Chan Ortiz

08/10/2024 · High School

49. Marginal Productivity A manufacturer estimates that produc- tion (in hundreds of units) is a function of the amounts \( x \) and \( y \) of labor and capital used, as follows. \[ f(x, y)=\left(\frac{1}{4} x^{-1 / 4}+\frac{3}{4} y^{-1 / 4}\right)^{-4} \] a. Find the number of units produced when 16 units of labor and 81 units of capital are utilized. b. Find and interpret \( f_{x}(16,81) \) and \( f_{y}(16,81) \). c. What would be the approximate effect on production of increasing labor by 1 unit from 16 units of labor with 81 units of capital? 50. Marginal Productivity The production function \( z \) for the United States was once estimated as where \( x \) stands for the amount of labor and \( y \) the amount of capital. Find the marginal productivity of labor and of capital.