Why Contractionary Fiscal Policy Is Used
When actual real output exceeds the economy’s potential output, demand for goods and services is strong relative to the economy’s sustainable productive capacity. This situation is called an inflationary gap. A government may respond with contractionary fiscal policy, such as reducing government purchases or increasing taxes. These measures are intended to restrain aggregate demand and move output toward potential.
The aim is not automatically to push output below potential, nor is it necessarily to make the overall price level fall. In the short-run aggregate-demand and aggregate-supply model, a fiscal contraction shifts aggregate demand left. With an upward-sloping short-run aggregate-supply curve, the new equilibrium generally has lower real output and a lower price level than the starting equilibrium. Whether the policy fully closes the output gap depends on the size of the shift and the curves’ slopes.
Tracing a Fiscal Contraction in the AD-AS Model
For the short-run analysis here, assume an upward-sloping short-run aggregate-supply curve, an unchanged potential output, and no simultaneous supply shock or offsetting policy. The price level is \(P\), and real output is \(Y\). A reduction in government purchases lowers a component of aggregate expenditure. An increase in taxes reduces disposable income and, in the usual model, consumption. Either change shifts aggregate demand left. A reduction in transfers can also reduce household disposable income and demand.
The shift is a change in aggregate demand, not a movement along the original AD curve. The new equilibrium is found where the new AD curve intersects SRAS. Since the shift reduces demand at each price level, the equilibrium price level and output are both lower under the stated assumptions. The price-level decrease is relative to the initial equilibrium; it does not, by itself, establish that the economy is experiencing deflation.
Why Both Equilibrium Output and the Price Level Fall
At equilibrium, aggregate demand equals short-run aggregate supply. Setting the two linear equations equal gives \(A-bP=C+dP\). Rearranging yields \((b+d)P=A-C\), so the equilibrium price level is \(P=(A-C)/(b+d)\). Substituting that price level into SRAS gives equilibrium output.
Now suppose the fiscal contraction lowers the AD intercept by \(q\), where \(q>0\). The new intercept is \(A-q\). Comparing the old and new equilibria gives the change in price and output:
Both changes are negative. The size of the output decrease is less than \(q\), because \(d/(b+d)<1\). The price-level decrease moves the economy along the AD curve: at a lower price level, quantity of output demanded is higher than it would be at the old price level. That movement partly offsets the initial leftward shift’s effect on equilibrium output. This derivation assumes the linear curves remain applicable at both equilibria.
Compare initial equilibrium output with potential output. If \(Y>Y^*\), the economy has an inflationary gap.
A reduction in purchases or an increase in taxes reduces planned aggregate expenditure, other things equal.
Change the AD intercept as specified, then set the new AD equation equal to SRAS.
Compare the new equilibrium output with the unchanged \(Y^*\). A remaining positive gap means the contraction reduced, but did not eliminate, the inflationary gap.
Worked Example: A Spending Cut Reduces but Does Not Close the Gap
Suppose short-run aggregate demand and supply are \(Y=1600-20P\) and \(Y=400+10P\), respectively. Potential output is \(Y^*=700\). A fiscal contraction shifts AD left by lowering its intercept by 120, while leaving its slope and SRAS unchanged. Find the initial and new equilibria and the remaining output gap.
Method. Solve for each equilibrium by setting AD equal to SRAS, then compare each output level with potential. The common mistake to avoid is treating the 120-unit intercept shift as a 120-unit fall in equilibrium output.
Initial equilibrium. Set the curves equal:
Subtract 400 from both sides and add \(20P\) to both sides: \(1200=30P\), so \(P=40\). Substituting into SRAS gives \(Y=400+10(40)=800\). The initial output gap is \(800-700=100\), which is positive.
After the contraction. The new AD curve is \(Y=1480-20P\). Equating it to SRAS gives \(1480-20P=400+10P\), so \(1080=30P\) and \(P=36\). Then \(Y=400+10(36)=760\). Checking against AD gives \(1480-20(36)=760\), the same output.
The new output gap is \(760-700=60\). The price level falls by 4 and output falls by 40. The AD intercept fell by 120, but equilibrium output fell by only 40 because the lower price level partially offsets the demand shift along AD. The positive gap remains, reduced from 100 to 60.
Closing the Gap Is Not the Same as Reducing Inflation
An output gap and an inflation rate are different measures. The output gap compares current output with potential output. Inflation is the rate at which the price level changes over time. An inflationary gap indicates output above potential in this model; it does not specify a numerical inflation rate.
A contraction can reduce demand pressure and, in a model that tracks changes over time, may slow the rate of inflation. But a lower equilibrium price level in a two-equilibrium comparison is not the same statement as a lower inflation rate. Nor does it mean the price level must fall over time. To conclude that prices are falling over time would require information about the price level at different dates, not just the initial and final equilibrium levels in a comparative-static calculation.
A useful policy question is therefore: Has the fiscal contraction moved output closer to potential? A second, distinct question is: Has it reduced inflation? A diagram showing a leftward AD shift and a lower equilibrium price level supports conclusions about the short-run equilibrium comparison. It does not, by itself, quantify inflation over time.
Worked Example: A Contraction Leaves a Smaller Positive Gap
Let AD be \(Y=2000-20P\), SRAS be \(Y=200+10P\), and potential output be \(Y^*=740\). A package of tax increases shifts AD left, lowering its intercept by 90. Calculate both equilibria, the output gaps, and the change in the price level.
Method. Solve each AD-SRAS intersection and then calculate \(Y-Y^*\). This method avoids assuming that an AD-intercept change translates one-for-one into an output change.
