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

question 19

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 $r = \$ 20$ . What is the most efficient combination of labor and capital $( L , K )$ that also results in a total cost level of exactly $\$ 1,200$ ?

• A) \(( 20,50 )\)
• B) \(( 25,47.5 )\)
• C) \(( 30,45 )\)
• D) \(( 40,40 )\)

---

Definitions:

\(k ^ { 3 }\)

Represents the cube of a variable \(k\), equivalent to multiplying \(k\) by itself twice (\(k*k*k\)).

\(k + 8\)

An algebraic expression representing the sum of a variable, \(k\), and the number 8.

\(d = \frac { 3 } { 7 }\)

Represents a specific value of the variable d, which is equal to the fraction three-sevenths.