Expansionary Demand Shocks In The AD-AS Model

Why a Rightward Demand Shift Matters

A rise in aggregate demand can increase production in the short run, but it can also put upward pressure on the price level. The size of each effect depends on the slopes of aggregate demand and short-run aggregate supply. Tracing the shock from an initial equilibrium makes it possible to distinguish the change in output from the change in the output gap.

The analysis here is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus. It uses the short-run AD-AS framework: aggregate demand shifts to the right, short-run aggregate supply stays fixed, and potential output does not change during the adjustment being analyzed.

Definition: An expansionary aggregate-demand shock is an increase in aggregate demand that shifts the AD curve to the right: at each price level, the quantity of real output demanded is higher than before. The short-run equilibrium is the intersection of AD and SRAS, where planned real output demanded equals real output supplied. The output gap is actual real output minus potential output, \(Y-Y^*\). A positive gap means output is above potential; a negative gap means it is below potential.

Tracing the Shock in the AD-AS Diagram

Put the price level \(P\) on the vertical axis and real output \(Y\) on the horizontal axis. In the standard short-run diagram, AD slopes downward and SRAS slopes upward. An expansionary demand shock shifts AD rightward, while SRAS remains in place. The new short-run equilibrium is where the shifted AD curve meets the unchanged SRAS curve.

Because the new intersection lies farther to the right along an upward-sloping SRAS curve, both equilibrium output and the price level rise. This is a short-run comparison between two equilibria. It does not by itself describe how the economy adjusts over a longer period or what caused the demand increase.

To calculate the changes, use the linear inverse-curve forms \(P=A-bY\) for AD and \(P=C+dY\) for SRAS, where \(A,C\) are intercepts and \(b,d>0\) are slopes in absolute value. The shock raises the AD intercept from \(A\) to \(A+\Delta A\), with \(\Delta A>0\), and leaves all SRAS parameters fixed. These equations describe a particular linear model; the formulas derived from them do not automatically apply to nonlinear curves or to a shock that also shifts SRAS.

Model assumptions: The AD and SRAS curves are linear over the range considered; \(b>0\) and \(d>0\); the demand shock increases the AD intercept by \(\Delta A>0\); SRAS and potential output \(Y^*\) are fixed between the two equilibria. The calculated effects are short-run effects under these assumptions.

Why Output and the Price Level Both Rise

At equilibrium, the price level given by AD must equal the price level given by SRAS. Equating the two expressions gives the equilibrium output directly. Substituting that output into either curve gives the equilibrium price level.

$$ A-bY=C+dY $$

Y_0=\frac{A-C}{b+d}

After the shock, the AD intercept is \(A+\Delta A\). Applying the same equilibrium condition gives the new output. Subtracting the initial equilibrium output from the new output shows exactly how much output changes.

Y_1=\frac{A+\Delta A-C}{b+d}

\Delta Y=Y_1-Y_0 =\frac{A+\Delta A-C}{b+d}-\frac{A-C}{b+d} =\frac{\Delta A}{b+d}>0

The price level change follows from SRAS, which has not shifted. The initial price is \(P_0=C+dY_0\); the new price is \(P_1=C+dY_1\). Subtracting these equations gives the price change.

\Delta P=P_1-P_0=d(Y_1-Y_0) =\frac{d\Delta A}{b+d}>0

The derivation explains the two effects rather than merely predicting their signs. The rightward shift raises equilibrium output by \(\Delta A/(b+d)\). As output moves up the unchanged, upward-sloping SRAS curve, the equilibrium price level also rises. With potential output fixed, the change in the output gap, measured in output units, equals the change in output: \(\Delta(Y-Y^*)=\Delta Y\). A demand expansion therefore makes the gap larger, although whether the new gap is positive or negative depends on the initial gap and the size of the shock.

Worked Example: A Demand Shock That Moves the Economy Above Potential

Suppose output is measured in billions of dollars and the price level in index points. Initially, AD is \(P=150-0.5Y\), SRAS is \(P=30+0.5Y\), and potential output is \(Y^*=125\). The AD intercept then rises by 18, while SRAS and potential output remain fixed. Find both equilibria and output gaps, and check the post-shock equilibrium.

Method. At each equilibrium, set the AD price-level expression equal to the SRAS expression, solve for \(Y\), and then substitute into a curve to find \(P\).

