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) \(( 40,40 )\)

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Definitions:

Production Possibilities Curve

A graphical representation showing the maximum number of goods or services that can be produced with a given set of resources and technology.

Resources Are Scarce

The principle that the availability of natural, human, and capital resources is limited, necessitating choices about their allocation and use.

Normative Statements

Statements that express opinions on how the world ought to be, involving value judgments rather than factual claims.

Expressions Of Facts

Statements that aim to convey information about reality or actual events without alteration.