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(a) Suppose a firm is a price taker in all markets. Write down the Necessary First Order Condition of the firm's short-run labor demand problem, assuming a generic production function Q = F(K,L). Write down the Su- cient Second Order Condition. Interpret the intuition behind the Second Order Condition. (very brief interpretation -- can be one sentence)
(b) Suppose that F (K, L) = θ L. The firm does not use capital. Suppose also that pθ > w, where w is the wage rate and p is the price of output. Explain why the short-run labor demand problem has no solution for a price taker. Include some intuition - not only mathematical reasoning. Connect this to your discussion in part a).
(c) Now suppose that instead of being a price-taker, the firm is a monopoly in the output market (but a price taker in all input markets). Explain why there may be an interior solution to this problem even though there is no solution in part (b) with the same production function. No need to solve the model for L*, but you can set up the problem if you think it will help your explanation.
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