1. Consider the production functions for good X and good Y: X = K? +L ; Y = 20/KL A. Show and discuss which production function(s) exhibit(s) diminishing marginal productivity of labor and capital. (5 pts)

1. Consider the production functions for good X and good Y: X = K? +L ; Y = 20/KL A. Show and discuss which production function(s) exhibit(s) diminishing marginal productivity of labor and capital. (5 pts)

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter21: Production And Costs

Section: Chapter Questions

Problem 11QP

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Consider a firm that produces a single output good Y with two input goods: labor (L) and capital (K). The firm has a technology described by the production function f : R? → R+ defined by f(1, k) = Vĩ + vk, where l is the quantity of labor and k is the quantity of capital. (a) In an appropriate diagram, illustrate the map of isoquants for the firm's production function. (b) Does the firm's technology satisfy the following properties: (i) strict monotonicity (i.e., are the marginal product of labor and the marginal product of capital strictly positive), (ii) the no-free-lunch property, (iii) constant/decreasing/increasing returns to scale? (iv) 1
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