Initial equilibrium. Equate the initial curves: \(150-0.5Y=30+0.5Y\). Subtract 30 from both sides and add \(0.5Y\) to both sides, giving \(120=Y\). Thus \(Y_0=120\). Substitution into SRAS gives \(P_0=30+0.5(120)=30+60=90\). The initial output gap is \(120-125=-5\), or 5 billion dollars below potential.

Post-shock AD curve. Raising the intercept by 18 gives \(P=168-0.5Y\). Equate this curve to unchanged SRAS: \(168-0.5Y=30+0.5Y\). Therefore \(138=Y\), so \(Y_1=138\). Substitution into SRAS gives \(P_1=30+0.5(138)=30+69=99\). The post-shock output gap is \(138-125=13\), or 13 billion dollars above potential.

Check. At \(Y=138\), shifted AD gives \(168-0.5(138)=168-69=99\), and SRAS gives \(30+0.5(138)=99\). Both curves agree. Output rose by \(138-120=18\), and the price level rose by \(99-90=9\).

Common mistake avoided. A proposed post-shock output of 129 does not satisfy equilibrium: shifted AD gives \(168-0.5(129)=103.5\), while SRAS gives \(30+0.5(129)=94.5\). Since the two prices differ, \(Y=129\) is not their intersection.

Worked Comparisons with Different Slopes

The same calculation works for different slopes and starting gaps. A steeper SRAS means a larger price-level response relative to the output response. For each scenario, solve the intersection after the shock rather than assuming that the initial equilibrium quantity or price remains valid.

Worked Example: A Modest Shock with Output Initially Above Potential

A hypothetical economy measures real output in billions of dollars and the price level in index points. Its initial curves are \(P=200-0.4Y\) and \(P=20+0.2Y\), and potential output is 280. A demand shock raises the AD intercept by 12. Calculate the initial and post-shock equilibria, the output gaps, and the changes in output and price.

Method. Solve the two intersections separately; use the fixed potential output to compute each gap.

Initial equilibrium. Set \(200-0.4Y=20+0.2Y\). Then \(180=0.6Y\), so \(Y_0=300\). The price level is \(P_0=20+0.2(300)=20+60=80\). The initial gap is \(300-280=20\).

Post-shock equilibrium. The shifted AD curve is \(P=212-0.4Y\). Set it equal to SRAS: \(212-0.4Y=20+0.2Y\), so \(192=0.6Y\), and \(Y_1=320\). The price level is \(P_1=20+0.2(320)=20+64=84\). The new gap is \(320-280=40\).

Check and interpretation. Shifted AD at \(Y=320\) gives \(212-128=84\), which matches SRAS. Output increased by \(320-300=20\), the price level increased by \(84-80=4\), and the gap widened by \(40-20=20\). The shock raises both output and the price level, but this economy's relatively flatter SRAS produces a smaller price-level increase than in a model with a steeper SRAS and otherwise comparable conditions.

Common mistake avoided. The increase in the AD intercept is 12, not the increase in equilibrium output. The equilibrium output change must be found by solving the two-curve system; here it is 20.

Worked Example: A Shock That Changes the Sign of the Output Gap

In another hypothetical economy, output is in billions of dollars and the price level is an index. Initially, \(P=126-0.3Y\) and \(P=6+0.2Y\). Potential output is 250. An expansionary demand shock raises the AD intercept by 10. Find the initial and new equilibrium, and determine whether output is above or below potential after the shock.

Method. Find each AD-SRAS intersection, then compare each equilibrium output with the same potential-output benchmark.

Initial equilibrium. Equating the curves gives \(126-0.3Y=6+0.2Y\). Thus \(120=0.5Y\), so \(Y_0=240\). Substitution into SRAS gives \(P_0=6+0.2(240)=6+48=54\). The initial output gap is \(240-250=-10\).

Post-shock equilibrium. The shifted AD curve is \(P=136-0.3Y\). Equating it to SRAS gives \(136-0.3Y=6+0.2Y\), so \(130=0.5Y\), and \(Y_1=260\). The new price level is \(P_1=6+0.2(260)=6+52=58\). The new output gap is \(260-250=10\), so output is now above potential.

Check and interpretation. At \(Y=260\), shifted AD gives \(136-0.3(260)=136-78=58\), matching SRAS. Output rose by 20, while the price level rose by 4. The gap changed from \(-10\) to \(+10\), a change of 20, equal to the output change because potential output was held fixed.

