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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.

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closed as off-topic by Giskard, Bayesian, Herr K., Regio, E. Sommer May 1 at 10:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • $\begingroup$ 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. $\endgroup$ – Bayesian Apr 30 at 10:05
  • $\begingroup$ @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. $\endgroup$ – Abhi Minhas Apr 30 at 10:20
  • $\begingroup$ No, I am confident that that's it. $\endgroup$ – Bayesian Apr 30 at 11:53
  • $\begingroup$ (-1) There is no question... $\endgroup$ – Giskard Apr 30 at 13:07
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In a perfectly competitive industry, we have $p=MC$ in equilibrium.

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 regardless of how demand looks like. That is, firm A cannot operate in a perfectly competitve industry.

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.

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