According to the BEA, real GDP in the fourth quarter of 2024 was
𝑌
𝑡
=
$
23.67
trillion. According to the Congressional Budget Office, potential (real) output in the same quarter was
𝑌
¯
𝑡
=
23.02
trillion. Short-run output in the fourth quarter of 2024 was ______ percent.

Round your answer to the nearest tenth of a percent.

Question

According to the BEA, real GDP in the fourth quarter of 2024 was 
𝑌
𝑡
=
$
23.67
 trillion. According to the Congressional Budget Office, potential (real) output in the same quarter was 
𝑌
¯
𝑡
=
23.02
 trillion. Short-run output in the fourth quarter of 2024 was ______ percent.

Round your answer to the nearest tenth of a percent.

BlackTom AI · Accepted Answer

Short-run output (the output gap) is defined as (Yt − Ȳt) / Ȳt × 100%.

Relevant knowledge points:
- Yt is actual (real) GDP; Ȳt is potential (real) output.
- The output gap measures how far actual output deviates from potential, expressed as a percent of potential output.
- A positive gap means the economy is operating above potential (expansionary); a negative gap means below potential (slack).

Step-by-step calculation:
1. Compute the difference: Yt − Ȳt = 23.67 − 23.02 = 0.65 (trillion dollars).
2. Divide the difference by potential output: 0.65 / 23.02.
   - To show an intermediate check: 23.02 × 0.02825 = 0.650315, so 0.65 / 23.02 ≈ 0.028246...
3. Convert to percent: 0.028246... × 100% ≈ 2.8246...
4. Round to the nearest tenth of a percent: 2.8%.

Why this is correct:
- The formula uses potential output (Ȳt) as the denominator by convention, because the gap expresses deviation relative to the economy’s capacity. Using actual output as the denominator would misstate the relative size of the gap.
- The arithmetic is straightforward: the gap is 0.65 trillion on a 23.02 trillion base, which is about 2.8%.

Common mistakes to avoid:
- Treating the raw difference (0.65) as a percent (that would be 65% and incorrect).
- Using Yt instead of Ȳt in the denominator (would yield ~2.7% instead of 2.8%).
- Forgetting to convert the decimal to a percent or misrounding.

Conclusion: The short-run output in Q4 2024 is 2.8%, which matches the provided answer.

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