Consider the Cobb-Douglas production function F(L,K)= AL^αK^β.Which of the following statements is true? A) Increases in α increase labor's productivity and raise MRTS_LK. B) Decreases in α increase labor's productivity and raise MRTS_LK. C) Increases in α increase labor's productivity and lower MRTS_LK. D) Changes in α will not affect MRTS_LK.

Question

Quizplus · Accepted Answer

The Cobb-Douglas production function shows that output is determined by the levels of labor (L) and capital (K) inputs, with parameters α and β representing their respective contributions to output. An increase in α increases the productivity of labor, which means that a given increase in labor input results in a larger increase in output. This leads to an increase in the marginal product of labor (MPL), which is the rate at which output increases with an additional unit of labor input. The marginal rate of technical substitution (MRTS) measures the rate at which a producer can substitute one input (in this case, labor) for another (capital) while maintaining the same level of output. As MPL increases, the MRTS between labor and capital also increases. Therefore, when α increases, MRTS increases, and MRTS equals MRTS_LK. Choice A is the correct answer.

Consider the Cobb-Douglas Production Function F(L,K)= ALαKβ

Consider the Cobb-Douglas Production Function F(L,K)= AL^αK^β