# Equilibrium in the AD-AS Model

> AP Macroeconomics · National Income and Price Determination
> Source: https://www.owlsprep.com/study/ap-macroeconomics-u3-equilibrium-in-the-ad-as/

This guide covers short-run and long-run equilibrium in the aggregate demand-aggregate supply model, output gap analysis, calculation, and automatic self-correction, core concepts tested heavily on AP Macroeconomics.

**Prerequisites:** [Aggregate demand (AD) curves and shifters](https://www.owlsprep.com/study/ap-macroeconomics-u3-aggregate-demand/); [Short-run and long-run aggregate supply curves](https://www.owlsprep.com/study/ap-macroeconomics-u3-aggregate-supply/); [Natural rate of unemployment](https://www.owlsprep.com/study/ap-macroeconomics-u2-unemployment-inflation/)

## Learning objectives

- Define macroeconomic equilibrium and distinguish short-run vs long-run equilibrium
- Calculate equilibrium output and price level from linear AD and SRAS equations
- Identify, classify, and calculate recessionary and inflationary output gaps
- Explain the automatic self-correction mechanism of the AD-AS model
- Avoid common exam mistakes in AD-AS equilibrium analysis

## Core Definition of AD-AS Equilibrium

Equilibrium in the AD-AS model occurs at the intersection of the aggregate demand (AD) curve and the relevant aggregate supply curve. This intersection gives the economy’s equilibrium price level (PL) and equilibrium real output (real GDP, Y).

Equilibrium means the total quantity of goods and services demanded in the economy equals the total quantity supplied, so there is no unintended inventory accumulation or depletion, and no inherent upward or downward pressure on the overall price level. When the economy is out of equilibrium, market forces automatically push it back to equilibrium: if output is above equilibrium, unsold goods pile up, leading firms to cut production and prices; if output is below equilibrium, excess demand leads firms to increase production and raise prices.

According to the AP Macroeconomics CED, this topic accounts for 10-15% of Unit 3’s weighting, and it is tested on both multiple-choice (MCQ) and free-response (FRQ) sections of the exam. Mastery of equilibrium conditions is required for nearly all AD-AS related questions.

**Macroeconomic Equilibrium** — A state of the AD-AS model where aggregate quantity demanded equals aggregate quantity supplied, with no inherent pressure to change output or the overall price level.

## Short-Run Macroeconomic Equilibrium

Short-run equilibrium occurs at the intersection of the AD curve and the upward-sloping short-run aggregate supply (SRAS) curve. In the short run, nominal wages and input prices are sticky (slow to adjust to changing economic conditions), so firms respond to higher price levels by increasing output, resulting in the upward slope of SRAS.

$$AD(Y) = SRAS(Y)$$

Where $AD(Y)$ is the price level at which aggregate demand equals output $Y$, and $SRAS(Y)$ is the price level at which short-run aggregate supply equals output $Y$. Solving this condition gives two equilibrium values: $PL^*$ (equilibrium price level) and $Y^*$ (equilibrium short-run real GDP). Importantly, short-run equilibrium output does not need to equal full-employment output ($Y_F$, the output at which LRAS is vertical); it can fall above, below, or exactly at $Y_F$.

**Worked example:** Suppose an economy has aggregate demand given by $PL = 150 - 0.5Y$, and short-run aggregate supply given by $PL = 30 + 0.25Y$, where $PL$ is the price level and $Y$ is real GDP in billions of dollars. Calculate the equilibrium short-run output and price level.

1. Apply the short-run equilibrium condition: set AD equal to SRAS

   $$150 - 0.5Y = 30 + 0.25Y$$
2. Rearrange terms to isolate $Y$

   $$150 - 30 = 0.25Y + 0.5Y \implies 120 = 0.75Y$$
3. Solve for $Y$

   $$Y = 120 / 0.75 = 160$$
4. Plug $Y$ back into the SRAS equation to find $PL$

   $$PL = 30 + 0.25(160) = 30 + 40 = 70$$
5. Verify consistency with the AD equation

   $$150 - 0.5(160) = 150 - 80 = 70, which matches$$

> **Exam tip:** On FRQs, always explicitly label both equilibrium output $Y^*$ and equilibrium price level $PL^*$ on your graph. AP exam rubrics almost always award 1 full point for correctly labeling both values, and missing one label will cost you a free point.

