Question

Production of burgers at Hamburger Heaven is given by the following production function: Hamburgers per hour: q = 2√(LK). Does this function exhibit constant, increasing, or decreasing returns to scale in the context of burger production at Hamburger Heaven?

Answer 1

The question addresses the returns to scale for Hamburger Heaven's production function q = 2√(LK). By scaling L and K and observing the proportionality of output, we can conclude that the production function exhibits constant returns to scale.

Step-by-step explanation:

The question concerns the nature of returns to scale for the production function q = 2√(LK), where 'q' represents the number of hamburgers produced per hour, 'L' represents labor, and 'K' represents capital.

When analyzing returns to scale, the production function is multiplied by a scalar to see how output (q) reacts. If output increases by the same proportion as the inputs, it exhibits constant returns to scale. If output increases by more than the inputs, it exhibits increasing returns to scale. If output increases by less than the inputs, it exhibits decreasing returns to scale.

Let's multiply both inputs labor (L) and capital (K) by a scalar 't'. The new function becomes q' = 2√(tL * tK) = 2t√(LK). Since 'q' increases proportionally with 't', Hamburger Heaven's production function shows constant returns to scale.