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A firm uses labor as an input and produces with the following technology: Y = F (L) = AL^ where is less than 1. The price of labor (wage) is constant...

A firm uses labor as an input and produces with the following technology: Y = F (L) = AL^α where α is less than 1. The price of labor (wage) is constant and is given by w. Firm can sell each unit produced at a price p. There is a fixed cost F independent of how much the firm is producing.

(a) What is the returns to scale property of this production function?

(b) Write down the profit function of the firm.

(c) Solve for the formula of optimal amount of labor that the firm will use.

(d) When F increases to 2F , given the firm is still producing, does the optimal amount of labor change? Why? 

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