The observed capital-to-labor ratio in China is higher than in Brazil. However, China's GDP per capita is lower than Brazil's. It must be that Brazil's TFP is
[ Select ]
lower than
the same as
higher than
China's.

Question

The observed capital-to-labor ratio in China is higher than in Brazil. However, China's GDP per capita is lower than Brazil's. It must be that Brazil's TFP is 
[ Select ]
lower than
the same as
higher than
 China's.

BlackTom AI · Accepted Answer

The per-worker production function Y/L = A · f(K/L) (e.g., Cobb–Douglas Y/L = A (K/L)^α) directly links output per worker to capital per worker and TFP (A). 1) Relevant concepts - Y/L: output (GDP) per worker or per capita approximated by output per worker. - K/L: capital per worker (capital-to-labor ratio). - A (TFP): total factor productivity, a multiplier capturing technology, efficiency, institutions, etc. - f(·) is increasing in K/L (more capital per worker raises output per worker). 2) Step-by-step reasoning Let y = Y/L and k = K/L. For two countries (China C and Brazil B): y_C = A_C · f(k_C) y_B = A_B · f(k_B) We are told k_C > k_B but y_C < y_B. Because f is increasing, f(k_C) > f(k_B). Yet the observed y_C is smaller than y_B. That can only happen if A_C is smaller than A_B (so Brazil’s A_B must be larger). 3) Algebraic demonstration (intermediate steps) Using Cobb–Douglas f(k) = k^α (α>0) for clarity: A_C = y_C / k_C^α A_B = y_B / k_B^α Compare the ratio: A_C / A_B = (y_C / y_B) · (k_B / k_C)^α Given y_C / y_B < 1 and k_B / k_C < 1, both multiplicative factors are less than 1, so A_C / A_B < 1 ⇒ A_C < A_B. Hence Brazil’s TFP is higher. 4) Why the correct answer is correct Because higher capital per worker would, all else equal (same A), produce higher output per worker. Observing the reverse (more capital but lower output) implies the “all else” — TFP — must be lower in China. Therefore Brazil’s TFP must be higher. 5) Why the other options are incorrect - “Lower than”: Would imply Brazil’s TFP is lower; that would make the output gap even harder to reconcile because China has both more capital and higher TFP—then China would surely have higher GDP per capita, contradicting facts. - “The same as”: If A were equal, higher k in China would yield higher y_C (since f is increasing), contradicting the observation y_C < y_B. Therefore A cannot be equal. 6) Conclusion Brazil’s TFP is higher than China’s, which matches the provided correct answer: higher than.

The observed capital-to-labor ratio in China is higher than in Brazil. However, China's GDP per capita is lower than Brazil's. It must be that Brazil's TFP is [ Select ] lower than the same as higher than China's.多重下拉选择题

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