A profit-maximizing competitive firm uses just one input, x.Its production function is q = 8x^1/2.The price of output is $24 and the factor price is $8.The amount of the factor that the firm demands is

A) 11.
B) 128.
C) 144.
D) 27.71.
E) None of the above.

Question

Shawn Forrest · Accepted Answer

Final Answer : C, Explanation :  To find the profit-maximizing amount of input x, set the marginal revenue product (MRP) equal to the factor price. MRP is the derivative of the production function with respect to x, multiplied by the price of output. The derivative of q = 8x^(1/2) is (4/x^(1/2)), so MRP = 24 * (4/x^(1/2)). Set this equal to the factor price of $8: 24 * (4/x^(1/2)) = 8. Solving for x gives x = 144.

A profit-maximizing competitive firm uses just one input, x.Its production function is q = 8x^1/2.The price of output is $24 and the factor price is $8.The amount of the factor that the firm demands is

A) 11.
B) 128.
C) 144.
D) 27.71.
E) None of the above.

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A profit-maximizing competitive firm uses just one input, x.Its production function is q = 8x1/2.The price of output is $24 and the factor price is $8.The amount of the factor that the firm demands isA) 11.B) 128.C) 144.D) 27.71.E) None of the above.

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Related questions

A profit-maximizing competitive firm uses just one input, x.Its production function is q = 8x^1/2.The price of output is $24 and the factor price is $8.The amount of the factor that the firm demands is

A) 11.
B) 128.
C) 144.
D) 27.71.
E) None of the above.