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Answer :
The correct answer is a. The exponent on capital in the production function is much lower than one.
In standard neoclassical growth theory, the production function that describes how inputs of capital and labor generate output is often assumed to have a Cobb-Douglas form:
Y = A * K^α * L^(1-α)
where:
- Y = Output (GDP)
- A = Total factor productivity (TFP)
- K = Capital
- L = Labor
- α = Capital's share of income (0 < α < 1)
In this production function, capital (K) is raised to the power of α, and labor (L) is raised to the power of (1-α). The exponent α represents the share of output attributed to capital.
When there are large differences in capital per worker across countries, it means that some countries have significantly more capital (K) relative to their labor (L) compared to other countries. However, the exponent α is typically less than one (0 < α < 1), implying that the marginal product of capital diminishes as more capital is added.
As a result, even if there are large differences in capital per worker, the impact of additional capital on predicted GDP becomes relatively smaller. This is because the diminishing marginal returns to capital lead to diminishing gains in output as capital accumulates. Consequently, the differences in predicted GDP across countries caused by differences in capital per worker tend to be relatively small.
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The correct format of the question should be:
Why do large differences in capital per worker lead to relatively small differences in predicted GDP across countries?
a. The exponent on capital in the production function is much lower than one
b. Capital is not an input in production
c. Capital has a high depreciation rate
d. Workers exert more effort when they have less capital
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