Question

Morgan and Doyle have a business. The production function for that business can be described by the following expression: Y=LL2, where L = hours of work put in by Morgan and L2 = hours of work put in by Doyle. This production function exhibits: O constant returns to scale. increasing returns to scale, i.e., when doubling all inputs increases output by more than double. decreasing returns to scale, i.e., when doubling all inputs increases output by less than double. O diminishing returns to scale.

Answer 1

The given production function is:
$\dpi{80} \fn_phv \small f(L_1,L_2)=L_1L_2$

To check for returns to scale, we'll observe the effect on output when both inputs increase by $\dpi{80} \fn_phv \small \alpha$ times.|
$\dpi{80} \fn_phv \small f(\alpha L_1,\alpha L_2)=\alpha L_1\alpha L_2=\alpha^2(L_1L_2)=\alpha^2f(L_1,L_2)$
Increasing inputs by $\dpi{80} \fn_phv \small \alpha$ times increases output by more than $\dpi{80} \fn_phv \small \alpha$ times. Hence, the production function exhibits increasing returns to scale. B is correct.