In the second quarter of 2020, potential output was $20,965 billion per year. Short-run output was -9.1 percent.

Compute
𝑌
𝑡
.

Round your answer to the nearest billion.

Question

In the second quarter of 2020, potential output was $20,965 billion per year. Short-run output was -9.1 percent.

Compute 
𝑌
𝑡
.

Round your answer to the nearest billion.

BlackTom AI · Accepted Answer

Interpret the problem carefully: the given figure of 20,965 billion is the potential (long-run) output, and the short-run output change is a deviation of -9.1% from that potential. The key relationship is: Y_t = Y_potential × (1 + percent_change). Here, the percent_change is -9.1%, which equals -0.091 in decimal form.

Step 1: Convert the percentage to a decimal. -9.1% = -0.091.
Step 2: Apply the percentage change to the potential output. Y_t = 20,965 × (1 - 0.091) = 20,965 × 0.909.
Step 3: Compute the product. 20,965 × 0.909 can be broken down as 20,965 × (0.900 + 0.009) = 20,965 × 0.900 + 20,965 × 0.009.
- 20,965 × 0.900 = 18,868.5
- 20,965 × 0.009 = 188.685
Add them together: 18,868.5 + 188.685 = 19,057.185.
Step 4: Round to the nearest billion as requested. 19,057.185 rounds to 19,057.

Result interpretation: The economy’s actual output in that quarter is about 19,057 billion, reflecting a negative output gap of 9.1% relative to potential.

Notes on edge cases: If one interpreted the drop differently (for example, applying the percentage decrease directly as 20,965 × -0.091 and adding to potential), you would still arrive at the same final value, since the correct formula is Y_t = Y_potential × (1 + percentage_change). If the problem had provided different units or asked for a different rounding rule, you would adjust accordingly, but in this case the steps above yield the requested 19,057 when rounding to the nearest billion.

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

In the second quarter of 2020, potential output was $20,965 billion per year. Short-run output was -9.1 percent. Compute 𝑌 𝑡 . Round your answer to the nearest billion.

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