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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.6: Permutations
Problem 5E
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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..
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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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