(b) Prove that the per-worker production function has the following properties:f'(k) ≥ 0, lim f'(k)= +∞, andk-0lim 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.. (b) Prove that the per-worker production function has the following properties:f'(k) > 0, lim f'(k)lim f'(k) = 0.= +00,andk-0k00(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 →and as k → o? Derive the expression for the factor price frontier (FPF), i.e. theexpression linking W and r, and illustrate it graphically. Show what happensto the FPF if general productivity increases.

We know, f(k)≡F(k,1) Where k=K/L, Y=Lf(k) {if f(k)=y} So that:…

Answered: (b) Prove that the per-worker…

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

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(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..

(b) Prove that the per-worker production function has the following properties:
f'(k) > 0, lim f'(k)
lim f'(k) = 0.
= +00,
and
k-0
k00
(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 →
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.

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