Real GDP in the U.S. in 2024 was $27,720 billion. Short-run output for the same year was +2.69 percent.

Compute
𝑌
¯
𝑡
.

Round your answer to the nearest billion.

Question

Real GDP in the U.S. in 2024 was $27,720 billion. Short-run output for the same year was +2.69 percent.

Compute 
𝑌
¯
𝑡
.

Round your answer to the nearest billion.

BlackTom AI · Accepted Answer

We start by restating the given information to ensure we are using the correct figures. Real GDP in 2024 (Y_t) is 27,720 billion dollars, and the short-run output for the same year is +2.69 percent, which implies the actual GDP exceeded the potential by 2.69%.

Next, we need to solve for the potential (trend) output, often denoted as Ȳ_t, using the relationship: Y_t = Ȳ_t × (1 + short-run percentage deviation). In this context, Y_t = Ȳ_t × 1.0269, so Ȳ_t = Y_t / 1.0269.

Now, we perform the division with the given numbers: Ȳ_t = 27,720 / 1.0269. To approximate, one way is to multiply 27,720 by the reciprocal of 1.0269. The reciprocal is about 0.9738 (since 1 / 1.0269 ≈ 0.9738). Multiplying 27,720 × 0.9738 yields roughly 27,010 to 27,012.

For more precise checking, you can refine the calculation: 27,720 ÷ 1.0269 ≈ 27,011. Therefore, the potential or trend output Ȳ_t is about 27,011 billion dollars when rounded to the nearest billion.

If you want to cross-check quickly, multiply the result by 1.0269: 27,011 × 1.0269 ≈ 27,720 (within rounding tolerance), which confirms the consistency of the calculation.

Summary of the key steps: identify Y_t and the short-run growth, use Y_t = Ȳ_t × (1 + growth), isolate Ȳ_t by division, compute the division, and finally round to the nearest billion.

Note: Some sources or datasets might show slightly different rounded figures (e.g., due to using 2.69% as 0.0269 exactly), which can yield minor variations in the final rounded value. The method, however, remains the same and the result should be the Ȳ_t value rounded to the nearest billion.

FA25 ECON 302 002 Midterm Exam #3 (Chapters 7-9): Sample Questions

Real GDP in the U.S. in 2024 was $27,720 billion. Short-run output for the same year was +2.69 percent. Compute 𝑌 ¯ 𝑡 . Round your answer to the nearest billion.

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