Determine a market with demand function P = 20 - Q. There are 30 potential competing firms with identical cost functions C(q) = q, but to enter the market they each need to pay an entry cost of 2. In particular, each firm first decides whether it will pay the cost to enter the market; no firm can see others' decisions in this phase. Then the firms who enter the market play Cournot competition.
1. What are their profits after taking into account the entry cost if there are two firms in the market?
2. Would it be profitable for a third firm to pay the cost to enter the market?
3. Determine the numbers of firms would be in the market in the SPNE?