Suppose TC = 100 + 10q + q^2, so that MC = 10 + 2q (where q is the firm's quantity of output). Let's work with this setup to get a feel for what the curves look like.

1. Find fixed costs, and find the equation for average costs (AC).
2. Suppose this firm faces a price of 30.What is its profit-maximizing output quantity?
3. Find the q such that AC is minimized.
4. Make a graph with AC and MC accurately enough to show points of interest.
5. Suppose instead that TC = 100 + 10q. What is the q that minimizes average costs (does it reach a minimum)?What does this entail about how many firms "fit" in this market? Explain. [Note that marginal cost is no longer given by MC = 10+2Q]