Integrated AD-AS Scenarios With Shocks And Policy

Why Integrated AD-AS Scenarios Need a Sequence

A demand shock, a supply shock, and a policy response can all affect output and the price level at once. The challenge is to keep track of which shift occurs, how it changes the short-run equilibrium, and whether the shock or policy remains in place over time. A correct analysis therefore treats the scenario as a sequence, not as one isolated movement on a diagram.

This tutorial uses a linear aggregate demand–aggregate supply model to make that sequence explicit. The numbers are illustrative model values, not measurements of an actual economy. The approach is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.

Definition: Let \(y\) be the output gap, measured in percentage points of potential output: \(y=0\) means output equals potential, \(y<0\) is a recessionary gap, and \(y>0\) is an expansionary gap. Let \(p\) be the price-level deviation from a reference price index, in index points. A negative \(p\) means the price level is below the reference level; it does not mean the price level itself is negative. In this model, \(A\) is the aggregate-demand intercept, \(E\) is the expected-price or wage-setting intercept, and \(S\) is a supply-shock intercept. Positive \(A\) raises demand; positive \(S\) is an adverse supply shock that raises prices at a given output level.

The Linear Model and Its Equilibrium

Assume aggregate demand (AD) slopes downward in the output-gap–price-level plane, and short-run aggregate supply (SRAS) slopes upward. For the scenarios below, use the following equations:

y=A-\beta p,\qquad p=E+\gamma y+S,

Here \(\beta>0\) and \(\gamma>0\). The first equation says that, holding the demand intercept fixed, a higher price level reduces output demanded. The second says that, holding the supply intercept fixed, higher output is associated with a higher price level in the short run. A positive demand shift raises \(A\); an adverse supply shift raises \(S\); a change in expected prices or wage setting changes \(E\).

The model is a short-run model with given \(E\) and \(S\). It assumes that the shocks affect the intercepts, not potential output, and that there are no other shifts during the calculation. For long-run comparisons, assume output returns to potential and the expected-price or wage-setting intercept adjusts. The model is not a forecast: its linear relationships are a simplified way to organize the effects of stated shocks.

Substituting the AD equation into SRAS gives the short-run equilibrium. This derivation matters because it shows how both curves jointly determine the result.

p=E+\gamma(A-\beta p)+S

(1+\beta\gamma)p=E+\gamma A+S

p=\frac{E+\gamma A+S}{1+\beta\gamma}, \qquad y=\frac{A-\beta(E+S)}{1+\beta\gamma}.

The expression for \(y\) follows by substituting the equilibrium \(p\) into AD and collecting terms. The positive denominator \(1+\beta\gamma\) means that the effect of a shift is shared across changes in output and the price level rather than appearing in only one variable.

For all worked examples, use \(\beta=0.5\) and \(\gamma=2\). The equations become:

y=A-0.5p,\qquad p=E+2y+S, \qquad p=A+\frac{E+S}{2},\qquad y=\frac{A-0.5(E+S)}{2}.

Treat \(y\) and \(p\) as numerical values in their stated units. For example, \(y=-2\) is a two-percentage-point recessionary gap. A change in \(A\) or \(S\) is an intercept shift in this model, not a percentage change in actual GDP or in the actual price index.

Worked Example: A Recessionary Gap, a Further Demand Shock, and Partial Stabilization

An economy initially has \(A=-4\), \(E=0\), and \(S=0\). A further contractionary demand shock reduces \(A\) by 2. A policy-induced demand shift then raises \(A\) by 4. Find the initial short-run equilibrium, the equilibrium after the shock, and the equilibrium after policy. If the final demand intercept persists in the long run, also find long-run output and the price-level deviation.

Method. Calculate each equilibrium from the intercepts in force at that stage. The demand shock changes \(A\) from \(-4\) to \(-6\); the policy shift then changes it from \(-6\) to \(-2\). Neither \(E\) nor \(S\) changes.

Initial equilibrium. With \(A=-4\), \(E=0\), and \(S=0\):

p=-4+\frac{0+0}{2}=-4,\qquad y=\frac{-4-0.5(0+0)}{2}=-2.

The initial economy has a 2-percentage-point recessionary gap and a price level 4 index points below the reference.

After the demand shock. The new intercept is \(A=-4-2=-6\):

p=-6+\frac{0+0}{2}=-6,\qquad y=\frac{-6-0.5(0+0)}{2}=-3.

The shock deepens the recessionary gap from \(-2\) to \(-3\) and lowers the price-level deviation from \(-4\) to \(-6\).

