Introduction
A short-run equilibrium in the AD-AS model identifies an output level where aggregate demand intersects short-run aggregate supply. To interpret that level, compare it with potential output: the economy’s sustainable level of production when labor and other resources are employed at their normal, long-run rates. The difference is the output gap.
A negative gap means actual output is below potential; a positive gap means it is above potential. This comparison gives a useful way to describe the position of short-run equilibrium relative to long-run aggregate supply (LRAS). It does not, by itself, say what caused the gap or predict how the economy will adjust.
Connecting the Gap to the AD-AS Diagram
In the AD-AS model, the short-run equilibrium is the intersection of aggregate demand (AD) and short-run aggregate supply (SRAS). Potential output is represented by LRAS, drawn as a vertical line at \(Y^*\). The equilibrium output coordinate \(Y_e\) and the location of that vertical line together determine the sign of the gap.
| Comparison | Output gap | Position of short-run equilibrium relative to LRAS |
|---|---|---|
| \(Y_e<Y^*\) | Negative; recessionary | Left of LRAS |
| \(Y_e=Y^*\) | Zero | On LRAS |
| \(Y_e>Y^*\) | Positive; inflationary | Right of LRAS |
“Left” and “right” refer to the horizontal output axis. The equilibrium can have any price level while still being left of, on, or right of LRAS; the price-level coordinate does not determine the output gap. For a numerical comparison, use actual real output and potential output measured in the same units and for the same period.
The terms “recessionary” and “inflationary” describe the direction of the output comparison, not a complete diagnosis of economic conditions. A negative gap does not by itself establish the official dates of a recession. A positive gap is not the same thing as a measured inflation rate, which describes the rate of change in the price level over time.
Why the Percentage Uses Potential Output
The output-unit gap is a difference, so its size depends on the units in which output is measured. Dividing by potential output expresses that difference relative to the economy’s benchmark capacity. Multiplying by 100 converts the ratio to a percentage.
This identity also shows why output equal to potential gives a zero gap: if \(Y_e=Y^*\), then \(Y_e/Y^*=1\), so the ratio minus one is zero. If equilibrium output is below potential, the ratio is less than one and the percentage gap is negative. If it is above potential, the ratio is greater than one and the gap is positive. The denominator is potential output because the question is how large the difference is relative to the benchmark, not relative to the observed value.
If AD and SRAS are given as equations, set their output expressions equal and solve for the equilibrium price level. Substitute that price level into either curve to obtain \(Y_e\).
Use the stated value of \(Y^*\), or read it from the location of LRAS. Keep its units consistent with \(Y_e\).
Compute \(Y_e-Y^*\), then divide by \(Y^*\) and multiply by 100 for the percentage gap. The sign tells you whether equilibrium is left or right of LRAS.
Worked Applications
Worked Example: Calculating a Gap From Output Data
A hypothetical economy has potential annual real output of $2.40 trillion and short-run equilibrium real output of $2.28 trillion. Calculate the gap in dollars and as a percentage of potential output, then classify it.
Method. Subtract potential output from equilibrium output, then use potential output as the percentage denominator.
The output-unit gap is:
The negative sign means equilibrium output is $0.12 trillion, or $120 billion, below potential. The percentage gap is:
Conclusion and check. The economy has a 5.0% recessionary output gap, so its short-run equilibrium is to the left of LRAS. The result is consistent with the raw figures: $2.28 trillion is below $2.40 trillion. The calculation avoids the common mistake of treating the absolute difference, $0.12 trillion, as a percentage.
Worked Example: Finding the Gap From Linear AD and SRAS
In a hypothetical economy, real output \(Y\) is measured in billions of dollars per year and the price level \(P\) is an index. The curves are \(Y=1400-20P\) for AD and \(Y=560+20P\) for SRAS. Potential output is $1,000 billion per year. Find the short-run equilibrium and output gap.
Method. At equilibrium, the output demanded equals the output supplied at the same price level. Set the two expressions for \(Y\) equal:
Subtract 560 from both sides and add \(20P\) to both sides:
Substitute \(P=21\) into AD:
Check using SRAS: \(560+20(21)=560+420=980\), so both curves give the same equilibrium output. Compare that output with potential:
Conclusion. Equilibrium output is $20 billion below potential, a 2.0% recessionary gap. The intersection is left of LRAS. A common mistake is to stop after finding \(P=21\): the price level is not output, so it cannot be compared with potential output. The equilibrium quantity \(Y_e=980\) is the value to compare.
