022 Sample Final A, Problem 8

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Find ther marginal productivity of labor and marginal productivity of capital for the following Cobb-Douglas production function:

(Note: You must simplify so your solution does not contain negative exponents.)

Foundations:  
The word 'marginal' should make you immediately think of a derivative. In this case, the marginal is just the partial derivative with respect to a particular variable.
The teacher has also added the additional restriction that you should not leave your answer with negative exponents.

 Solution:

Marginal productivity of labor:  
we take the partial derivative with respect to :
Marginal productivity of capital:    
Now, we take the partial derivative with respect to :


Final Answer:  
Marginal productivity of labor:
Marginal productivity of capital:

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