Refer to the following table when answering the following questions.

In the following calculations, you should assume
𝛼
=
1
3
.

The TFP that reconciles predicted and observed GDP per capita in India is ______.

Round your answer to the nearest hundredth.

Question

Refer to the following table when answering the following questions.

In the following calculations, you should assume 
𝛼
=
1
3
 .

The TFP that reconciles predicted and observed GDP per capita in India is ______.

Round your answer to the nearest hundredth.

BlackTom AI · Accepted Answer

Using a Cobb–Douglas per‑worker production function y = A k^α with α = 1/3, total factor productivity A is the scalar that reconciles the model prediction A k^α with the observed per‑capita output y. Relevant facts from the table: India’s observed capital per person k = 0.082 and observed per‑capita GDP y_obs = 0.107. The model prediction with A = 1 is y_pred = k^(1/3) = 0.434 (this value is shown in the table).

Step‑by‑step reasoning and calculations:
1. Compute k^(α) with α = 1/3: k^(1/3) = (0.082)^(1/3) = 0.434 (table value).
2. Set the production function equal to observed output: y_obs = A · k^(1/3).
3. Solve for A: A = y_obs / k^(1/3).
4. Substitute numbers: A = 0.107 / 0.434 = 0.246543… .
5. Round to the nearest hundredth: A ≈ 0.25.

Why this is correct: The model’s predicted output with A = 1 (0.434) is higher than India’s actual observed output (0.107), so A must be less than 1 to scale down the model prediction to match observations. Dividing observed output by k^(1/3) gives the exact scaling factor A required.

Common mistakes to avoid: reversing the ratio (k^(1/3) / y_obs) or using k instead of k^(1/3) would give incorrect values. Using α other than 1/3 would also change the exponent and the result.

Conclusion: The TFP that reconciles predicted and observed GDP per capita in India is 0.25, which matches the provided answer.

Refer to the following table when answering the following questions. In the following calculations, you should assume 𝛼 = 1 3 . The TFP that reconciles predicted and observed GDP per capita in India is ______. Round your answer to the nearest hundredth.数值题

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