Consider the Production Function: Y = 1.5 K L¹, where a = 0.7. K is capital, and Lis labor a) Using the gradient, find the marginal product of capital and the marginal product of labor. : b) Let's explore the marginal products further. b.1) What happens to the marginal productivity of capital when labor increases?" b.2) What happens to the marginal productivity of labor when capital increases? ^ c) Assume that alpha is not a constant. 0 < a < 1, and is considered as another variable in the above production function, find the total differential of Y.
Consider the Production Function: Y = 1.5 K L¹, where a = 0.7. K is capital, and Lis labor a) Using the gradient, find the marginal product of capital and the marginal product of labor. : b) Let's explore the marginal products further. b.1) What happens to the marginal productivity of capital when labor increases?" b.2) What happens to the marginal productivity of labor when capital increases? ^ c) Assume that alpha is not a constant. 0 < a < 1, and is considered as another variable in the above production function, find the total differential of Y.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.2P
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![Consider the Production Function:
Y = 1.5 Kº L-a, where a = 0.7, K is capital, and Lis labor
a) Using the gradient, find the marginal product of capital and the marginal product of labor.
b) Let's explore the marginal products further.
b.1) What happens to the marginal productivity of capital when labor increases?"
b.2) What happens to the marginal productivity of labor when capital increases?
c) Assume that alpha is not a constant. 0 < a < 1, and is considered as another variable in the above production function,
find the total differential of Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9a8d142-b25c-408d-9b46-e62ec9cc8e18%2F96480a03-a48c-41e5-8837-3cf70417d26b%2Fjixenbr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the Production Function:
Y = 1.5 Kº L-a, where a = 0.7, K is capital, and Lis labor
a) Using the gradient, find the marginal product of capital and the marginal product of labor.
b) Let's explore the marginal products further.
b.1) What happens to the marginal productivity of capital when labor increases?"
b.2) What happens to the marginal productivity of labor when capital increases?
c) Assume that alpha is not a constant. 0 < a < 1, and is considered as another variable in the above production function,
find the total differential of Y.
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