Answer to Question #254396 in Microeconomics for Sam

Question

Do the production functions below exhibit diminishing returns to labor (to get full credit, you will need to show mathematically whether or not these functions exhibit diminishing returns to labor –for example, answering only “yes” will get you no credit)?

(a) Q = F(K,L) = √1000K^3.5L². Make sure to 1) show the mathematical steps (3 pts) and 2) explain your answer (2 pts).

Answer 1

$Q = F(K,L)$

Q is the quantity of output.

F = production function.

K = Units of capital

L=Units of Labor

$Q=\sqrt(1000 K\\^3\\^.\\^5L\\^2)$

For example:

Originally, let K be 25 and L be 25

$Q=\sqrt(1000\times 25\\^3\\^.\\^5 \times 25\\^2)$

$Q = 220971$

When labor is increased to 30, the new Q will be:

$New\ Q=\sqrt(1000\times 25\\^3\\^.\\^5 \times 30\\^2) \\ New\ Q = 265165$

Therefore, the production function will exhibit diminishing returns to labor as the new quantity output is greater than the original quantity.