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).

b)maximum production level

ML=MC,where MC =0,then

ML=$\frac{dq}{dl}$𝟏𝟎,𝟎𝟎𝟎𝑳−𝟑𝑳$^2$

=10,000-6l

therefore

10,000-6l=0

6l=10,000

l=1667

Q=10,000l-3l$^2$

=(10000$\times$1667)-(3$\times$1667$^2$ )

16,666,666.67-8,336,667

Q=8,329,999.67

c)at maximun,labor

ML=MC,where MC =0,then

ML=$\frac{dq}{dl}$𝟏𝟎,𝟎𝟎𝟎𝑳−𝟑𝑳$^2$

=10,000-6l

therefore

10,000-6l=0

6l=10,000

l=1667