What a Contractionary Demand Shock Does
A reduction in planned spending can shift aggregate demand to the left. In the short run, when short-run aggregate supply is unchanged, the new equilibrium has lower real output and a lower price level. Whether that lower output is below potential depends on where the economy started: a contraction can create a recessionary gap or make an existing one larger.
The distinction between the shock and the resulting gap matters. A leftward shift describes a change in aggregate demand. A recessionary gap describes the position of equilibrium output relative to potential output. The shock does not automatically imply a recessionary gap; the equilibrium must be compared with potential output.
Possible sources of a contractionary shift include households becoming less willing to spend, businesses reducing planned investment, lower government purchases, or weaker demand for domestic exports. The AD-AS analysis describes the direction of the change; identifying a particular source requires evidence about the scenario. A fall in spending caused by a change in the price level itself is not, by itself, a shift of AD.
A Linear Short-Run Model
For calculation, use a linear model in which real output \(Y\) is measured in the stated output units and \(P\) is a price-level index. The aggregate-demand relation is \(Y=A-bP\), and short-run aggregate supply is \(Y=C+sP\). Here \(A\) and \(C\) are constants, while \(b>0\) and \(s>0\). Potential output \(Y^*\) is held fixed during the short-run comparison.
A contractionary demand shock lowers \(A\), leaving the other parameters and the SRAS curve unchanged. These equations are a local, simplified representation: use them over the range described by the problem, not as a claim that the curves are linear at every possible output or price level. If SRAS shifts too, the effects cannot be attributed to a demand shock alone.
The equilibrium is found where the output demanded equals the output supplied. After solving for \(P\), substitute it into either curve to find \(Y\). Do not compare the intercepts alone with potential output: the relevant quantity is equilibrium output at the intersection.
Why Both Equilibrium Values Fall
The direction of the changes can be shown directly. Let the demand intercept fall from \(A\) to \(A-D\), where \(D>0\), while SRAS remains fixed. Subtract the original equilibrium equations from the new ones. The original and new equilibria are both intersections with the same SRAS curve.
Before the shock, \(A-bP_0=C+sP_0\). After the shock, \(A-D-bP_1=C+sP_1\).
Rearranging gives \((b+s)(P_1-P_0)=-D\), so \(P_1-P_0=-D/(b+s)<0\). The equilibrium price level falls.
Because \(Y=C+sP\), \(Y_1-Y_0=s(P_1-P_0)=-sD/(b+s)<0\). Equilibrium output also falls.
The derivation also shows why the entire demand shift does not generally become an equal-sized output decline: part of the adjustment appears as a lower price level. For a fixed shock size \(D\) and AD slope parameter \(b\), a larger SRAS slope \(s\) means a larger output decrease, since \(s/(b+s)\) is larger. This is a comparative result within the stated linear model, not a separate supply shock.
Worked Examples
Worked Example: A Contraction Creates a Recessionary Gap
In a hypothetical economy, output is measured in billions of dollars and the price level is an index. Initially, AD is \(Y=1500-20P\) and SRAS is \(Y=300+20P\). A contractionary shock lowers the AD intercept by 120, leaving its slope and SRAS unchanged. Potential output is \(Y^*=880\). Find both equilibria and decide whether the shock creates or deepens a recessionary gap. Report percentage gaps to two decimal places.
Method. Set AD equal to SRAS in each case, then compare equilibrium output with potential. The common mistake to avoid is assuming the 120-unit intercept reduction means output itself must fall by 120.
Before the shock:
Substitute into SRAS: \(Y_0=300+20(30)=300+600=900\). The initial output gap is \(900-880=20\), or \(20/880\times100=2.27\%\) above potential.
After the shock: The new AD curve is \(Y=1380-20P\). Thus,
Then \(Y_1=300+20(27)=300+540=840\). The new gap is \(840-880=-40\), or \(-40/880\times100=-4.55\%\). Output fell by \(900-840=60\), and the price index fell by \(30-27=3\). Since output was initially above potential and ends below it, the shock creates a recessionary gap. Check: \(1380-20(27)=1380-540=840\), matching SRAS.
Worked Example: A Contraction Deepens an Existing Gap
A second hypothetical economy has AD \(Y=1400-20P\), SRAS \(Y=500+10P\), and potential output \(Y^*=900\). A demand shock lowers the AD intercept by 120. Find the change in equilibrium and quantify how the gap changes. Report percentage gaps to two decimal places.
Method. Solve the equilibrium on each AD curve; then compare both outputs with potential. Do not describe this as creating a recessionary gap if the initial equilibrium is already below potential.
Initially, \(1400-20P=500+10P\), so \(900=30P\) and \(P_0=30\). Output is \(Y_0=500+10(30)=800\). The initial gap is \(800-900=-100\), or \(-100/900\times100=-11.11\%\).
After the shock, AD is \(Y=1280-20P\). Equating AD and SRAS gives \(1280-20P=500+10P\), hence \(780=30P\), so \(P_1=26\). Output is \(Y_1=500+10(26)=760\). The new gap is \(760-900=-140\), or \(-140/900\times100=-15.56\%\).
