A firms technology for producing its output from labor l, Microeconomics

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A firms technology for producing its output from labor l

A firm's technology for producing its output from labor (L) and capital (K) is Q =(?4LK + K^2) where |MRTSLK| =2K / 2L+K. The wage rate is $2 per unit of labor and the cost of capital is $5 per unit of capital. The firm is initially producing 30 units of output and capital is fixed in the short run. What are the short-run and long-run supply functions of the firm? (You may assume fixed costs are sunk in the short run.)

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Microeconomics: A firms technology for producing its output from labor l

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