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What is the demand for labor from the production function Q = 12L - L^2?

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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? (Hint: The marginal product of labour, MPL is 12 - 2L).

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This solution shows how to calculate the demand for labor in the attached Word document.

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SOLUTION:

Given,
Q=12L - L^2 for L=0 to 6

MPL=dQ/dL= 12 - 2L

The demand curve for labor is ...

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