Problem
Suppose an industry produces an undifferentiated product for which market demand is given by X = A-P. There are many potential producers for this product, each of whom has a production function of the form: Fixed costs of F must be paid for being in business, and the marginal cost of a unit of production is a constant k. We imagine that firms decide whether to enter the industry under the supposition that, after all the firms that are going to enter do so, competition will be according to the Cournot model. That is, if N firms are in the market each has Cournot conjectures. An equilibrium is achieved with N firms in the industry if each firm, having its Cournot conjectures, does no worse than break even, whereas if another firm entered and made this an N + 1 firm Cournot oligopoly, all the firms would lose money. What is the equilibrium in this case? What (if anything) would be the equilibrium if firms had Bertrand conjectures throughout?
(Note well: The number of firms is set and then firms compete. The exercise is not that firms charge a price, say, and then other firms can enter assuming firms already in the industry will stick to that price. But as long as we're sketching this alternative, what would be the Cournot and Bertrand equilibria with entry under this alternative scenario?)
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.