Expansionary Fiscal Policy During a Recessionary Gap

Expansionary Fiscal Policy and a Recessionary Gap

When actual output is below the economy’s productive potential, workers and other resources are underused. Expansionary fiscal policy—such as higher government purchases or lower taxes—is intended to raise aggregate demand and support production. The short-run result is not necessarily a one-for-one increase in output: if firms respond to stronger demand partly by raising prices, the price level changes as well.

The key question is therefore two-part: how far does output move toward potential, and what happens to the price level along the way? The answer depends on the fiscal multiplier and on the short-run aggregate supply response.

Definition: Potential output, $Y^*$, is the level of real output the economy can produce sustainably with normal use of its resources. A recessionary gap exists when actual output $Y_0$ is below potential output, so the output gap is $Y^*-Y_0>0$. Expansionary fiscal policy is a discretionary increase in government purchases, a reduction in taxes, or an increase in transfers intended to raise aggregate demand.

Reading the Short-Run AD-AS Model

In an aggregate demand–aggregate supply diagram, the vertical axis measures the price level $P$, and the horizontal axis measures real output $Y$. The aggregate demand curve (AD) shows the combinations of the price level and real output consistent with planned spending. The short-run aggregate supply curve (SRAS) shows the combinations firms are willing to produce in the short run. In the standard short-run model, AD slopes downward and SRAS slopes upward. Long-run aggregate supply (LRAS) is vertical at potential output $Y^*$.

During a recessionary gap, the initial equilibrium is to the left of LRAS. An expansionary fiscal change raises planned spending, shifting AD to the right. If SRAS slopes upward, the new intersection generally has both higher output and a higher price level. The higher price level is a movement along the existing SRAS curve, not a shift of SRAS. In this tutorial, assume that short-run production costs and the SRAS curve are otherwise unchanged.

The following linear schedules will be used for the worked examples. Output is measured in billions of dollars, and $P$ is a price-level index. The AD schedule is written in output form; a fiscal change that shifts demand to the right by $\Delta A$ adds that amount to its intercept.

Y=1000+\Delta A-20P \qquad\text{and}\qquad P=0.5+0.005Y

Here $\Delta A=0$ before a fiscal change. The second equation is the fixed SRAS schedule. Potential output is $Y^*=1000$. These equations are an illustrative short-run model, not a general estimate for an actual economy. They hold other influences on demand and supply constant; for example, they do not separately model a change in interest rates or a monetary-policy response.

Worked Example: A Purchase Increase Narrows the Gap

Method: First calculate the spending multiplier to find the rightward shift in AD, then solve the new AD-SRAS equilibrium. Suppose the initial recessionary-gap equilibrium is described by the schedules above. The marginal propensity to consume is $0.80$, and there are no proportional income taxes or imports in this fixed-price multiplier calculation. The government increases purchases by $\$40$ billion. Find the new output and price level, and state how much of the initial gap remains.

Step 1: Check the initial equilibrium. With $\Delta A=0$, substitute the SRAS equation into AD:

$$ Y=1000-20(0.5+0.005Y) =990-0.1Y $$

Thus $1.1Y=990$, so $Y_0=900$. The initial price level is $P_0=0.5+0.005(900)=5.0$. The initial gap is $1000-900=100$ billion dollars.

Step 2: Calculate the demand shift. With no taxes or imports in this simple expenditure model, the spending multiplier is $1/(1-\text{MPC})$. Therefore it is $1/(1-0.80)=5$. The fixed-price increase in aggregate demand is $5(40)=200$ billion dollars. Hence $\Delta A=200$.

Step 3: Solve the AD-SRAS equilibrium. The shifted AD schedule is $Y=1200-20P$. Substituting $P=0.5+0.005Y$ gives $Y=1190-0.1Y$, so $1.1Y=1190$, and $Y=1081.82$. Then $P=0.5+0.005(1081.82)=5.9091$. Rounding only at the final step, output is $\$1{,}081.82$ billion and the price-level index is $5.9091$.

Check and interpretation. At $P=5.9091$, AD gives $Y=1200-20(5.9091)=1081.82$, consistent with SRAS. Output has risen by $\$181.82$ billion, less than the fixed-price multiplier estimate of $\$200$ billion, while the price level has increased. In this example output passes potential; the calculation illustrates why a large fiscal change must be assessed in the AD-AS model rather than assumed to close only the initial gap. The method avoids treating the fixed-price multiplier as the final equilibrium response.

