibrium condition into the Aggregate Demand Function (8.14) we get:
(8.16a) Y = E = A + [c(1 – t) – m]Y
And solving for Y (collecting Y terms on left-hand side) gives:
(8.16b) Y[1 – c(1 – t) + m] = A
Thus equilibrium income is:
(8.16) Y = 1/[1 – c(1 – t) + m]A
The expenditure multiplier (α) is the coefficient next to the A term in Equation (8.16):
(8.17) α = ΔE/ΔY = 1/[1 – c(1 – t) + m]
So if A changes by $1 then Y changes by 1/[1 – c(1 – t) + m] or α times the change in A.
By inspecting the terms that define the expenditure multiplier, you can see that it is a ratio involving the marginal propensity to consume (c), the marginal tax rate (t) and the marginal propensity to import.
Applying the tools you learned in Chapter 4, you can observe the following things:
- Other things equal, the higher is the marginal propensity to consume the higher is the expenditure multiplier.
- Other things equal, the lower is the tax rate the higher is the expenditure multiplier.
- Other things equal, the lower is the marginal propensity to import, the higher is the expenditure multiplier.
- The opposite is the case if c is lower and t and m are higher.
The task now is to explain the economic processes that lead to these conclusions.
We start with the essential insight that aggregate demand drives output with generates incomes (via payments to the productive inputs). Accordingly, what is spent will generate income in that period which is then available for use. For example, workers who are hired by firms to produce goods and services spend the incomes they earn as do suppliers of raw materials and other inputs to the production process.
There are various ways in which the income derived from the payments arising from output production can be used. The income can be used for:
- Increased consumption.
- Increased saving.
- Relinquishing tax obligations to government.
- Increased import spending.
SPECIAL TOPIC: Inventory movements and planned investment
We have learned that unplanned changes in inventory stocks lead to real GDP and national income adjustments because they signal to the firms that their expectations with respect to current aggregate demand, which they formed in the past and based their current production decisions upon were astray.
If inventories start to rise, beyond the normal level firms keep on hand to meet the daily flux in spending, it signals that firms were overly optimistic about the state of aggregate spending. Once they form the view that the discrepancy is not happenstance, they will cut back on production and national income will fall.
Conversely if inventories start to be depleted below the normal level and firms think this is not an ephemeral episode then real GDP will rise because firms will revise their expectations of aggregate demand upwards. Employment and national income rise as a result.
There is an interesting disjuncture between this view of inventories and the concept of planned aggregate demand or expenditure which pervades our analysis.
We have defined national income equilibrium as occuring when planned aggregate demand equals real GDP or national income. In Chapter 5, we learned that the national accounts always set aggregate spending equal to real GDP or national income.
However, the accounting concept of total expenditure is slightly different to our macroeconomic concept of planned aggregate demand. The difference is that the flow of spending on inventories in any given period need not accord with the planned expenditure on inventories that firms choose to make to meet the normal fluctuations in their sales.
The way the national accounts deal with this discrepancy is to classify all inventory expenditure in a period as part of gross capital formation of investment.
In macroeconomics we conceptualise the discrepancy in terms of planned (p) and unplanned (u) aggregates. So total investment, I = Ip + Iu, where the second term, Iu is the unplanned inventory build-up, which lead to changes in real GDP and national income.
So in the national accounts for a period, Iu would be included as part of inventory investment. But from a macroeconomic theory perspective, we would consider a positive or negative value for Iu in any period as providing evidence that the firms expectations have been amiss and that a dynamic exists in the economy to vary real GDP and national income.
Equilibrium thus implies that Iu = 0.
What happens if autonomous spending changes?
In Figure 8.6 we learned that if any of the components of autonomous aggregate expenditure changes, the Aggregate Demand Function shifts up or down, with the extent of the shift being measured by the change in the vertical intercept.
Assume that government spending rises as a result of the government being concerned that the rate of unemployment is too low. In Chapter 10, we will learn that mass unemployment is always the result of deficient aggregate demand relative to the productive potential of the economy and a simple remedy is for governments to increase total spending.
Figure 8.10 shows the change in equilibrium expenditure and income when government spending increases (ΔG). Point A is the initial equilibrium real GDP and national income level, Y*0, which corresponds to aggregate expenditure of E*0. The Aggregate Demand Function is given as E = C + I + G0 + NX).
At this point there are no unplanned inventory changes and firms are production decisions based upon there expected aggregate demand are being realised.
Now government spending increases by ΔG, which increases the Aggregate Demand Function (such that E = C + I + G1 + NX) and real GDP and national income increases to Y*1, which corresponds to aggregate expenditure of E*1. The new equilibrium national income is at Point B.
The reason that equilibrium real GDP and national income increases relates to the firms revision of expected expenditure. When the government injects the new autonomous spending in to the economy, aggregate spending at the current equilibrium is greater than real Output. The difference is the line segment AA’.
This distance indicates the excess aggregate demand (relative to current real GDP) and inventories would be becoming depleted. Firms would soon revise their expectations of aggregate demand upwards and start to produce more real output and pay out higher levels of national income.
They would continue to increase production and national income until their aggregate demand expectations were consistent with actual aggregate demand, a state which occurs at Point B (where the new Aggregate Demand Function cuts the 450 aggregate supply line).
Note that the change in equilibrium national income, ΔY is greater than the initial change in autonomous expenditure, ΔG. The difference between the two changes is given by the line segment CD.
How do we explain this difference?
The expenditure multiplier indicates by how much real GDP and national income changes when there is a change in autonomous expenditure. The larger is the multiplier, the larger is the change in real GDP and national income for a given change in autonomous expenditure.
The total change in aggregate demand (ΔE) following a change in autonomous expenditure (in this case, ΔG) is the sum of ΔG and the induced consumption spending that follows the initial rise in national income. Refer back to Figure 8.9 if you are unsure about this point.
The induced consumption spending is the lower chain of events in Figure 8.9. As firms react to the initial disequilibrium at Point A (the excess aggregate demand AA’) by increasing real GDP and national income, households, in turn, increase their consumption expenditure. But at the same time, imports are rising my mΔY tax revenue is rising by tΔY and households save a portion of each extra dollar of disposable income, (1-c)ΔYd.
These leakages mean that each subsequent round of induced spending is smaller than the last and eventually become zero. At that point, the economy reaches the new equilibrium at Point B in Figure 8.10.
So the total change in real output and national income, ΔY is equal to the total change in aggregate expenditure, ΔE, which is equal to the initial change in autonomous spending, ΔA plus the induced consumption ΔC.
Numerical example of the expenditure multiplier at work
Imagine that the marginal propensity to consume (c) is 0.80, the current tax rate is 0.20, and the marginal propensity to import is 0.20. This means that for every dollar of national income produced:
The way to think of the second-round expenditure injection is to focus on the leakages. After taxation is taken out, consumers determine how much they wish to spend on increased consumption, with saving then being the residual that drains further demand.
But as a result of the higher national income, total imports have also risen by 20 cents in the dollar and so the actual new spending that occurs is the difference between consumption spending and imports, which in this example is 44 cents.[MORE TO COME HERE NEXT WEEK]
Net week I will finish this chapter by finishing the numerical example and analysing a change in the slope of the Aggregate Demand Function (that is, considering a changes in the value of the multiplier rather than a shift in autonomous expenditure).
Then I plan to move onto the chapter on Sectoral Balances.
The Saturday Quiz will be back again tomorrow. It will be of an appropriate order of difficulty (-:
That is enough for today!
(c) Copyright 2012 Bill Mitchell. All Rights Reserved.