*Calculator:* allowed

## Long-Run Equilibrium and Output Gaps

Long-run equilibrium occurs when short-run equilibrium output equals full-employment (potential) output $Y_F$, meaning AD, SRAS, and LRAS all intersect at the same point. LRAS is vertical at $Y_F$ because in the long run, all nominal wages and input prices are fully flexible, so changes in the price level do not change the economy’s maximum sustainable output.

$$AD(Y_F) = SRAS(Y_F) = PL^*$$

At long-run equilibrium, the economy is at full employment: the unemployment rate equals the natural rate of unemployment, there are no output gaps, and the economy is operating at its potential output. If short-run equilibrium is not at $Y_F$, the economy has an output gap.

**Output Gap** — The difference between short-run equilibrium output $Y^*$ and full-employment output $Y_F$, divided into two types: recessionary (contractionary) when $Y^* < Y_F$, and inflationary (expansionary) when $Y^* > Y_F$.

**Worked example:** Suppose the economy from the previous worked example has a full-employment output $Y_F = 200$ billion. Is the economy in long-run equilibrium? If not, what type of output gap exists, and what is the size of the gap?

1. Recall we found short-run equilibrium output $Y^* = 160$ billion
2. Compare $Y^*$ to $Y_F$: $160 < 200$, so $Y^* \neq Y_F$, meaning the economy is not in long-run equilibrium
3. By definition, when short-run equilibrium output is less than full-employment output, the gap is a recessionary output gap
4. Calculate the gap size

   $$\text{Gap} = Y_F - Y^* = 200 - 160 = 40$$

> **Exam tip:** Always remember that LRAS is vertical at $Y_F$, so long-run equilibrium requires all three curves to intersect at the same output level. A common exam mistake is only checking for intersection of AD and LRAS, but SRAS must also intersect at that point for the economy to be in long-run equilibrium.

## Automatic Long-Run Adjustment

In the absence of government or central bank intervention, the economy automatically adjusts back to long-run equilibrium through shifts in SRAS driven by changes in nominal wages and input prices:

- **Recessionary gap**: High unemployment leads workers to accept lower nominal wages, and input prices fall. Lower production costs shift SRAS right, lowering the price level and increasing output until $Y^* = Y_F$.
- **Inflationary gap**: Low unemployment leads workers to demand higher nominal wages, and input prices rise. Higher production costs shift SRAS left, raising the price level and decreasing output until $Y^* = Y_F$.

**Worked example:** Suppose an economy initially in long-run equilibrium experiences a positive AD shock (e.g., a surge in consumer confidence that increases consumption spending) that shifts AD right. Describe the automatic adjustment back to long-run equilibrium step-by-step.

1. Initial long-run equilibrium: $AD_1$ intersects $SRAS_1$ and $LRAS$ at $Y_F$, with initial price level $PL_1$
2. The positive AD shock shifts AD right to $AD_2$. The new short-run equilibrium is at the intersection of $AD_2$ and $SRAS_1$, with new output $Y_2 > Y_F$ and new price level $PL_2 > PL_1$, creating an inflationary gap of $Y_2 - Y_F$
3. Because unemployment is below the natural rate, workers negotiate higher nominal wages in new long-term contracts, and other input prices rise to reflect the higher price level
4. Higher production costs for firms shift SRAS left from $SRAS_1$ to $SRAS_2$
5. The new long-run equilibrium forms at the intersection of $AD_2$, $SRAS_2$, and $LRAS$. Output returns to $Y_F$, and the price level rises to $PL_3 > PL_2$, eliminating the inflationary gap

**Check your understanding**

Test your understanding with this AP-style multiple choice question:

1. An economy has AD given by $PL = 200 - Y$, SRAS given by $PL = 50 + 0.5Y$, and LRAS at $Y_F = 120$. Which of the following correctly describes the economy's current equilibrium?

   - A) Short-run equilibrium at Y = 100, PL = 100, with a \$20 billion recessionary gap
   - B) Short-run equilibrium at Y = 120, PL = 80, with no output gap
   - C) Short-run equilibrium at Y = 100, PL = 100, with a \$20 billion inflationary gap
   - D) Short-run equilibrium at Y = 140, PL = 60, with a \$20 billion inflationary gap

   *Answer:* A) Short-run equilibrium at Y = 100, PL = 100, with a \$20 billion recessionary gap

   *Why:* Correct. Setting AD equal to SRAS gives $200 - Y = 50 + 0.5Y$, so $150 = 1.5Y$ and $Y = 100$. $PL = 200 - 100 = 100$. Since $100 < 120$, the gap is a \$20 billion recessionary gap.

