Answered: the quantity, q, of a product…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 44RE

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Question

the quantity, q, of a product manufactures depends on the number of workers.
W , and the amount of capital invested, K, and is represented by the Cobb-Douglas
function
q = 64W^3/4 K^1/4 .
Suppose further that labor costs $18 per worker and capital costs $28 per unit, and the
budget is $4600. Let λ be the Lagrange multiplier. Does increasing the budget by $1 allow the
production of λ extra units of the product? Explain why as shown in the image below..

(W- 84 (41.08)
18
W. 191.7
4. 7. 44.5 kģ
7-44.5
4
18W 14
Q = 64 w 3/4 K 1/4
k
16 (3) (41.07)
18(191.47) 14
(1.81)
4601 = 64 (191.76)
64 (191.76) 014. (41.08) 74
4400
V
=
8347.78
64 (1967) 54 (91-08)/4
= 8345.97
.
= 11.81
8347-78-8345.97 =
1-81=1.81

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Follow-up Questions

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Follow-up Question

Does the value of λ change if the budget changes from $4600 to $5600?
What condition must a Cobb-Douglas production function q = cKαW β satisfy to
ensure that the marginal increase of production is not affected by the size of the
budget?

Solution