After the policy shift. The new demand intercept is \(A=-6+4=-2\):

p=-2+\frac{0+0}{2}=-2,\qquad y=\frac{-2-0.5(0+0)}{2}=-1.

Policy reduces the short-run gap from \(-3\) to \(-1\), but does not close it. A useful check is to put \(y=-1\) into AD: \(y=-2-0.5(-2)=-1\), as required.

Long-run comparison. Assume the final \(A=-2\) persists, potential output is unchanged, and \(E\) adjusts so output returns to zero. AD at \(y=0\) requires \(0=-2-0.5p\), so \(p=-4\). SRAS can then be consistent with \(y=0\) and \(p=-4\) when \(E=-4\). Thus the long-run output gap is zero and the price-level deviation is \(-4\).

Common mistake avoided: Adding the policy shift to the original \(A=-4\) while ignoring the intervening shock would give \(A=0\). The correct sequence is \(-4-2+4=-2\).

Combining an Adverse Supply Shock with Demand Policy

An adverse supply shock creates a different policy problem from a demand contraction. In this model, a positive \(S\) raises the price level at a given output, and it lowers short-run output when the demand intercept is fixed. A demand expansion can support output, but it also adds upward pressure to the price level. The calculation reveals the trade-off rather than assuming that policy can remove both effects.

Worked Example: Supporting Output After a Temporary Cost Shock

Start from \(A=0\), \(E=0\), and \(S=0\). A temporary adverse supply shock raises \(S\) to 4. A policy-induced demand shift raises \(A\) to 2 while the supply shock is still present. Find the short-run equilibria before and after the policy. Then find the long-run price-level deviation if the supply shock expires but the policy-induced demand shift persists.

Method. First hold the supply shock fixed and compare the two short-run equilibria. For the long run, remove the temporary \(S=4\), retain \(A=2\), and impose \(y=0\).

With the supply shock, before policy: \(A=0\), \(E=0\), and \(S=4\).

p=0+\frac{0+4}{2}=2,\qquad y=\frac{0-0.5(0+4)}{2}=-1.

The shock produces a one-percentage-point recessionary gap and a price-level deviation of 2 index points. This combination of lower output and a higher price level relative to the no-shock reference is the short-run effect of this adverse supply shift.

With the shock and policy: \(A=2\), \(E=0\), and \(S=4\).

p=2+\frac{0+4}{2}=4,\qquad y=\frac{2-0.5(0+4)}{2}=0.

The policy shift closes the short-run output gap. It does so with a price-level deviation of 4, two index points above the pre-policy short-run result.

Long run after the temporary shock expires. Now \(S=0\), while the persistent policy shift leaves \(A=2\). At potential output, AD implies \(0=2-0.5p\), hence \(p=4\). The long-run price-level deviation is therefore 4. In this particular example, that equals the short-run result with the supply shock and policy, but the equality is specific to the chosen intercepts; it is not a general rule.

A check on the pre-policy result is \(p=2y+S=2(-1)+4=2\). This returns the same price level as the equilibrium calculation.

Common mistake avoided: Treating policy as if it directly shifts SRAS would miss the mechanism. In the stated model, policy changes \(A\), so it shifts AD; the short-run price-level result follows from the intersection of AD and SRAS.

Mixed Shocks and Long-Run Adjustment

When demand and supply shocks occur together, calculate their net effect through the equilibrium equations rather than trying to infer the answer from one shock at a time. Long-run analysis requires another distinction: a temporary supply shock can disappear, while a persistent demand shift can remain. Under the assumptions used here, long-run output returns to potential; the price level is pinned down by the demand curve at that output.

Long-run result: If potential output is unchanged and long-run output is \(y=0\), then AD implies \(p=A/\beta\). The expected-price or wage-setting intercept adjusts to make SRAS consistent with this equilibrium. This result does not mean that the short-run price level equals \(A/\beta\); it applies after the long-run adjustment and depends on the demand intercept that remains in force.

Worked Example: A Demand Expansion, an Adverse Supply Shift, and a Policy Reversal

Suppose a persistent demand expansion raises \(A\) to 3, while an adverse supply shock raises \(S\) to 2. Initially, \(E=0\). A policy-induced contractionary demand shift then lowers \(A\) by 2, leaving the supply shock in place in the short run. Calculate the short-run equilibrium before and after policy. Then find the long-run price-level deviation if the supply shock is temporary and the final demand intercept persists.

Method. Combine the intercepts at each stage, then use the short-run equations. For the long run, remove the temporary supply shift and set output to potential.

Before policy: \(A=3\), \(E=0\), \(S=2\).

p=3+\frac{0+2}{2}=4,\qquad y=\frac{3-0.5(0+2)}{2}=1.

