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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Definitions:

Potential Output

The highest level of real gross domestic product (GDP) that can be sustained over the long term without increasing inflation, reflecting the maximum productive capacity of an economy.

Short-Run Aggregate Supply

The total production of goods and services in an economy at different price levels in the short-term, considering wages and resource prices as sticky.

Short-Run Aggregate Supply

The total production of goods and services in an economy at different price levels over a short period, during which some production costs are fixed.

Potential Output

The highest level of real GDP that can be sustained over the long term without increasing inflation.