$P(Q)$ represents a market where demand $Q$ is related to price $P$ by $P(Q) = Q^{-\frac{1}{2}}$ In this market there are $m$ identical producers, say firm 1, 2, up to $m$ which can produce any non-negative quantity say $q$ at costs $q^2$
We make the profit function: $\Pi=Q^{-\frac{1}{2}}\cdot q -q^2$ For firm $q_i$: $\Pi=q_i\cdot\sum q_{-i} - q_i^2$ Deriving and set to $0$: $q_i=\frac{2m-1}{4m}$ And $q*=\frac{1}{m-1}$
Is this ok? I just don't know anymore, have been working for hours on this......