Reading the Direction of the Changes
The AD-AS model can help interpret an observed change in real output and the aggregate price level. The key is to consider both variables together. A fall in output, for example, may follow either a contractionary aggregate-demand shift or an adverse short-run supply shift. The price-level direction distinguishes those explanations under a specific simplifying assumption: only one of the two curves shifts.
The direction rules follow from the standard short-run AD-AS model. Aggregate demand slopes downward: holding other factors fixed, a higher price level is associated with lower quantity of output demanded. Short-run aggregate supply slopes upward: holding other factors fixed, a higher price level is associated with greater quantity of output supplied. A shock changes a curve’s position; a change in the equilibrium is not, by itself, proof of which curve moved.
With those assumptions, the diagnostic patterns are:
| Observed equilibrium change | Consistent single shift | Direction of the shift |
|---|---|---|
| Output rises; price level rises | Aggregate demand | Expansionary AD shift |
| Output falls; price level falls | Aggregate demand | Contractionary AD shift |
| Output rises; price level falls | Short-run aggregate supply | Favorable SRAS shift |
| Output falls; price level rises | Short-run aggregate supply | Adverse SRAS shift |
The table gives conditional predictions, not a way to identify causes from data with certainty. It presumes that the observed changes compare equilibria, that the measures are reliable, and that one curve shifted while the other stayed fixed. If those conditions are not reasonable, the sign pattern alone may not settle the diagnosis.
Why the Sign Patterns Hold
A short derivation makes the logic explicit. Suppose, for this illustration, the curves are linear:
where \(Y\) is real output, \(P\) is the aggregate price level, \(A\) and \(C\) are intercepts, and \(b>0\) and \(d>0\) describe the slopes. These equations represent a downward-sloping AD curve and an upward-sloping SRAS curve. At equilibrium, planned aggregate demand and short-run aggregate supply are equal, so the two expressions for \(P\) must match:
Rearrange to obtain the equilibrium output, then substitute it into either curve to obtain the equilibrium price level:
Now consider an AD shift with SRAS fixed. A rightward shift raises \(A\) by \(\Delta A>0\). The resulting equilibrium changes are:
Thus, output and the price level move in the same direction after an AD shift. For an SRAS shift, hold AD fixed and change \(C\). An adverse shift raises \(C\), so \(\Delta C>0\); a favorable shift lowers \(C\), so \(\Delta C<0\). The changes are:
When supply is adversely affected, output falls and the price level rises. When supply improves, output rises and the price level falls. These results explain the table: AD and SRAS shifts generate different sign patterns because the two curves slope in opposite directions. The equations are an illustrative linear model, not a claim that actual aggregate curves are straight lines.
Worked Applications
Worked Example: Output Falls While the Price Level Rises
A hypothetical economy has a real-output index of 250 before a disturbance and 235 afterward. Its aggregate price-level index rises from 140 to 147. Assume the observations are comparable short-run equilibria, AD slopes downward, SRAS slopes upward, and exactly one of the two curves shifted. Diagnose the shock.
Method. Calculate the change in each measure, then compare the pair of directions with the one-shock sign patterns.
Output changes by \(235-250=-15\), so output falls. The price-level index changes by \(147-140=+7\), so the price level rises. The observed pattern is therefore output down and price level up.
Under the stated one-shock assumption, this is consistent with an adverse SRAS shift. An adverse supply shift raises the price level at a given output and moves the short-run equilibrium toward lower output and a higher price level. A contractionary AD shift would instead reduce both output and the price level.
Check. The calculated changes have opposite signs, as the adverse-supply pattern requires. The conclusion is conditional on the assumption that AD did not also shift.
Common mistake avoided: Calling every fall in output a contractionary demand shock. Output alone does not distinguish the two possibilities; the rising price-level index is essential here.
Worked Example: Calculating the Effect of an Expansionary AD Shift
In a hypothetical short-run model, output \(Y\) is measured in output-index units and \(P\) in price-index units. Initially, AD is \(P=150-0.5Y\) and SRAS is \(P=50+0.5Y\). A demand shock changes AD to \(P=170-0.5Y\), while SRAS is unchanged. Find the initial and new equilibria and use their changes to diagnose the shock.
Method. At each equilibrium, set the AD price expression equal to the SRAS price expression and solve for \(Y\). Then substitute the result into either curve to calculate \(P\).
Initially, set the two original expressions equal:
The initial equilibrium is \(Y=100\), \(P=100\). After the shift, equate the new AD curve to the unchanged SRAS curve:
The new equilibrium is \(Y=120\), \(P=110\). The changes are \(\Delta Y=120-100=+20\) and \(\Delta P=110-100=+10\). Both output and the price level rise, which is consistent with the specified rightward, expansionary AD shift.
