Question

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consider the cobb - douglas production function:
$p(l,k)=23l^{0.4}k^{0.6}$
find the total units of production when $l = 15$ units of labor and $k = 19$ units of capital are invested. (give your answer to three (3) decimal places, if necessary.)
production = \\(\\) units.
enter an integer or decimal number more..
question help: video

Explanation:

Step1: Substitute L and K values

Substitute \( L = 15 \) and \( K = 19 \) into the Cobb - Douglas Production function \( P(L,K)=23L^{0.4}K^{0.6} \).
So we have \( P(15,19)=23\times(15)^{0.4}\times(19)^{0.6} \).

Step2: Calculate \( 15^{0.4} \)

Using a calculator, \( 15^{0.4}=e^{0.4\ln(15)}\approx e^{0.4\times2.70805}\approx e^{1.08322}\approx 2.953 \)

Step3: Calculate \( 19^{0.6} \)

Using a calculator, \( 19^{0.6}=e^{0.6\ln(19)}\approx e^{0.6\times2.94444}\approx e^{1.76666}\approx 5.843 \)

Step4: Calculate the product

Now, multiply the three values: \( 23\times2.953\times5.843 \)
First, \( 2.953\times5.843\approx17.255 \)
Then, \( 23\times17.255 = 396.865 \)

Answer:

\( 396.865 \)