PROFIT for a monopolist`s product, the cost function is

c=0.004q^3 + 20q + 5000

and the demand function is

p=450 - 4q

Find the profit-maximizing output.

Please assist step by step?(Worried)

Printable View

- Oct 12th 2008, 08:01 AMAndrew1380Differentiation - Calculus help!
PROFIT for a monopolist`s product, the cost function is

c=0.004q^3 + 20q + 5000

and the demand function is

p=450 - 4q

Find the profit-maximizing output.

Please assist step by step?(Worried) - Oct 13th 2008, 04:31 AMCaptainBlack
Revenue is:

$\displaystyle pq =450q -4q^2$

profit is revenue minus costs:

$\displaystyle pr(q)=450q -4q^2 - (0.004q^3 + 20q + 5000)=-0.004q^3-4q^2+430q-50000$

Now find the extrema of this by differentiating and setting the derivative to zero and solving for the critical values of q, the critical value that maximises the profit will be the profit maximising output.

q=50 and profit=6000

CB