Check. At the new equilibrium, AD gives \(170-0.5(120)=110\), and SRAS gives \(50+0.5(120)=110\). The two curves agree.
Common mistake avoided: Calculating only the output change and forgetting to verify the price-level change. The pair of changes, not a single variable, supports the diagnosis.
Worked Example: Calculating the Effect of a Favorable SRAS Shift
A different hypothetical model has AD \(P=160-0.5Y\). Initially, SRAS is \(P=40+0.5Y\). A favorable supply shock shifts SRAS to \(P=20+0.5Y\); AD is unchanged. Find both equilibria and check the sign pattern.
Method. Solve the intersection before and after the SRAS intercept changes, keeping the AD equation fixed.
Initially, set AD equal to the original SRAS:
The initial equilibrium is \(Y=120\), \(P=100\). After the favorable shift, use the new SRAS expression:
The new equilibrium is \(Y=140\), \(P=90\). Hence \(\Delta Y=140-120=+20\) and \(\Delta P=90-100=-10\). Output rises while the price level falls, as expected after a favorable SRAS shift.
Check. At \(Y=140\), AD gives \(160-0.5(140)=90\); the shifted SRAS gives \(20+0.5(140)=90\). The calculated equilibrium satisfies both equations.
Common mistake avoided: Treating a supply improvement as if it shifted AD. In this example, output rises, but the lower price level is the clue that distinguishes this supply pattern from an expansionary AD shift.
When the Diagnosis Is Inconclusive
A sign pattern can be informative without proving a unique cause. First, the table depends on the one-shock restriction: if there is reason to doubt that one curve stayed fixed, a sign pattern cannot by itself establish which curve or curves moved. Second, measured changes may be too small or imprecise to classify reliably. A reported value can be rounded, revised, or measured over a period that does not correspond to a clear before-and-after short-run equilibrium.
Consider output reported as 400 before and 400 afterward, while the price-level index rises from 100 to 102. The exact reported changes are \(\Delta Y=400-400=0\) and \(\Delta P=102-100=+2\). That pair does not match any of the four nonzero, single-shift sign patterns in the table. It is not sound to label it an AD or SRAS shock from these figures alone. Greater measurement precision or additional information about the model and the shocks would be needed.
The diagnostic also relies on the usual curve slopes and a consistent definition of output and the aggregate price level across the two observations. If those assumptions are not supported, applying the table mechanically can give a misleading answer. The correct conclusion may be that the evidence is consistent with a particular shock under stated assumptions, or that it is insufficient to diagnose one.
Common Exam Traps
- Using output alone. Falling output can be consistent with a contractionary AD shift or an adverse SRAS shift. Check the price-level direction before deciding.
- Reversing the supply pattern. An adverse SRAS shift gives output down and the price level up; a favorable shift gives output up and the price level down.
- Confusing a curve shift with movement along a curve. A change in equilibrium output and price is an observed outcome. To name a shock, determine which curve shifted and state the assumptions that support that inference.
- Overstating the conclusion. A sign pattern can be consistent with a one-curve shift without proving that the other curve stayed fixed. Describe the condition, rather than presenting the diagnosis as certain.
Check Your Understanding
For each problem, compare the directions of the changes and apply the stated assumptions. Treat the observations as comparable short-run equilibria unless the question says otherwise.
- A hypothetical economy’s output index moves from 600 to 618, while its price-level index moves from 125 to 129. Under a one-shock assumption, which shift is consistent with the observations? (Answer: Expansionary AD shift.)
- Output falls from 2,000 to 1,940, and the price-level index falls from 98 to 96. Assuming one curve shifted, identify the shock and state both changes’ directions. (Answer: Contractionary AD shift; output and the price level both fall.)
- A regional production index rises from 80 to 84 while its price-level index falls from 110 to 107. If AD is fixed, which type of SRAS shift is consistent with the data? (Answer: Favorable SRAS shift.)
- A hypothetical economy’s output index falls from 310 to 300, while its price-level index rises from 140 to 145. Under the standard slopes and one-shock assumption, diagnose the shock. (Answer: Adverse SRAS shift.)
- Output is reported as 500 both before and after a disturbance, while the price-level index rises from 101 to 103. Can the reported signs be classified as one of the four ordinary nonzero, single-shift patterns? (Answer: No; the reported output change is zero, so the evidence does not match any of the four patterns and is inconclusive on its own.)