This example also shows that “expansionary” describes the direction of the demand shift; it does not guarantee that a particular policy size will leave output below potential. The amount of the shift and the slope of SRAS matter. A smaller change can narrow the gap without closing it, while a larger one can carry output past potential in the short-run model.

Why Prices Reduce the Output Response

The relationship between the fiscal demand shift and the new equilibrium can be derived directly. Write the AD schedule as $Y=A-bP$, where $A$ is its intercept and $b>0$. Let SRAS be $P=P_0+s(Y-Y_0)$, where $s>0$. Suppose fiscal policy raises the AD intercept by $\Delta A$, with no other curve shifting. Subtract the initial equilibrium equations from the new ones:

\Delta Y=\Delta A-b\Delta P \qquad\text{and}\qquad \Delta P=s\Delta Y

Substituting the second relationship into the first gives:

\Delta Y=\Delta A-bs\Delta Y \quad\Longrightarrow\quad (1+bs)\Delta Y=\Delta A \quad\Longrightarrow\quad \Delta Y=\frac{\Delta A}{1+bs}

Since $\Delta A>0$, $b>0$, and $s>0$, output increases, but $\Delta Y<\Delta A$. The price-level change is $\Delta P=s\Delta Y>0$. The mechanism is that greater demand raises production and, along upward-sloping SRAS, the price level. The higher price level reduces quantity demanded along AD, moderating the output increase. If SRAS were horizontal in this simplified model, $s=0$: prices would not rise and output would increase by the full $\Delta A$. That limiting case is not the assumption used in the examples here.

Result: With upward-sloping short-run aggregate supply and other factors fixed, an expansionary fiscal shift raises equilibrium output and the price level. The rise in the price level dampens the output response compared with a calculation that holds prices fixed. This result describes the model’s short-run equilibrium; it does not by itself establish how quickly policy takes effect or what happens after the short run.

Calibrating a Fiscal Change to the Gap

A fixed-price multiplier calculation is useful for estimating the initial shift in demand. It is not, by itself, a precise calculation of the fiscal change required to close a recessionary gap when prices respond. For the linear schedules above, the equilibrium output satisfies:

Y=\frac{990+\Delta A}{1.1}

To find the demand shift that puts output exactly at potential, set $Y=Y^*=1000$ and solve for $\Delta A$. The result can then be converted into a government-purchase change using the relevant spending multiplier, if that multiplier’s assumptions apply.

Worked Example: Finding the Purchase Increase That Reaches Potential

Method: Work backward from the target equilibrium using both AD and SRAS, then convert the needed AD shift into a purchase change. Use the same schedules as above, with a recessionary gap of $\$100$ billion, and assume a spending multiplier of $2.5$. Find the government-purchase increase that brings output to potential.

Step 1: Find the price level at the target output. At $Y^*=1000$, SRAS gives $P=0.5+0.005(1000)=5.5$.

Step 2: Find the required AD shift. At the target equilibrium, AD must also give output $1000$:

1000=1000+\Delta A-20(5.5)

Therefore $1000=1000+\Delta A-110$, so $\Delta A=110$ billion dollars.

Step 3: Convert the shift into a purchase increase. If the applicable spending multiplier is $2.5$, then $2.5\Delta G=110$, giving $\Delta G=44$ billion dollars.

Check and interpretation. With $\Delta A=110$, AD at $P=5.5$ gives $Y=1110-20(5.5)=1000$; SRAS at $Y=1000$ gives $P=5.5$. The schedules agree, so the target is reached. The method avoids assuming that a fixed-price estimate alone is enough to find the fiscal change needed in an upward-sloping-SRAS model.

Tax Reductions and the Same Demand-Shift Logic

A tax reduction can also shift AD to the right by increasing disposable income and consumption. The size of the initial shift depends on the tax and spending assumptions. For example, in a simple model with a proportional income-tax rate $t$, marginal propensity to consume $c$, and marginal propensity to import $m$, the fixed-price spending multiplier is $1/[1-c(1-t)+m]$. The corresponding tax multiplier is $-c/[1-c(1-t)+m]$. These expressions assume the specified spending, tax, and import relationships remain constant; they are not universal measures of the eventual AD-AS output change.

Worked Example: A Tax Cut Narrows but Does Not Close the Gap

Method: Calculate the tax multiplier, use it to determine the initial demand shift, and then solve the AD-SRAS equilibrium. Suppose $c=0.80$, $t=0.25$, and $m=0.10$. The government reduces taxes by $\$25$ billion, so $\Delta T=-25$. Use the same initial schedules and potential output as in the other examples.