Common mistake avoided. A demand expansion does not imply that the output gap remains negative simply because it was initially negative. Calculate the new output and compare it with potential; here the shock moves the equilibrium across potential output.

Interpreting the Results Carefully

For this linear model with upward-sloping SRAS, the formulas summarize the short-run response:

Theorem: If AD is \(P=A-bY\), SRAS is \(P=C+dY\), \(b,d>0\), and the AD intercept rises by \(\Delta A>0\) with SRAS fixed, then equilibrium output rises by \(\Delta A/(b+d)\) and the price level rises by \(d\Delta A/(b+d)\). If potential output is fixed, the output gap rises by the same amount as output.

The result depends on the stated conditions. A horizontal SRAS curve (\(d=0\)) would imply no price-level increase in this linear model, while the usual upward-sloping case \(d>0\) gives a positive price-level change. If SRAS shifts at the same time, the changes cannot be attributed to a demand shock alone; both shifts must be included when solving for equilibrium. If the curves are nonlinear, the direction of change may still be assessed from the diagram, but these particular linear formulas need not give the magnitude.

The output gap is a comparison with potential output, not a second name for output itself. If actual output rises by 20 while potential output is unchanged, the gap rises by 20 whether the starting gap was negative, zero, or positive. A positive gap after the shock is not evidence that potential output itself increased.

Common Errors and a Reliable Check

Changing the wrong curve. A pure demand shock shifts AD; in the model here, it does not change the SRAS equation.
Reading the intercept change as the output change. The AD intercept increase \(\Delta A\) is divided by \(b+d\) to obtain the equilibrium output change.
Using only one curve to declare an equilibrium. A candidate equilibrium must give the same price level from both AD and SRAS at the same output.
Holding the output gap fixed. If \(Y^*\) stays fixed, a change in \(Y\) changes \(Y-Y^*\) by that same amount.
Reporting only the direction of change. When the equations are supplied, compute both equilibria and show the output-gap comparison rather than stopping at “output and prices rise.”

A dependable solution sequence is to write the shifted AD equation, equate it with unchanged SRAS, solve for the new output, substitute into both curves to check the price level, and compare initial and new output with \(Y^*\). This sequence catches sign errors and prevents a plausible-looking number from being mistaken for an equilibrium.

Check Your Understanding

For each problem, calculate the requested equilibrium values and output gaps. Assume the stated curves remain linear over the relevant range, and that potential output and SRAS do not change during the demand shock.

Output is in billions of dollars and \(P\) is an index. Initially AD is \(P=100-0.2Y\), SRAS is \(P=20+0.2Y\), and \(Y^*=190\). The AD intercept rises by 8. Find the initial and new output, price level, and gap. (Answer: Initially \(Y=200,\ P=60\), gap \(+10\); afterward \(Y=220,\ P=64\), gap \(+30\).)
Initially AD is \(P=180-0.5Y\), SRAS is \(P=30+0.25Y\), and \(Y^*=220\). The AD intercept rises by 15. Determine the new equilibrium and gap, and state whether the shock moves output to potential. (Answer: New equilibrium \(Y=220,\ P=85\), gap \(0\); output moves to potential.)
For a hypothetical economy, AD is initially \(P=250-0.4Y\), SRAS is \(P=10+0.1Y\), and potential output is 500. The AD intercept rises by 20. Find both equilibria and gaps, and check the new equilibrium using both curves. (Answer: Initially \(Y=480,\ P=58\), gap \(-20\); afterward \(Y=520,\ P=62\), gap \(+20\); both post-shock curves give \(P=62\).)
Suppose AD is \(P=170-0.25Y\), SRAS is \(P=10+0.25Y\), and potential output is 300. What increase in the AD intercept is needed to raise equilibrium output from its initial level to 360? Find the resulting price level and output gap. (Answer: Initial \(Y=320,\ P=90\); the intercept must rise by 20; at \(Y=360\), \(P=100\) and the gap is \(+60\).)
An economy has AD \(P=220-0.3Y\), SRAS \(P=40+0.2Y\), and \(Y^*=360\). What increase in the AD intercept would make the new equilibrium output gap \(+30\)? Find the resulting price level and verify the required shift. (Answer: Target output \(Y=390\), target \(P=118\); the AD intercept must rise by 15, to 235, and \(235-0.3(390)=118\).)

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