Long run equilibrium An industry has a total cost function : TC=$4Q^2+100Q+100$ . Where $Q$ is the quantity produced. They are asking me to find the long run equilibrium price. How do I find it? What I've found is that i calculate the sratc(short run average total cost) and then solve for Q (while equating the derivative of sratc to 0), then find Price after substituting Q. Is this the way to go?

Hint: In a competitive market the firms produce on the long run at a level where the average total cost function has its minimum. Thus you have to find the minimum of

$$\frac{TC(Q)}{Q}=4Q+100+\frac{100}{Q}$$

The minimum can be found by setting the derivative equal to $0$. In this case it is good to remember that $Q$ is defined for non-negative values only. The picture below shows the course of the average cost function.

![enter image description here](

The price of the product will be equal the solution.