(b) Prove that the per-worker production function has the following properties: f'(k) > 0, lim f' (k) = +0, and k-0 lim f'(k) = 0. (c) Assume that the production factors receive their respective marginal products. Derive the expressions for the wage rate, W, and the rental rate on capital, r+ 8, when technology is Cobb-Douglas. What happens to (W,r) as k 0 and as k → o0? Derive the expression for the factor price frontier (FPF), i.e. the expression linking W and r, and illustrate it graphically. Show what happens to the FPF if general productivity increases.
(b) Prove that the per-worker production function has the following properties: f'(k) > 0, lim f' (k) = +0, and k-0 lim f'(k) = 0. (c) Assume that the production factors receive their respective marginal products. Derive the expressions for the wage rate, W, and the rental rate on capital, r+ 8, when technology is Cobb-Douglas. What happens to (W,r) as k 0 and as k → o0? Derive the expression for the factor price frontier (FPF), i.e. the expression linking W and r, and illustrate it graphically. Show what happens to the FPF if general productivity increases.
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter7: Production Economics
Section: Chapter Questions
Problem 10E
Related questions
Question
(b) Prove that the per-worker production function has the following properties:
f'(k) ≥ 0, lim f'(k)= +∞, and
k-0
lim f'(k)
(c) Assume that the production factors receive their respective marginal products. Derive the expressions for the wage rate, W, and the rental rate on capital, r + 8, when technology is Cobb-Douglas. What happens to (W,r) as k 0 and as k→ ∞o? Derive the expression for the factor price frontier (FPF), i.e. the expression linking W and r, and illustrate it graphically. Show what happens to the FPF if general productivity increases.
= 0..
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Managerial Economics: Applications, Strategies an…
Economics
ISBN:
9781305506381
Author:
James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:
Cengage Learning
Microeconomics: Principles & Policy
Economics
ISBN:
9781337794992
Author:
William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:
Cengage Learning
Managerial Economics: Applications, Strategies an…
Economics
ISBN:
9781305506381
Author:
James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:
Cengage Learning
Microeconomics: Principles & Policy
Economics
ISBN:
9781337794992
Author:
William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:
Cengage Learning