uppose that a company's production for Q units of its product is given by the Cobb-Douglas production function Q = 30K/4L3/4 here K is dollars of capital investment and L is labor hours. (a) Find Q if K = $10,000 andL = 81 hours. Q = (b) Show that if both K and L are doubled, then the output is doubled. (Write your answer in terms of K and L.) Q(2K, 2L) = (c) If a capital investment is held at $10,000, graph Q as a function of L.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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A graphing calculator or computer algebra system is recommended.
Suppose that a company's production for Q units of its product is given by the Cobb-Douglas production function
Q3 3ок1/4, 3/4
where K is dollars of capital investment and L is labor hours.
(a) Find Q if K = $10,000 and L = 81 hours.
%D
Q
(b) Show that if both K and L are doubled, then the output is doubled. (Write your answer in terms of K and L.)
Q(2K, 2L) =
(c) If a capital investment is held at $10,000, graph Q as a function of L.
Transcribed Image Text:A graphing calculator or computer algebra system is recommended. Suppose that a company's production for Q units of its product is given by the Cobb-Douglas production function Q3 3ок1/4, 3/4 where K is dollars of capital investment and L is labor hours. (a) Find Q if K = $10,000 and L = 81 hours. %D Q (b) Show that if both K and L are doubled, then the output is doubled. (Write your answer in terms of K and L.) Q(2K, 2L) = (c) If a capital investment is held at $10,000, graph Q as a function of L.
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