Why Simultaneous Shifts Can Leave an Outcome Uncertain
In the short-run aggregate demand and aggregate supply model, a change in the economy can shift more than one curve at once. For example, an increase in government purchases may shift aggregate demand to the right, while a rise in firms’ production costs shifts short-run aggregate supply to the left. Each change affects equilibrium output and the price level, but their combined effects need not point in the same direction for both variables.
The key is to separate what the directions of the shifts establish from what requires information about their relative sizes. Sometimes both shifts push one outcome in the same direction, making that outcome determinate, while they push the other outcome in opposite directions. In that case, the second outcome is ambiguous without more information.
This analysis concerns short-run equilibrium, with potential output and the underlying slopes of the curves held fixed. AD slopes downward in the price level and output space; SRAS slopes upward. The usual short-run explanation is that some wages and input prices adjust slowly, so changes in demand can affect production as well as prices. A rightward shift of AD tends to raise both equilibrium output and the price level. A leftward shift tends to lower both. A rightward shift of SRAS tends to raise output and lower the price level; a leftward shift tends to lower output and raise the price level.
Four Combinations of Shifts
Track each shift’s effect on each outcome, then combine those effects. When the effects reinforce one another, the direction is determined. When they oppose one another, shift magnitudes matter.
| AD shift | SRAS shift | Equilibrium output | Price level |
|---|---|---|---|
| Right | Left | Ambiguous | Rises |
| Left | Right | Ambiguous | Falls |
| Right | Right | Rises | Ambiguous |
| Left | Left | Falls | Ambiguous |
For instance, a rightward AD shift raises output, while a leftward SRAS shift lowers it. Those output effects oppose each other, so the net change cannot be inferred from directions alone. Both shifts raise the price level, however, so its increase is determinate. If AD and SRAS both shift right, their output effects reinforce, but their price-level effects oppose.
A Linear Model to Measure the Ambiguity
Directional reasoning identifies what is certain. A simple linear model shows how shift sizes determine the uncertain outcome. Suppose output \(Y\) and the price level \(P\) are related by the following inverse AD and SRAS equations:
Here \(A\) and \(C\) locate the curves, while \(b\) and \(d\) describe their slopes. A rise in \(A\) shifts AD right; a fall in \(A\) shifts AD left. A rise in \(C\) shifts SRAS right; a fall in \(C\) shifts SRAS left. Assume the curves remain linear with unchanged slopes while the shifts occur, and that equilibrium is where planned output demanded equals output supplied.
Let \(\Delta A\) be the change in the AD intercept and \(\Delta C\) the change in the SRAS intercept. At equilibrium, \(Y_D=Y_S\), so \(A-bP=C+dP\). Solving for the initial price level gives \(P=(A-C)/(b+d)\). After the shifts, the intercepts are \(A+\Delta A\) and \(C+\Delta C\). Subtracting the initial equilibrium from the new one gives:
Since \(b+d>0\), the sign of the price-level change is the sign of \(\Delta A-\Delta C\). A rightward AD shift has \(\Delta A>0\); a leftward SRAS shift has \(\Delta C<0\). Both changes make \(\Delta A-\Delta C\) positive, so the price level rises. A leftward AD shift and a rightward SRAS shift both make that expression negative, so the price level falls.
To find the output change, use \(Y=A-bP\), so \(\Delta Y=\Delta A-b\Delta P\). Substituting the price-level result yields:
This expression explains why output can be ambiguous. With AD shifting right and SRAS left, \(\Delta A>0\) but \(\Delta C<0\), so the two terms in the numerator have opposite signs. Output rises if \(d\Delta A>-b\Delta C\), falls if \(d\Delta A<-b\Delta C\), and is unchanged if \(d\Delta A=-b\Delta C\). The slopes matter as well as the shift sizes. For both curves shifting right, the numerator is positive, so output rises, while the sign of \(\Delta P\) depends on which intercept increases more.
Label each curve’s movement as right or left; do not confuse a shift with movement along a curve.
For output and the price level separately, check whether the shifts push in the same or opposite directions.
If the effects on an outcome oppose one another, use shift sizes and, when provided, slopes to determine the net result.
Worked Applications
Worked Example: Demand Expansion and an Adverse Supply Shift
An economy has \(Y_D=1200-20P\) and \(Y_S=200+30P\), with output measured in index points. A demand expansion shifts AD to \(Y_D=1300-20P\). At the same time, an adverse supply shock shifts SRAS to \(Y_S=140+30P\). Find the initial and new equilibria, and state which outcome is determinate. Use the equilibrium method; avoid assuming that the two shifts’ opposing output effects cancel.
Initial equilibrium. Set demand equal to supply:
Substitute into either curve: \(Y=1200-20(20)=800\). The initial equilibrium is \(P=20\), \(Y=800\).
New equilibrium. Set the shifted curves equal:
New output is \(Y=1300-20(23.2)=1300-464=836\). Checking SRAS gives \(140+30(23.2)=140+696=836\), so the curves agree. The price level rises by \(23.2-20=3.2\) points, and output rises by \(836-800=36\) points.