Initially, set \(2000-20P=200+10P\). Then \(1800=30P\), so \(P=60\). SRAS gives \(Y=200+10(60)=800\). The initial gap is \(800-740=60\).
After the tax increase, AD is \(Y=1910-20P\). Set the new AD equal to SRAS: \(1910-20P=200+10P\). Thus \(1710=30P\), so \(P=57\). Output is \(Y=200+10(57)=770\). Checking with AD gives \(1910-20(57)=770\).
The new gap is \(770-740=30\). The price level falls from 60 to 57, a decrease of 3 model units, and output falls by 30. The contraction halves the positive output gap but does not close it. The check matters: substituting the new price into either curve must give the same equilibrium output.
Comparing Spending Cuts and Tax Increases
Different fiscal instruments can reduce demand by different amounts for a given policy change. The earlier material on fiscal multipliers provides the tools for measuring this difference. The following fixed-price expenditure model illustrates why the size of a tax increase cannot be compared directly with the size of a government-purchases cut. It is a separate calculation from the AD-AS equilibrium examples: the model holds the price level fixed and does not calculate the new price level.
Worked Example: Equal Demand Reductions From Two Fiscal Tools
In a simple open-economy expenditure model, suppose the marginal propensity to consume is \(c=0.8\), the proportional tax rate is \(t=0.25\), and the marginal propensity to import is \(m=0.10\). Assume prices are fixed, investment and other autonomous spending do not change, and a change in lump-sum taxes is denoted by \(\Delta T_0\). Compare a government-purchases cut of 15 with a lump-sum tax increase of 18.75.
Method. Use the government-purchases and lump-sum-tax multipliers for this model. The common mistake to avoid is applying the spending multiplier to a tax change; a tax change first affects consumption, so its multiplier is different.
The denominator common to these multipliers is \(1-c(1-t)+m\). Substituting the given values gives \(1-(0.8)(0.75)+0.10=1-0.60+0.10=0.50\). Thus the government-purchases multiplier is \(1/0.50=2\), while the lump-sum-tax multiplier is \(-c/0.50=-0.8/0.50=-1.6\).
For the purchases cut, \(\Delta G=-15\), so \(\Delta Y=2(-15)=-30\). For the tax increase, \(\Delta T_0=18.75\), so \(\Delta Y=-1.6(18.75)=-30\). The arithmetic checks: \(1.6(18.75)=30\). Both changes reduce equilibrium expenditure-model output by 30 under these assumptions.
This fixed-price result does not say that the two policies produce a 30-unit fall in output in every AD-AS model, and it says nothing directly about the price-level change. In an AD-AS problem, use the stated curve shift and solve the new intersection. The distinction between a multiplier-model output change and an AD-intercept shift is essential.
How to Judge the Result and Avoid Common Errors
After calculating a new equilibrium, report the new output gap explicitly. If \(Y_{\text{new}}>Y^*\), the contraction has not fully removed the inflationary gap. If \(Y_{\text{new}}=Y^*\), it closes the gap in the model. If \(Y_{\text{new}}<Y^*\), it has moved output past potential and created a negative output gap. These are comparisons with potential output, not judgments about whether the policy was desirable in every respect.
- Do not equate the AD shift with the equilibrium output change. The price level changes at the new intersection, so the movement along AD partly offsets the shift’s direct effect on output.
- Do not confuse a lower price level with lower inflation. A comparison of two equilibrium price levels does not calculate the rate of change over time.
- Do not assume every contraction closes the gap. Calculate the new intersection and compare it with \(Y^*\).
- Do not apply a fixed-price multiplier as if it were an AD-AS equilibrium calculation. State which model is being used and follow its assumptions.
These calculations are aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus. The central exam skill is to identify the direction of the fiscal change, shift AD in the correct direction, solve the new equilibrium consistently, and interpret the remaining output gap without claiming more than the model establishes.
Check Your Understanding
For each problem, state the relevant equilibrium or output-gap calculation. Treat the curves and assumptions given in each question as the complete short-run model.
- AD is \(Y=1300-10P\), SRAS is \(Y=300+10P\), and \(Y^*=700\). A fiscal contraction lowers the AD intercept by 100. Find the initial and new equilibria and the remaining output gap. (Answer: Initially \(P=50,\ Y=800\), with a gap of 100; afterward \(P=45,\ Y=750\), with a remaining gap of 50.)
- AD is \(Y=1600-20P\), SRAS is \(Y=400+20P\), and \(Y^*=700\). A spending cut shifts AD left by lowering its intercept by 160. Calculate the new equilibrium and output gap. (Answer: New AD is \(Y=1440-20P\); \(P=26,\ Y=920\), so the remaining gap is 220.)
- In the model \(Y=A-bP\), \(Y=C+dP\), a contraction lowers \(A\) by 75. If \(b=15\), \(d=10\), and the initial equilibrium has an output gap of 90, find the changes in equilibrium price and output and the new gap. (Answer: \(\Delta P=-3\), \(\Delta Y=-30\), and the new gap is 60.)
- In a fixed-price expenditure model, \(c=0.75\), \(t=0.20\), and \(m=0.05\). Find the change in output caused by a government-purchases cut of 12. (Answer: The denominator is \(1-0.75(0.80)+0.05=0.45\), the purchases multiplier is \(1/0.45=20/9\), and \(\Delta Y=-80/3\), approximately \(-26.67\).)
- A short-run AD-AS calculation shows that a contraction lowers the equilibrium price level from 108 to 105. Can this result alone establish that the inflation rate has fallen? Explain. (Answer: No. It establishes a lower price level in the model’s equilibrium comparison, not the change in the price level over time or the inflation rate.)