One of the key characteristics of the Cobb-Douglas production function with exponents (for capital) and (for labor) and a common productivity across countries (where the markets for labor and capital are competitive) is that:

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One of the key characteristics of the Cobb-Douglas production function with exponents  (for capital) and  (for labor) and a common productivity  across countries (where the markets for labor and capital are competitive) is that:

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The question concerns the Cobb-Douglas production function with exponents α (for capital) and (1−α) (for labor), and a common productivity term A across countries, under competitive markets for labor and capital.

First, let's restate what a Cobb-Douglas production function looks like in this setup: Y = A K^α L^{1−α}, where Y is output, K is capital, L is labor, α is the capital income share, and (1−α) is the labor income share. When markets are competitive and production exhibits constant returns to scale, the share of income going to capital is determined by α, and the share going to labor is determined by 1−α. These shares are constant with respect to the level of output, the distribution of K and L, and even across countries, provided the technology parameter A is exogenous and does not alter the shares themselves.

Now, evaluating the given statement: “the income shares of capital and labor are constant.” This is a direct consequence of the Cobb-Douglas specification under the stated conditions. Since the exponents α and 1−α are fixed and do not depend on prices or distributional factors, the shares of income accruing to capital and to labor remain constant across different contexts, including different countries, as long as we stay within the same production function form and competitive assumptions.

To reinforce why the other options (if any) would be incorrect, note that under a Cobb-Douglas form, you do not generally expect the capital or labor shares to vary with the scale of output, with factor prices, or due to different country productivity parameters A alone, because the functional form enforces constant shares by construction. If an option claimed that shares vary with income levels, technology, or factor prices, that would contradict the standard result for a Cobb-Douglas function with constant returns to scale and competitive factor markets.

In summary, the defining feature of this setup is that the income shares allocated to capital and labor are captured directly by the exponents α and 1−α and remain constant across countries and levels of income, given the model assumptions.

SP25 ECON 312 001 Midterm Exam #1 (Chapters 1-5): Sample Questions

One of the key characteristics of the Cobb-Douglas production function with exponents (for capital) and (for labor) and a common productivity across countries (where the markets for labor and capital are competitive) is that:

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