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:

Value Of Marginal Product

describes the additional revenue generated from employing one more unit of input, such as labor or capital.

Wage Rate

The amount of compensation a worker receives per unit of time or per task performed, often expressed per hour or per piece.

Supply Of Labor

The total number of workforce hours available for work in an economy at a given wage rate.

Perfectly Elastic

A situation where the quantity demanded or supplied changes infinitely in response to any change in price.