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Suppose a firm is operating in perfectly competitive product market where the price of its output can be sold at the price p=$10. The firm can hire any number of workers at the wage of W=$50. The total product (or short-run production function) is given by Q=100*L-2.5*Lsquared, and the marginal product of labor curve is MPL=100-5*L. Using this information, determine the optimal number of workers the firm will hire, the quantity of output it will produce, and the profit it will make in the short run. Assume that there are no costs to capital.
Question: Explain why the free rider problem makes it difficult for perfectly competitive markets to provide the Pareto efficient level of a public good.
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