The fringe supply refers to the supply from new firms that enter a market that was initially a monopoly with only one producer. The new firms entering the market are able to satisfy some of the demand but are not at a level playing field with the dominant firm. As a result of having been the only producer when the monopoly existed, the dominant firm can produce at a lower price and is able to satisfy a greater demand.
In the problem, the fringe supply curve is defined by the equation: Q = -1 + 0.2*P and the demand is Q = 11 - P. As there is no dominant firm, the fringe producers are no longer price takers but instead are in a position to deliver products at a rate that suits the cost incurred by them and which has to be accepted by the consumers.
The equilibrium price in this case is determined by solving -1 + 0.2*P = 11 - P or 1.2P = 12 which gives the equilibrium price as 10 and the corresponding equilibrium output is 1.