Question

Consider a firm with the following production function 𝑸 = 𝟓𝟎𝟎𝟎𝑳 − 𝟐𝑳².

a. Find the maximum production level.

b. How many units of labor are needed at that point.

c. Obtain the function of marginal product of labor (𝑀𝑅𝐿).

d. Graph the production function and the 𝑀𝑅�

Answer 1

$Q=5000L-2L^2,$

$Q'=5000-4L,$

$Q'=0,$

$L=1250,$

$Q=3125000.$