A firm's production function is Q(L) = 12L² – L³, where L denotes the number of workers (“labor"), with L € [0, 200]. (a) What size of the work force (L*) maximizes output, Q(L)? (b) What size of the work force (L**) maximizes output per worker, Q(L)/L? (c) Note that Q'′(L**) = Q(L**)/L**. Is this a coincidence?
A firm's production function is Q(L) = 12L² – L³, where L denotes the number of workers (“labor"), with L € [0, 200]. (a) What size of the work force (L*) maximizes output, Q(L)? (b) What size of the work force (L**) maximizes output per worker, Q(L)/L? (c) Note that Q'′(L**) = Q(L**)/L**. Is this a coincidence?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Problem 2.
20
A firm's production function is Q(L) = 12L² - L³, where L denotes the number
of workers ("labor"), with L = [0, 200].
(a) What size of the work force (L*) maximizes output, Q(L)?
(b) What size of the work force (L**) maximizes output per worker, Q(L)/L?
(c) Note that Q'(L**) = Q(L**)/L**. Is this a coincidence?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a46b8d2-68f8-4ff5-85d9-0145753bf32f%2F5a4b3961-bfee-459a-a0d8-983928a13ec8%2Fbdgtgvv_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2.
20
A firm's production function is Q(L) = 12L² - L³, where L denotes the number
of workers ("labor"), with L = [0, 200].
(a) What size of the work force (L*) maximizes output, Q(L)?
(b) What size of the work force (L**) maximizes output per worker, Q(L)/L?
(c) Note that Q'(L**) = Q(L**)/L**. Is this a coincidence?
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