Download Helpful Hint The Simple Government Spending and Tax Multipliers

Helpful Hint
The Simple Government Spending and Tax Multipliers
This Helpful Hint describes the intuition and the algebra of the simple government spending
multiplier and the simple tax multiplier.
We use the term "simple" multiplier to indicate that we will ignore all feedback effects involving
investment, net exports, interest rates, and income taxes. In section you'll learn about these
complications; here we'll stick to the basics.
When we study the government spending multiplier, we're trying to determine how much the
aggregate demand curve shifts in response to a change in fiscal policy. So when we describe the
multiplier effects below, we'll talk as if whatever goods demanded will automatically be
supplied. Another way to think of this is to picture an AS/AD graph with a horizontal AS curve.
Of course, after we understand how fiscal policy affects the AD curve, we'll put it together with
a more realistic view of aggregate supply when we return to the AS/AD model.
Government Spending
We start with a simple circular flow model in which:
1)
C depends only on disposable income: C = C0 + CY(Y - T),
2)
the marginal propensity to consume (MPC) = CY = .75, and
3)
I, NX, and T are fixed.
Suppose that G increases by $1. This represents an additional injection into the circular flow.
The initial effect:
Aggregate quantity demanded increases by $1 and firms produce what the government
would like to purchase. If output increases by $1, then income (Y) increases by $1,
because if something is produced, somebody gets paid for producing it.
Tracing through the circular flow:
Households have $1 more in income. With taxes remaining unchanged, disposable
income also increases by $1. C increases by MPC times ªY: households want to buy an
additional $.75 worth of goods and services from firms. Output increases by an
additional $.75, and hence Y will increase by an additional $.75.
From that additional $.75 in disposable income, households want to purchase an additional
(.75)($.75) worth of goods. Output increases by an additional (.75)($.75), and so will income.
So far, Y has increased by $1 + ($.75) + (.75)($.75).
If we keep tracing through loops in the circular flow, the ultimate increase in Y due to the
increase in G of $1 will be:
$1 + ($.75) + (.75)($.75) + (.75)(.75)($.75) + ... = $1/(1 - .75) = $4
Of this total increase in Y of $4, C has increased by $3 [$.75 + (.75)($.75) + ...], G has increased
by $1, and I and NX have remained unchanged.
The government spending multiplier measures the change in aggregate quantity demanded for a
given change in G. In other words, it tells us how much (C + I + G + NX)d increases when G
increases by $1. In this simple example, the multiplier is 4. Thus aggregate quantity demanded
increases by $4 when government spending increases by $1. Graphically, the AD curve shifts to
the right by $4.
Y = C + I + G + NX
Y = C 0 + C Y (Y - T) + I + G + NX
(1 - C Y )Y = C 0 - C Y T + I + G + NX
Y =
⎛ 1 ⎞
⎛ C ⎞
C 0 + I + NX
+ ⎜⎜
⎟⎟ G + ⎜⎜ - Y ⎟⎟ T
1 - CY
⎝ 1 - CY ⎠
⎝ 1 - CY ⎠
The equations below show how to solve for the multiplier algebraically:
⎛ 1 ⎞
ΔY = ⎜⎜
⎟⎟ ΔG .
⎝ 1 - CY ⎠
Thus for any change in G, the resulting change in Y is:
Taxes
$
CY
.
1 - CY
Looking at equation (*) above, you can see that decreasing T by $1 will increase Y by
The tax multiplier is thus -CY/(1 - CY). This means that for any change in T, the resulting change
⎛ - CY ⎞
ΔY = ⎜⎜
⎟⎟ ΔT
⎝ 1 - CY ⎠
in Y can be found by:
In our simple model, with CY = .75, the tax multiplier is -.75/(1 - .75) = -3.
Notice that decreasing T by $1 leads to a smaller increase in Y than increasing G by $1. This
may seem puzzling, but here's the explanation.
If T decreases by $1, this is a decrease in withdrawals from the circular flow.
The initial effect is that disposable income (Y - T) increases by $1. Households now
want to increase consumption by $.75. Firms produce an additional $.75 worth of goods,
so output increases by $.75, and hence so will Y.
Tracing through the circular flow, the increase in Y due to decreasing T by $1 will be:
$.75 + (.75)($.75) + (.75)(.75)($.75) + ... = $3.
As in the case of a $1 increase in G, C has increased by $3, but there is no increase in G when T
is decreased. The decrease in taxes increases aggregate demand only through its effects on
consumption.
The Importance of the Multiplier
The idea of the fiscal multiplier was introduced by John Maynard Keynes in the 1930's. During
this time, the United States, as well as most of Europe, was experiencing a severe economic
downturn known as the Great Depression. In the United States, the unemployment rate peaked
at over 25% while extreme poverty spread throughout the population. Given these conditions,
CY, people's marginal propensity to consume, was probably very large, which implied that the
multiplier was very large. You can see the enormous appeal that this proposition had: by
spending one dollar, the government could increase aggregate demand by factors many times
more than one dollar.
However, economists today do not believe that fiscal multipliers are very large. In an economy
that is far below its potential level of output, which was the case during the Depression,
expansions in aggregate demand do lead to large increases in output, with little or no effect on
prices and inflation. That is, in Depression-like times, the SRAS curve is close to horizontal,
which is the implicit assumption behind the multiplier analysis we just discussed. However, if
the economy operates very near the full-employment level, the fiscal multiplier is quite small,
even in the short run. Increases in government spending, for example, will be partially "crowded
out" by decreases in other components of aggregate demand, especially investment.