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Zucchini  production involves two inputs, capital (measured by the size of the field in acres) and labor (measured in worker hours)

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Zucchini  production involves two inputs, capital (measured by the size of the field in acres) and labor (measured in worker hours). In China, production is typically described with the following production function: 

Q= 43+3LK +4L²+4K²

The average price of labor is $11.60 per hour and the price of capital is $145.00 per acre. 

 

A. At the optimal mix of capital and labor, what is the relationship between the two inputs? Solve for one in terms of the other. 

 

B.  A more accurate production function would have three inputs: skilled labor (measured in worker hours), less skilled labor (also measured in worker hours), and capital (measured in acres).  the following structure for the production function is: 

Q= 24 +4S² U² + 2S²K² +3U³ +5S³K +USK 

 the price of skilled labor is $22 per hour and the price of unskilled labor is $9.70. The price of capital is still $145 Use this information to write the optimal input mix condition for these three inputs. 

 

Please ANSWER A & B