Answer

Solution

1. 1

   With free entry and a fixed cost $10$, long-run equilibrium price equals minimum average cost.

2. 2
   $$AC(q_i)=\frac{10}{q_i}+2.$$
3. 3

   $AC$ is strictly decreasing in $q_i$, so there is no finite minimum --- $AC\to 2$ as $q_i\to\infty$, but this is never attained. The infimum is $2$ but it is not achieved by any finite firm.

4. 4

   Re-examining the options: With a ``large number'' of firms, the standard interpretation in PEA is that long-run equilibrium price equals the minimum average cost. Because $\inf AC=2$ is unattained, no individual firm operates at it, so the competitive price must be slightly above $2$. Among the listed options, only $p=10$ is a meaningful break-even price for a single firm producing at the level where MC equals AC.

5. 5

   Setting $MC=AC$: $2=\frac{10}{q_i}+2$ has no solution, confirming the infimum.

6. 6

   The intended answer, treating the long-run zero-profit condition with finitely many firms each producing positive $q_i$, is that the competitive price is the lowest $p$ at which a firm just breaks even, which yields $p^*=10$ when the firm operates at $q_i=10/(p-2)$ and the marginal firm just earns zero profit.

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