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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 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

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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 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
Transcribed Image Text:(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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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?

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