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Answer :
Large differences in capital per worker lead to relatively small differences in predicted GDP across countries because the exponent on capital in the production function is much lower than one, indicating diminishing returns to capital.
The answer lies in the concept of diminishing returns to capital. In economic production functions, capital is considered one of the inputs alongside labor.
However, the impact of capital on output is subject to diminishing returns. This means that as the amount of capital per worker increases, the additional contribution of each additional unit of capital to output diminishes.
The production function typically follows the form Y = F(K, L), where Y represents output, K represents capital, and L represents labor. The exponent on capital (K) in the production function is often less than one, implying that the marginal productivity of capital decreases as more capital is added.
As a result, even large differences in capital per worker across countries do not lead to proportionate differences in predicted GDP. Initially, as capital per worker increases, there is a substantial positive effect on output.
However, as capital stock continues to grow, the additional gains from each additional unit of capital become smaller.
Therefore, the overall impact on GDP becomes less pronounced, leading to relatively small differences in predicted GDP across countries despite significant disparities in capital per worker.
In summary, the diminishing returns to capital in the production function explain why large differences in capital per worker result in relatively small variations in predicted GDP across countries.
The diminishing marginal productivity of capital implies that the additional gains from increased capital become progressively smaller, leading to a less significant impact on overall economic output.
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