China exports 180 million dollar tires to the U.S. The U.S. exports 20 million dollar tires to China. The Grubel-Lloyd index for this case is ...

Question

BlackTom AI · Accepted Answer

Grubel-Lloyd index measures the extent of intra-industry trade between two partners. It is defined for a product i as GLi = (Xi + Mi − |Xi − Mi|) / (Xi + Mi), which is algebraically equivalent to GLi = 1 − |Xi − Mi| / (Xi + Mi). The index ranges from 0 (pure inter-industry trade, only exports or only imports) to 1 (perfect two-way intra-industry trade, exports = imports).

1) Relevant knowledge points and concepts
- Xi = exports of product i (here, China’s exports of tires to the U.S. = $180 million).
- Mi = imports of product i (here, China’s imports of tires from the U.S. = $20 million).
- GL index formula and its interpretation (0–1 scale; higher = more intra-industry trade).

2) Step-by-step reasoning
- Use the GL formula GL = (X + M − |X − M|) / (X + M), or the equivalent GL = 1 − |X − M|/(X + M).

3) Calculations with intermediate steps
- Sum: X + M = 180 + 20 = 200 (million dollars).
- Absolute difference: |X − M| = |180 − 20| = 160 (million dollars).
- Ratio of difference to sum: |X − M| / (X + M) = 160 / 200 = 0.8.
- GL = 1 − 0.8 = 0.2 (or using the other form: (200 − 160)/200 = 40/200 = 0.2).

4) Why the correct answer is correct
- The arithmetic follows directly from the definition: large asymmetry in exports versus imports (180 vs. 20) produces a large |X − M| relative to the sum, so GL is low (0.2), indicating mostly inter-industry trade rather than balanced two-way trade.

5) Why other (common mistaken) answers would be incorrect
- Mistaking GL for |X − M|/(X + M) would yield 0.8, which is actually the complement (measures imbalance), not the GL index.
- Using min(X, M)/(X + M) = 20/200 = 0.1 is another incorrect formula sometimes confused with specialization indices.
- Ratio min/max = 20/180 ≈ 0.111 also does not match the GL definition.

6) Conclusion
- The calculated Grubel-Lloyd index is 0.20, which matches the provided correct answer 0.20.

China exports 180 million dollar tires to the U.S. The U.S. exports 20 million dollar tires to China. The Grubel-Lloyd index for this case is ...单项选择题

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