The short-run output gap is \(+1\), and the price level is 4 index points above the reference.

After policy: \(A=3-2=1\), with \(E=0\) and \(S=2\).

p=1+\frac{0+2}{2}=2,\qquad y=\frac{1-0.5(0+2)}{2}=0.

The contractionary policy shift removes the short-run positive output gap. The equilibrium price-level deviation falls from 4 to 2.

Long run. The supply shock expires, so \(S=0\), but the final demand intercept \(A=1\) persists. With \(y=0\), AD gives \(0=1-0.5p\), so \(p=2\). The long-run output gap is zero and the price-level deviation is 2. If instead the demand shift also expired, this long-run price-level conclusion would change; it depends on the stated persistence assumption.

Check the short-run post-policy result using both curves: AD gives \(1-0.5(2)=0\), and SRAS gives \(0+2(0)+2=2\). Both equations hold.

Common mistake avoided: Reversing the policy shift’s sign would raise \(A\) from 3 to 5, not lower it to 1. A contractionary demand shift reduces the AD intercept.

A Reliable Process for Multi-Step Scenarios

A disciplined sequence reduces sign errors and prevents a short-run result from being mistaken for a long-run one. Record the intercepts in force at each stage before substituting into the equations.

Set the reference and units.
Identify the reference price level, the potential-output benchmark, and the units of the output gap and price deviation.

Translate each shock into an intercept change.
A demand increase raises \(A\); a demand contraction lowers \(A\); an adverse supply shock raises \(S\); a change in expected prices or wage setting changes \(E\).

Calculate one equilibrium at a time.
Use the intercepts currently in force. Do not carry a shock into a later stage if the scenario says it has expired.

Check both equations.
Substitute the calculated \(p\) into AD and the calculated \(y\) into SRAS. Each equation must reproduce the other calculated value.

Apply the long-run assumption separately.
If output returns to potential, set \(y=0\) and use AD to find the long-run \(p\). State which demand and supply shifts persist.

Common Errors and What the Model Does Not Say

Mixing up a price-level change and inflation. \(p\) is a deviation in the price level from a reference. A change in \(p\) between periods describes a price-level movement in this simplified setting; the level itself is not an inflation rate.
Combining shocks without tracking their signs. Keep a running value of \(A\), \(E\), and \(S\). A contractionary policy response subtracts from \(A\), even if it follows an earlier expansionary shock.
Using the long-run condition too early. Set \(y=0\) only when the problem asks for the long-run outcome under the model’s adjustment assumption. Short-run output can differ from potential.
Assuming policy eliminates every consequence of a supply shock. A demand shift can offset the output effect under some parameter values, but it also changes the price-level outcome. The two objectives need not be simultaneously achieved.
Ignoring persistence. Long-run conclusions depend on whether \(A\) remains shifted and whether \(S\) expires. If the scenario does not specify persistence, state the assumption instead of silently choosing one.

The model’s value is that it forces each assumption into view. Its linear equations allow exact calculations for the stated scenario, but actual economies may have nonlinear relationships, changing potential output, and additional shocks. The results should be read as conditional conclusions: given these equations and these shifts, this is the implied equilibrium.

Check Your Understanding

For these questions, use \(\beta=0.5\), \(\gamma=2\), \(p=A+(E+S)/2\), and \(y=(A-0.5(E+S))/2\), unless the question asks for a long-run result.

An economy has \(A=2\), \(E=0\), and \(S=0\). Find the short-run equilibrium output gap and price-level deviation. (Answer: \(y=1\), \(p=2\).)
With \(A=-3\), \(E=0\), and an adverse supply shock \(S=2\), calculate the short-run equilibrium. (Answer: \(y=-2\), \(p=-2\).)
Suppose \(A=1\), \(E=2\), and \(S=0\). Find the short-run equilibrium and identify whether there is an output gap. (Answer: \(y=0\), \(p=2\); output is at potential.)
Start with \(A=0\), \(E=0\), and \(S=6\). A policy-induced demand shift raises \(A\) to 3 while the supply shock remains. Find the pre-policy and post-policy short-run equilibria. (Answer: Before policy, \(y=-1.5\), \(p=3\); after policy, \(y=0\), \(p=6\).)
Let \(A=-2\), \(E=-1\), and \(S=3\) in the short run. Calculate \(y\) and \(p\). Then suppose the supply shock expires, \(A\) persists, output returns to potential, and \(E\) adjusts. Find the long-run price-level deviation. (Answer: Short run \(y=-1.5\), \(p=-1\); long run \(y=0\), \(p=-4\).)

What You'll Learn