Worked Example: Equilibrium to the Right of LRAS
A hypothetical economy has AD \(Y=1800-30P\), SRAS \(Y=600+30P\), and potential output of $1,100 billion per year. Output is measured in billions of dollars per year; \(P\) is a price-level index. Find the equilibrium price level and output, calculate the gap, and describe the equilibrium’s location relative to LRAS.
Method. Equate AD and SRAS:
Subtract 600 and add \(30P\) to both sides:
Substitute this price level into either curve. Using AD:
Using SRAS gives the check \(600+30(20)=600+600=1200\). Thus the two curves agree on equilibrium output. The output-unit gap is:
The percentage gap is:
Conclusion and check. The economy has a 9.1% inflationary output gap, and the short-run equilibrium is to the right of LRAS because \(1200>1100\). The percentage is rounded to one decimal place. The positive result agrees with the comparison of the two output levels.
Common Mistakes and Interpretation
The most frequent arithmetic trap is using actual output in the denominator. For the first worked example, that incorrect calculation would be:
The correction is to divide by potential output, \(2.40\), not actual output, \(2.28\), giving \(-5.0\%\). The numerator records the difference from the benchmark; the denominator must be that same benchmark.
Other checks help prevent misinterpretation:
- Keep units aligned. Do not compare output in billions with potential output in trillions without converting one of them.
- Use real output for the comparison. A price change can affect nominal GDP even when the quantity of production has not changed. The AD-AS output comparison is about real output.
- Use the sign, not the price level, to classify the gap. A high or low price-level index alone does not indicate whether equilibrium is left or right of LRAS.
- Do not confuse a gap with a growth rate. An output gap compares the level of current output with potential output; it is not the percentage change in output from an earlier period.
- Do not read more into the label than it says. The gap classifies equilibrium output relative to potential. By itself, it does not identify the source of the difference or quantify the rate of inflation.
The distinction is useful in macroeconomic analysis because the same measured output level can have a different interpretation when potential output differs. The sign and percentage size summarize that comparison in a consistent way. These definitions and calculations are aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
Check Your Understanding
For each problem, use real output and potential output in the same units. The percentage answers are rounded to one decimal place where needed.
- A hypothetical economy has equilibrium real output of $945 billion per year and potential output of $900 billion per year. Find the output gap in billions and as a percentage, and state its position relative to LRAS. (Answer: \(+\$45\) billion per year; \(+5.0\%\), an inflationary gap; right of LRAS.)
- Equilibrium real output is $1,176 billion per year and potential output is $1,200 billion per year. Calculate the gap in output units and percentage terms, and classify it. (Answer: \(-\$24\) billion per year; \(-2.0\%\), a recessionary gap; left of LRAS.)
- AD is \(Y=1600-20P\) and SRAS is \(Y=400+20P\), where \(Y\) is billions of dollars of real output per year and \(P\) is a price-level index. Potential output is $1,040 billion per year. Find the equilibrium price level, equilibrium output, percentage gap, and location relative to LRAS. (Answer: \(P=30\); \(Y_e=\$1{,}000\) billion per year; gap \(=-\$40\) billion per year or approximately \(-3.8\%\); left of LRAS.)
- AD is \(Y=2000-25P\) and SRAS is \(Y=500+25P\), with \(Y\) in billions of dollars of real output per year and \(P\) a price-level index. Potential output is $1,200 billion per year. Solve for equilibrium and calculate the percentage gap. (Answer: \(P=30\); \(Y_e=\$1{,}250\) billion per year; gap \(=+\$50\) billion per year or approximately \(+4.2\%\), to the right of LRAS.)
- Economy A has equilibrium output of $980 billion and potential output of $1,000 billion. Economy B has equilibrium output of $1,030 billion and potential output of $1,000 billion. Calculate each percentage gap and identify which economy is farther above potential. (Answer: A has a \(-2.0\%\) recessionary gap; B has a \(+3.0\%\) inflationary gap; B is farther above potential.)