Maximising levels of capital, Econometrics

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A perfectly competitive firm hires its machines at a constant rental rate of r = 5 euros per unit and its workers at a constant wage rate of w = 4 euros per unit. It can also sell as much output as it wishes at the ruling market price of P = 40 euros. The firm's production function is given by:  

 Q = K0.25 L0.5

where L  is labour and K  is capital.

(a) If the firm wishes to maximise profits, write down the constrained maximum problem that the firm faces.

(b) Determine the profit maximising levels of capital, labour and output. 


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