Question

3. The production function of a firm is described by the following equation 𝑸=𝟏𝟎,𝟎𝟎𝟎𝑳−𝟑𝑳 𝟐 where L stands for the units of labor.

a) Draw a graph for this equation. Use the quantity produced in the y-axis, and the units of labor in the x-axis.

b) What is the maximum production level?

c) How many units of labor are needed at that point?

Answer 1

a) The production curve

b) The Maximum production level

Find the marginal product

$\frac{\Delta Q}{\Delta L}$ $=10000-6L$

equate the MP to zero to find L

$10000-6L =0$

$L=1666.667=1667$

The maximum production is therefore;

$Q=10,000(1667)−3(1667)^2 =8333333$

c) The units of labour at this point is

1667 units as calculated above