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output, revenues, costs, and profits

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The Alex Co. uses two inputs, A and B, to produce boats. The production function for boats is given by
Q = A^0.5 x B^0.5, (or the square root of A multiplied times the square root of B)
and the marginal products of A and B are given by
MPa = 0.5Q/A
MPb = 0.5Q/B

The prices of inputs are given by Pa = $10 and Pb = $10
and the price of boats equals $30.

(a) If the Alex Co. has a total budget of $200 to spend on purchasing inputs, how many units of A and B should it hire?

(b)What will be its output, revenues, costs, and profits?

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This solutions finds output, revenues, costs, and profits.

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a)
We have budget equation as 10A+10B=200
Solving we get A=20-B ------1.

Also we know that for ...

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