A Firm's Production Function Is Given By $Q = K L$

question 59

Multiple Choice

A firm's production function is given by $Q = K L$ . The marginal products of labor and capital are, respectively, $M P _ { L } = K$ and $M P _ { K } = L$ . The wage rate of labor 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 yields a cost of exactly $\$ 1000$ ?

• A) \(( 10,45 )\)
• B) \(( 25,50 )\)
• C) \(( 50,25 )\)
• D) \(( 20,40 )\)

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Definitions:

Long-Run Equilibrium

A state in which all factors of production and variables in a market are in balance over a longer period, with no external pressures prompting change.

Decrease in Demand

A downward shift in the demand curve, indicating that consumers are willing to purchase less of a good or service at each price point.

Resource Prices

Refers to the costs associated with inputs used in the production of goods or services, such as raw materials, labor, and capital.

Market Demand

The total quantity of a product or service that all consumers in a market are willing and able to purchase at various prices.