Question

Consider the following production function q= 24LK + 512-6 Assume capital is fixed at K =25. In what range of employment does the marginal product of labor exhibit positive but diminishing marginal returns? The marginal product of labor is diminishing but positive when L ranges from to . (Enter numeric responses using integers)

Answer 1

Ans: We have production function:

$q=24L(25)+5L^{2}-(\frac{1}{3})L^{3}=600L+5L^{2}-(\frac{1}{3})L^{3}$

$MPL=\frac{dq}{dL}=600+10L-L^{2}$

It is positive till:

$600+10L-L^{2}>0$

gives: L < 300

MPL is diminishing when:

$\frac{dMPL}{dL}=10-2L<0$

gives: L > 5

Ans: Range: 5 to 300.

If you are satisfied with the answer, please provide a positive rating. Feel free to comment in case of queries.

Have a nice day ahead!