# Which of the following firms can operate in a perfectly competitive industry? [closed]

This was a question in a test. I am looking for an explanation for the answer.

Firm A's cost of producing output y > 0 is c(y) = 1 + y

Firm B's cost of producing output y is c(y) = y(1-y)^2

Answer: Firm B can operate in a perfectly competitive industry but A cannot.

• In a perfectly competitive industry, p=MC. If firm A prices at marginal cost, each sold unit contributes zero to profits. Because it also has to pay fixed cost 1, it makes a negative profit in a competitive market. – Bayesian Apr 30 '19 at 10:05
• @Bayesian i also thought along the same lines. Do you think there is any chance that there might be something more that we're missing out? Maybe I'm just stressed idk. – Abhi Minhas Apr 30 '19 at 10:20
• No, I am confident that that's it. – Bayesian Apr 30 '19 at 11:53
• (-1) There is no question... – Giskard Apr 30 '19 at 13:07

In a perfectly competitive industry, we have $$p=MC$$ in equilibrium.
For firm B, you can calculate marginal cost as $$\frac{\partial c(y)}{\partial y} =1-4y+3y^2$$. Consider the increasing part of this function as the supply curve. Indeed you can find demand functions that intersect this function at a price leading to nonnegative profits. That is, firm B can operate in a perfectly competitve industry.