A Firm's Production Function Is Given By $Q = K ^ { 2 } L$

question 72

Multiple Choice

A firm's production function is given by $Q = K ^ { 2 } L$ . The marginal products of labor and capital are, respectively, $M P _ { L } = K ^ { 2 }$ and $M P _ { K } = 2 K L$ . Further, the wage rate is $w = \$ 10$ and the rental rate of capital is $r = \$ 20$ . Suppose the firm wants to produce 27,000 units of output. What is the most efficient combination of labor and capital $( L , K )$ ?

• A) \(( 20,20 )\)
• B) \(( 30,30 )\)
• C) \(( 30,90 )\)
• D) \(( 90,30 )\)

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