Step 1: Calculate the multiplier denominator.

$$ 1-c(1-t)+m =1-0.80(1-0.25)+0.10 =1-0.60+0.10 =0.50 $$

The tax multiplier is $-0.80/0.50=-1.6$. Thus the fixed-price change in aggregate demand is $\Delta A=(-1.6)(-25)=40$ billion dollars. The positive sign is appropriate because this is a tax cut.

Step 2: Solve for output. The shifted AD schedule is $Y=1040-20P$. Using SRAS, $Y=1040-20(0.5+0.005Y)=1030-0.1Y$. Therefore $1.1Y=1030$, giving $Y=936.36$ billion dollars.

Step 3: Find the price level and remaining gap. SRAS gives $P=0.5+0.005(936.36)=5.1818$. The remaining recessionary gap is $1000-936.36=63.64$ billion dollars. Rounding only at the final step, the new output is $\$936.36$ billion and the price-level index is $5.1818$.

Check and interpretation. AD gives $1040-20(5.1818)=936.36$, matching SRAS. The tax cut raises output and the price level, but leaves a gap. The method avoids confusing the tax multiplier’s fixed-price estimate of the demand shift with the final output change.

Common Exam Trap and Policy Interpretation

Trap: divide the initial gap by the multiplier and call the result the exact policy required. In the calibration example, this shortcut gives $100/2.5=40$ billion dollars of extra purchases. But that creates an AD shift of only $2.5(40)=100$ billion dollars. Substituting $\Delta A=100$ into the equilibrium formula gives $Y=(990+100)/1.1=990.91$, not $1000$. The price level is $0.5+0.005(990.91)=5.4545$, and a gap of $9.09$ billion dollars remains. Under these model assumptions, the exact purchase increase is $\$44$ billion, not $\$40$ billion.

The shortcut is not useless: it is a fixed-price estimate that can indicate the scale of a policy change. The error is treating it as an exact AD-AS answer when SRAS slopes upward. A sound solution states whether it is calculating a demand shift at fixed prices or a new equilibrium with a price response, and checks the result against both AD and SRAS.

In practice, expansionary fiscal policy is intended to support output when resources are underused. Its modeled effect depends on the size and type of fiscal change, the multiplier assumptions, and the short-run supply response. A rise in output does not imply that the price level is unchanged; nor does a rise in prices mean output has failed to increase. These are separate outcomes of the new intersection of AD and SRAS.

Establish the gap.
Find initial output and compare it with potential output. A recessionary gap requires $Y_0<Y^*$.

Translate policy into a demand shift.
Use the appropriate multiplier only under its stated assumptions to calculate $\Delta A$.

Solve the new equilibrium.
Use the shifted AD curve and the given SRAS curve to find output and the price level.

Check the result.
Substitute the equilibrium values into both schedules, then compare output with potential to identify the remaining gap.

Check Your Understanding

For Questions 1–4, use $Y=1000+\Delta A-20P$, $P=0.5+0.005Y$, and $Y^*=1000$. Round output to two decimal places and the price-level index to four decimal places where needed.

A fiscal measure shifts AD right by $\Delta A=55$. Find equilibrium output, the price level, and the remaining gap. (Answer: $Y=950.00$, $P=5.2500$, gap $=50.00$ billion dollars.)
Suppose $c=0.70$, $t=0.20$, and $m=0.10$. Government purchases rise by $\$27$ billion. Find the spending multiplier, the AD shift, new output, and the price level. (Answer: multiplier $=1.8519$, $\Delta A=50.00$ billion dollars, $Y=945.45$, $P=5.2273$.)
Suppose $c=0.75$, $t=0.20$, and $m=0.10$. Taxes are cut by $\$20$ billion. Find the tax multiplier, the AD shift, new output, and the price level. (Answer: tax multiplier $=-1.5000$, $\Delta A=30.00$ billion dollars, $Y=927.27$, $P=5.1364$.)
If the spending multiplier is $2.5$, what increase in government purchases is needed to bring output exactly to potential under these AD and SRAS schedules? State the target price level as a check. (Answer: purchases increase by $\$44$ billion; target $P=5.5$.)
A fiscal package has a fixed-price multiplier of $2.2$ and raises purchases by $\$40$ billion. Find the AD shift, new output, price level, and remaining gap. (Answer: $\Delta A=88$ billion dollars, $Y=980.00$, $P=5.4000$, gap $=20.00$ billion dollars.)

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