Question 3. A manufacturer has modeled its yearly production function P (the value of its entire production, in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0.65 0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). ӘР Ət (a) Express the rate of change of production 07-2 in time, in terms of the rate of change of the labor force and the rate of change of the capital in time. (b) Suppose that when L = 30 and K = 8, the labor force is decreasing at a rate of 2000 labor hours per year and capital is increasing at a rate of 500,000 per year. What is the rate of change of production per year?

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
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Question 3. A manufacturer has modeled its yearly production function P (the
value of its entire production, in millions of dollars) as a Cobb-Douglas function
P(L, K) = 1.47L0.65 0.35
where L is the number of labor hours (in thousands) and K is the invested capital
(in millions of dollars).
ӘР
Ət
(a) Express the rate of change of production 07-2 in time, in terms of the rate of
change of the labor force and the rate of change of the capital in time.
(b) Suppose that when L =
30 and K = 8, the labor force is decreasing at a rate
of 2000 labor hours per year and capital is increasing at a rate of 500,000 per
year. What is the rate of change of production per year?
Transcribed Image Text:Question 3. A manufacturer has modeled its yearly production function P (the value of its entire production, in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0.65 0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). ӘР Ət (a) Express the rate of change of production 07-2 in time, in terms of the rate of change of the labor force and the rate of change of the capital in time. (b) Suppose that when L = 30 and K = 8, the labor force is decreasing at a rate of 2000 labor hours per year and capital is increasing at a rate of 500,000 per year. What is the rate of change of production per year?
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