I'm so stuck with an exercise about Cournot game and was hoping if someone could help me out here. Would appreciate all the help. This is the exercise:
Consider the market for Blue Turtle (a new de-energizer) in which demand $Q$ is related to price $P$ by $P(Q) = Q^{-0.5}$. In this market there are m identical producers, say firm 1; 2; up to m which can produce any non-negative quantity of Blue Turtle say $q$ at costs $C = q^2$. Assuming these firms are playing as in a non cooperative (Cournot) game. Determine the market price for Blue Turtle and the quantities produces by each of these firms? Show that price falls if the number of producers grows.
thanks again.