# Deriving Wages in a Competitive Economy

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Suppose a firm's production function is given by Q=12L-L^2 for L=0 to 6, where L is labour input per day and Q is output per day. Derive and draw the firm's demand for labour curve if the output sells for $10 in the competitive market. How many workers will the firm hire when the wage rate is $30 per day? $60 per day? (Hint: the marginal product of labour MPL is 12-2L).

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#### Solution Preview

The firm's production function is given to be Q = 12L - L^2. Differentiating this with respect to L gives us the marginal product of labor that is MPL = 12 - 2L.

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#### Solution Summary

Given a production function how do you determine the wage in a given competitive economy? This solution provides an answer to this question using a typical quadratic production function.

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