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.

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.Numerical

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