The above figure shows the cost curves for a typical firm in a competitive market. Note that if p = 10, then MC = p at both q = 5 and q = 60. Can they both yield maximum profit? Explain

What will be an ideal response?

No, at q = 5, p = MC, but this is not profit maximization; it is profit minimization. Profits expand as output increases since MR > MC for higher levels of output. At q = 60, an increase or decrease in output causes profits to fall, so this is the profit-maximizing q. Thus one way of wording the "second order condition" for profit maximization is that MC must cut the demand curve from below.