Equilibrium output falls by \(800-760=40\), and the price index falls by \(30-26=4\). The absolute shortfall grows from 100 to 140, so the shock deepens the recessionary gap by 40 output units. Check: at \(P=26\), both curves give \(760\).
Worked Example: The Same Demand Shock With Different SRAS Slopes
Two hypothetical economies begin at the same equilibrium. In both, initial AD is \(Y=1400-20P\), and the contraction changes it to \(Y=1280-20P\). Economy A has SRAS \(Y=500+10P\); Economy B has SRAS \(Y=200+20P\). Potential output is 780 in each. Find the initial and post-shock equilibria and each post-shock gap. Report all quantities to two decimal places where needed.
Method. First verify that the starting equilibrium is shared, then solve the new intersection separately for each SRAS curve. The trap is to assume that identical demand shifts must produce identical output changes when the supply slopes differ.
For Economy A initially, \(1400-20P=500+10P\), so \(900=30P\), \(P_0=30\), and \(Y_0=500+10(30)=800\). For Economy B initially, \(1400-20P=200+20P\), so \(1200=40P\), \(P_0=30\), and \(Y_0=200+20(30)=800\). Both start 20 units above potential.
For Economy A after the shift, \(1280-20P=500+10P\), so \(780=30P\), \(P_1=26\), and \(Y_1=500+10(26)=760\). Its post-shock gap is \(760-780=-20\).
For Economy B after the shift, \(1280-20P=200+20P\), so \(1080=40P\), \(P_1=27\), and \(Y_1=200+20(27)=740\). Its post-shock gap is \(740-780=-40\). Both economies enter a recessionary gap, but the output decline is 40 in A and 60 in B. The steeper SRAS in B produces a larger output change and a smaller price-level decline. Check: each post-shock output equals both its AD and SRAS value.
Reading the Output Gap Correctly
A reliable interpretation separates three questions: what shifted, how the short-run intersection changed, and where the new output sits relative to potential. The first is about the source of the shock; the second follows from the AD-AS intersection; the third determines whether the gap is recessionary.
| Starting position | After a leftward AD shift with unchanged SRAS | Interpretation |
|---|---|---|
| \(Y_0>Y^*\) | \(Y_1<Y^*\) | The shock creates a recessionary gap. |
| \(Y_0<Y^*\), with \(Y_1<Y_0\) | The output shortfall is larger. | The shock deepens the recessionary gap. |
| \(Y_0=Y^*\), with \(Y_1<Y^*\) | Output moves below potential. | The shock creates a recessionary gap from an initially closed gap. |
| \(Y_1\geq Y^*\) | Output is not below potential after the shift. | A leftward shift occurred, but it did not leave a recessionary gap. |
A common exam trap is to equate the size of the AD shift with the change in output. For instance, in Worked Example 1, the AD intercept fell by 120, but equilibrium output fell by 60. The remaining effect was a 3-unit decline in the price index. Another error is to call every leftward shift a recessionary gap without checking \(Y^*\). The correction is to solve for the new equilibrium first, then calculate \(Y_1-Y^*\).
This short-run comparison holds potential output and SRAS fixed; it does not explain how the economy may adjust over a longer horizon or how policy might respond. Those are different questions. The analysis here is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
Check Your Understanding
For each hypothetical economy, use the stated equations and units. Answers are provided so you can check the equilibrium calculations and gap interpretation.
- Output is in billions. Initially AD is \(Y=1100-10P\), SRAS is \(Y=300+10P\), and \(Y^*=700\). AD shifts to \(Y=1000-10P\). Find both equilibria and the post-shock output gap. (Answer: Initially \(P=40,\ Y=700\); afterward \(P=35,\ Y=650\); the new gap is \(-50\), so the shock creates a recessionary gap.)
- AD changes from \(Y=1700-30P\) to \(Y=1580-30P\); SRAS is \(Y=500+10P\), and \(Y^*=780\). Find both equilibria and state whether a recessionary gap is created. (Answer: Initially \(P=30,\ Y=800\); afterward \(P=27,\ Y=770\); the gap changes from \(+20\) to \(-10\), so a recessionary gap is created.)
- AD changes from \(Y=1300-15P\) to \(Y=1200-15P\); SRAS is \(Y=400+10P\), and potential output is 800. Calculate the initial and final output gaps. (Answer: Initial equilibrium \(P=36,\ Y=760\), gap \(-40\); final equilibrium \(P=32,\ Y=720\), gap \(-80\); the recessionary gap deepens by 40.)
- Two economies share initial AD \(Y=1200-20P\) and potential output \(Y^*=790\). After AD shifts to \(Y=1120-20P\), Economy A has SRAS \(Y=600+10P\), while Economy B has SRAS \(Y=400+20P\). Find each post-shock equilibrium and gap. (Answer: Both initially have \(P=20,\ Y=800\). Economy A ends at \(P=17.33,\ Y=773.33\), gap \(-16.67\); Economy B ends at \(P=18,\ Y=760\), gap \(-30\).)
- In the linear model, a demand-intercept decrease of \(D\) changes equilibrium output by \(-sD/(b+s)\). If \(b=10\), \(s=15\), and output falls by 30 units, find the required decrease in the intercept and the price-level change. (Answer: \(D=50\); the price-level change is \(-D/(b+s)=-2\).)