The total revenue and total cost function that faces firm A are:

TR=30Q

TC=100+8Q+0.01Q^2 (Note: Q^2 is q-squared)

What is firm's A profit maximizing quantity (Q)?

 

Answer:

The profit maximizing quantity is 1100 units.

Profit is maximized at the point where Marginal Revenue equals Marginal Cost.

We get marginal revenue and marginal cost by differentiating the total revenue and total cost function with respect to quantity.

TR=30Q

TC=100+8Q+0.01Q^2

Marginal Revenue=30

Marginal Cost=8+0.02Q

At the profit maximizing condition:

30=8+0.02Q

30-8=0.02Q

22=0.02Q

Q=22/0.02

Q=1100 Units.