Consider the market for Red Rambo (a new de-energizer) in which demand Q is related to price P by
P(Q) = Q ^ (-3) .
In this market there are 5 producers, say from 1 up to 5. Each firm i can produce any non-negative quantity of Red Rambo, say qi. larger than or equal to 1/10 at costs qi2.
So, there are no fixed costs and production starts at least at 1/10 . That is below 1/10 production costs are infinitely high. These firms produce identical products with no transaction costs. We assume that these firms are in a competitive market. Determine the market price and total quantity Q when these firms form a cartel at which they agreed to produce equal amounts.