We appreciate your visit to You are told that a profit maximizing firm employs 13 workers and 17 units of capital It produces output using the production function tex Y. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The marginal product of capital in the given production function is represented by 13/√K, where K is the amount of physical capital employed.
To compute the marginal product of capital, we differentiate the production function with respect to capital (K) while holding the number of workers (L) constant. The resulting expression represents the marginal product of capital, indicating the additional output produced when one additional unit of capital is employed.
The production function is given as [tex]Y = 2K^{0.5}L^{0.5}[/tex] where Y represents output, K is physical capital, and L is the number of workers. To compute the marginal product of capital (MPK), we differentiate the production function with respect to K, while holding L constant.
Taking the partial derivative of Y with respect to K, we have:
∂Y/∂K = [tex]0.5 \cdot 2 \cdot K^{(0.5-1)} \cdot L^{0.5}[/tex]
Simplifying further, we have:
∂Y/∂K = [tex]K^{-0.5} * L^{0.5}[/tex]
Since we are interested in the marginal product of capital when L is fixed at 13 workers, we substitute L = 13 into the expression:
∂Y/∂K = [tex]K^{-0.5} \cdot 13^{0.5}[/tex]
Simplifying the equation further, we have:
∂Y/∂K = 13/√K. Therefore, the marginal product of capital is given by 13 divided by the square root of K, where K represents the amount of physical capital employed by the firm.
Learn more about marginal product here:
https://brainly.com/question/31050533
#SPJ11
Thanks for taking the time to read You are told that a profit maximizing firm employs 13 workers and 17 units of capital It produces output using the production function tex Y. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
