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The production function is given by y=L1/2, where y is the output, and L is the...

The production function is given by y=L1/2, where y is the output, and L is the amount of labor input. Assume the wage rate is w so that the cost of using L unit of labor input is wL. Let p denote the unit price of the output. Note that w and p are exogenously given.

(1) Find the function for the profit (in terms of p, w and L).

(2) Find the optimal choice of labor input and the corresponding maximized profit (in terms of p and w).

(3) Suppose that both wage rate, w, and the price, p, double. How will this affect the firm's optimal decision? Explain.

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