Compute the Grubel-Lloyd index using the following data. Answer the number with one decimal (e.g., 0.14
⟶
0.1 and 0.15
⟶
0.2) in the box.

Chinese exports to Korea Chinese imports from Korea
Textiles 100 million dollars 180 million dollars

Question

Compute the Grubel-Lloyd index using the following data. Answer the number with one decimal (e.g., 0.14 
⟶
 0.1 and 0.15 
⟶
 0.2) in the box.

Chinese exports to Korea	Chinese imports from Korea
Textiles	100 million dollars	180 million dollars

BlackTom AI · Accepted Answer

The Grubel-Lloyd index for a single product i is GL_i = 1 − |X_i − M_i| / (X_i + M_i), which is algebraically equivalent to GL_i = (2 · min(X_i, M_i)) / (X_i + M_i).

1. Relevant knowledge points and concepts
- The Grubel-Lloyd index measures intra-industry trade for a product, ranging from 0 (pure inter-industry trade: only exports or only imports) to 1 (perfect two-way trade: exports equal imports).
- X_i = exports, M_i = imports for the product. Units cancel in the ratio, so using millions of dollars is fine.

2. Step-by-step reasoning
- Identify values: X = 100 (million dollars), M = 180 (million dollars).
- Compute the absolute difference and sum needed for the formula.

3. Intermediate calculations
- |X − M| = |100 − 180| = 80.
- X + M = 100 + 180 = 280.
- Using GL = 1 − |X − M| / (X + M): GL = 1 − 80 / 280.
- Compute 80 / 280 = 0.2857142857...
- GL = 1 − 0.2857142857... = 0.7142857143...

(Alternative check: GL = (2 · min(X, M)) / (X + M) = (2 · 100) / 280 = 200 / 280 = 0.7142857143..., same result.)

4. Why the correct answer is correct
- The calculated GL is 0.7142857...; the question requires a single decimal. Rounding 0.7142857 to one decimal gives 0.7 (the second digit after the decimal is 1, so we round down).

5. Why other plausible answers would be incorrect
- A value like 0.71 or 0.714 would be more precise but does not follow the instruction to report one decimal.
- Values such as 0.8 or 0.6 would be incorrect because they do not equal the computed 0.7142857 rounded to one decimal (0.7).

6. Conclusion and confirmation
- The Grubel-Lloyd index for textiles with X = 100 and M = 180 is 0.7142857..., which rounded to one decimal is 0.7. This matches the provided answer: 0.7.

Compute the Grubel-Lloyd index using the following data. Answer the number with one decimal (e.g., 0.14 ⟶ 0.1 and 0.15 ⟶ 0.2) in the box. Chinese exports to Korea Chinese imports from Korea Textiles 100 million dollars 180 million dollarsNumerical

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