Say Company A has a monopoly producing product E, at a constant marginal cost of $3$ USD. Say the ideal number of units produced is $1$ unit which produces a profit of $2$ USD (=$P_{A}$).
Next, Company B wants to enter the market and produce product E at a marginal cost $3$ USD, but it has initially invested $\frac{1}{2}P_{A}$ in order to enter the market.
Question:
$1.$ Under Cournot Competition, should Company B enter the market. Why/Why not?
$2.$ Under Bertrand Competition, should Company B enter the market. Why/Why not?
Ideas:
$1.$ No, since we are in Cournot competition, the price is determined by the total units that both Company A & B produce together. If Company B were also to produce, it would drive the price down as a result of excess supply, eventually forcing the price below the marginal cost, thus not profitable
$2.$ Yes, the price is driven down until the marginal cost. Although Company B will earn $\frac{1}{2}P_{A}$ less than company A.
Do my answers suffice, or rather, are they correct, and touch on the right point?