Answered: Production Function. Consider the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Production Function. Consider the Cobb-Douglas production function discussed in class:
F(K, L) = AK^1/3 L^2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10.

d) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com-
ment on how and why these numbers changed relative to (c) and why they did so.

E) Suppose that the quantity of capital K doubles as well. (So now both K and L are
twice their previous value). Calculate Y, w, r, Y/L, and K/L. Comment on how these
numbers changed relative to both their initial values, and their values in (d).

Expert Solution

Step 1

Given;

Production function; $F (K, L) = A K^{1 / 3} L^{2 / 3}$

where;

A= 1

K= 150

L= 10

$Y = 1 {(150)}^{1 / 3} {(10)}^{2 / 3} = 1 (5.31329) (4.64159) = 24.6621$

Wages and rent:-

$w = P \times M P_{L} h e r e; P i s n o t g i v e n, t h e r e f o r e : - w = M P_{L} t h e n; M P_{L} = \frac{2}{3} A K^{1 / 3} L^{- 1 / 3} = \frac{2}{3} \times 1 \times {(150)}^{1 / 3} {(10)}^{- 1 / 3)} = \frac{2}{3} \times 2.466 = 1.644 a n d; r = p \times M P_{K} H e r e; p r i c e i s n o t g i v e n, t h e r e f o r e r = M P_{K} t h e n; M P_{K} = \frac{1}{3} A K^{- 2 / 3} L^{2 / 3} = \frac{1}{3} (1) {(150)}^{- 2 / 3} {(10)}^{2 / 3} = \frac{1}{3} \times 1.181 = 0.3937$

Output per labor:-

$\frac{Y}{L} = \frac{24.6621}{10} = 2.46621$

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