Economics Stack Exchange Archive

Theory of the firm

What is the answer to this and why?

Suppose that a firm has fixed costs $F$ and variable costs given by $y+y^2$ where $y$ is output.

Assuming that this firm is operating in a competitive industry with unrestricted entry and exit, and firms all have a common production technology, what would be its output in long run equilibrium?

Answer 544

For any profit maximising, perfectly competitive firm, the following are true:

  1. $MR=MC$ (profit maximising condition)
  2. $P=MR$ (This is an identity; a characteristic of perfect competition)
  3. $P=ATC$ (This is the long-run zero profit condition)

Together the three give you $MC=ATC$. The quantity at which the marginal cost equals the average total cost is your long-run equilibrium quantity.

In your example, $ATC=TC/y=1+y+(F/y)$ and $MC=1+2y$. Therefore, $y^*=\sqrt{F}$.

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