2. Consider the Cobb-Douglas productivity function for a company given by f(x. y) = 125 x0.40.6 When x units of labor anf y units of capital are utilized a) Show that if the number of units of labor and the number of units of capital are both doubled, then the productivity itself also doubles b) Find the marginal productivity of labor and the marginal productivity of capital and evaluate them when 200 of units of labor and 150 units of capital are being used c) If the company wants to increase their productivity, should they invest more on labor or on capital? Explain

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Consider the Cobb-Douglas productivity function for a company given by
f(x. y) = 125 x 0.4 0.6
When x units of labor anf y units of capital are utilized
a)
Show that if the number of units of labor and the number of units of capital are both doubled, then the
productivity itself also doubles
b)
Find the marginal productivity of labor and the marginal productivity of capital and evaluate them when 200 of
units of labor and 150 units of capital are being used
c)
If the company wants to increase their productivity, should they invest more on labor or on capital? Explain
Transcribed Image Text:2. Consider the Cobb-Douglas productivity function for a company given by f(x. y) = 125 x 0.4 0.6 When x units of labor anf y units of capital are utilized a) Show that if the number of units of labor and the number of units of capital are both doubled, then the productivity itself also doubles b) Find the marginal productivity of labor and the marginal productivity of capital and evaluate them when 200 of units of labor and 150 units of capital are being used c) If the company wants to increase their productivity, should they invest more on labor or on capital? Explain
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