The price-level increase is determinate: rightward AD and leftward SRAS both raise it. Output is ambiguous from directions alone, though this example’s specified shift sizes produce an increase of 36 points. The method avoids treating the label “adverse supply shock” as enough to conclude that output must fall.
Worked Example: Demand Contraction and Favorable Supply Shift
Begin with \(Y_D=1200-20P\) and \(Y_S=200+30P\), whose initial equilibrium is \(P=20\), \(Y=800\). A decline in private spending shifts AD to \(Y_D=1080-20P\). A fall in production costs shifts SRAS to \(Y_S=250+30P\). Calculate the new equilibrium and identify the determinate outcome. The task is to evaluate both shifts, not to infer output from the demand contraction alone.
Set the shifted curves equal:
Substituting into AD gives \(Y=1080-20(16.6)=1080-332=748\). Checking SRAS gives \(250+30(16.6)=250+498=748\). Thus the new equilibrium is \(P=16.6\), \(Y=748\). Relative to the initial equilibrium, the price level falls by \(3.4\) points and output falls by \(52\) points.
The price-level fall is determinate because leftward AD and rightward SRAS both lower the price level. Output is ambiguous from directions alone: the demand contraction reduces it, while the favorable supply shift raises it. The specified magnitudes result in lower output. The calculation avoids mistaking a determinate price-level result for a determinate output result.
Worked Example: Both Curves Shift Right
An economy starts with \(Y_D=1200-20P\) and \(Y_S=200+30P\), so \(P=20\) and \(Y=800\). A stronger planned-spending outlook shifts AD to \(Y_D=1240-20P\), while improved productivity shifts SRAS to \(Y_S=300+30P\). Find the new equilibrium and explain which direction is known before calculating. Avoid assuming that two rightward shifts imply a higher price level.
Both curves shift right, so output must rise: the AD shift raises it and the SRAS shift raises it. Their effects on the price level oppose one another, so its direction is ambiguous without shift sizes.
For the specified shifts, equate the new curves:
Output is \(Y=1240-20(18.8)=1240-376=864\). SRAS gives \(300+30(18.8)=300+564=864\), confirming equilibrium. Output rises by \(864-800=64\) points, and the price level falls by \(18.8-20=-1.2\) points. Thus the shift sizes in this case make the price-level change negative, even though its direction was not determined by the shift directions alone.
Common Trap and Economic Interpretation
A common error is to assign each shift a separate effect and then report only the effect of one curve. For example, in a rightward AD shift combined with a leftward SRAS shift, it is wrong to conclude that output falls simply because the supply shift is adverse. The demand shift pushes output up, and the net result depends on both shifts and the slopes of the curves.
Another error is to say that a rightward shift of both curves must raise the price level because both curves move right. That conclusion overlooks the different effects on prices: rightward AD tends to raise the price level, while rightward SRAS tends to lower it. In Worked Example 3, output rises but the price level falls.
This distinction is useful when interpreting a short-run shock: the same combination of shifts can produce a clear price-level direction but an uncertain output direction. It also prevents a conclusion about the size or direction of an output gap from being drawn from a curve’s label alone. The analysis is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
Check Your Understanding
For each problem, distinguish the result implied by shift directions from the result implied by the specified magnitudes. Unless stated otherwise, treat output and the price level as the variables in the linear model above.
- AD shifts right by an intercept change of \(60\), while SRAS shifts left by an intercept change of \(-20\). Let \(b=20\) and \(d=30\). Find \(\Delta P\) and \(\Delta Y\). Which result is determinate from directions alone? (Answer: \(\Delta P=+1.6\), \(\Delta Y=+28\); the price-level increase is determinate, while output is ambiguous from directions alone.)
- AD shifts left by \(\Delta A=-50\), and SRAS shifts right by \(\Delta C=25\). Let \(b=20\) and \(d=30\). Find both changes and identify the determinate outcome. (Answer: \(\Delta P=-1.5\), \(\Delta Y=-20\); the price-level decrease is determinate, while output is ambiguous from directions alone.)
- AD shifts right by \(\Delta A=40\), and SRAS shifts right by \(\Delta C=100\). Let \(b=20\) and \(d=30\). Find both changes and explain why the output direction is known before calculating. (Answer: \(\Delta Y=+64\), \(\Delta P=-1.2\); output rises because both rightward shifts raise it, while the price-level direction is ambiguous from directions alone.)
- AD shifts right by \(\Delta A=80\), while SRAS shifts left by \(\Delta C=-120\). Let \(b=15\) and \(d=25\). Calculate both equilibrium changes and identify the outcome whose direction is determinate. (Answer: \(\Delta P=+5\), \(\Delta Y=+5\); the price-level increase is determinate, while output is ambiguous from directions alone.)
- An economy has initial curves \(Y_D=900-10P\) and \(Y_S=100+20P\). AD then shifts to \(Y_D=810-10P\) and SRAS shifts to \(Y_S=70+20P\). Find the initial and new equilibrium, then state which change is ambiguous based on shift directions. (Answer: initial \(P=26.6667\), \(Y=633.3333\); new \(P=24.6667\), \(Y=563.3333\); the price-level direction is ambiguous from directions alone, while output falls because both curves shift left.)