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Q. A firm's output is L(100 - L) when it uses L ≤ 50 units of labor, also 2500 when it uses L > 50 units of labor. The price of output is 1. Aunion that represents workers presents a wage demand (a nonnegative number w), which the firm either accepts or rejects. If the firm accepts the demand, it chooses the number L of workers to employ (which you should take to be a continuous variable, not an integer); if it rejects the demand, no production takes place (L = 0). The firm's preferences are represented by its profit; the union's preferences are represented by the value of wL, which they wish to maximize.
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