> **Exam tip:** When the question asks for automatic (self-correcting) adjustment without policy intervention, always shift SRAS, not AD or LRAS. Automatic adjustment works through input price changes that shift SRAS, not through changes in potential output or aggregate demand.

## Common pitfalls

- **Wrong:** Calling a gap where $Y^* > Y_F$ a recessionary gap, and $Y^* < Y_F$ an inflationary gap
  - Why it fails: Students mix up gap names with direction, confusing the label with the policy action needed to close the gap
  - Correct: Memorize the rule: the name describes the state of the economy relative to full employment. If output is lower than full employment, the economy is in a recession, so it is a recessionary gap
- **Wrong:** Shifting AD instead of SRAS during automatic long-run adjustment
  - Why it fails: Students confuse automatic self-correction with fiscal/monetary policy, which shifts AD
  - Correct: If the question explicitly says "no policy intervention" or "automatic adjustment," always shift SRAS to close the gap. Only shift AD if the question asks for government or central bank policy
- **Wrong:** Claiming long-run equilibrium occurs at the intersection of only AD and LRAS, with no requirement that SRAS intersects at that point
  - Why it fails: Students forget SRAS is always relevant even in the long run, and short-run equilibrium is required for the economy to be at rest
  - Correct: Always confirm all three curves intersect at $Y_F$ when identifying long-run equilibrium, and draw SRAS through the intersection point on FRQ graphs
- **Wrong:** Shifting LRAS during automatic adjustment to a demand-side output gap
  - Why it fails: Students confuse changes in potential output (which shifts LRAS) with the self-correction mechanism, which does not change potential output
  - Correct: LRAS only shifts when there is a change in productivity, labor force, capital stock, or a permanent supply shock. It never shifts during automatic adjustment to a demand shock
- **Wrong:** Failing to verify equilibrium calculations by plugging $Y^*$ into both AD and SRAS
  - Why it fails: Students rush through algebra and make simple arithmetic errors that are easy to catch
  - Correct: Always plug your solved $Y^*$ into both equations to confirm you get the same $PL^*$; this catches 90% of common calculation mistakes

## Cheatsheet

| Category | Formula / Rule | Notes |
| --- | --- | --- |
| Short-run equilibrium condition | $AD(Y) = SRAS(Y)$ | Gives equilibrium $Y^*$ and $PL^*$; $Y^*$ can be above, below, or equal to $Y_F$ |
| Recessionary gap | $\text{Gap} = Y_F - Y^*$, $Y^* < Y_F$ | Unemployment above natural rate; downward pressure on wages and input prices |
| Inflationary gap | $\text{Gap} = Y^* - Y_F$, $Y^* > Y_F$ | Unemployment below natural rate; upward pressure on wages and input prices |
| Long-run equilibrium condition | $Y^* = Y_F$, $AD(Y_F) = SRAS(Y_F) = PL^*$ | All three curves (AD, SRAS, LRAS) intersect at the same point |
| Automatic adjustment: recessionary gap | Shift SRAS right | Lower input prices shift SRAS; closes gap without changing $Y_F$ |
| Automatic adjustment: inflationary gap | Shift SRAS left | Higher input prices shift SRAS; closes gap without changing $Y_F$ |
| Long-run equilibrium output | $Y = Y_F$ | Potential output; no output gap; unemployment equals natural rate |
| Out-of-equilibrium adjustment | Excess supply → cut output/prices; excess demand → raise output/prices | Driven by unintended inventory changes that push the economy back to equilibrium |

## What's next

Equilibrium in the AD-AS model is the foundational framework for analyzing all macroeconomic shocks and policy effects in AP Macroeconomics, and it is a required prerequisite for all subsequent topics in the unit. Mastery of equilibrium conditions and output gap analysis is essential for nearly all free-response questions on the exam, and it will allow you to correctly analyze how government and central bank policymakers respond to recessions and inflationary booms. This topic alone makes up a significant portion of Unit 3, and concepts from here are tested across multiple units of the AP exam. Next, you will apply this framework to analyze how fiscal and monetary policy shift aggregate demand to close output gaps.

- [Fiscal Policy in the AD-AS Model](https://www.owlsprep.com/study/ap-macroeconomics-u3-fiscal-policy/)
- [Short-Run Changes to the AD-AS Model](https://www.owlsprep.com/study/ap-macroeconomics-u3-short-run-changes-to-the/)
- [Long-Run Adjustment to Macroeconomic Shocks](https://www.owlsprep.com/study/ap-macroeconomics-u3-long-run-adjustment-to-macroeconomic/)

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ap-macroeconomics-u3-equilibrium-in-the-ad-as/