A competitive firm reaches the minimum of the long$-$run average cost when it

operates with the short$-$run cost function $C=y^3-20y^2+100y+8000,$ where $y$ is the

production of the firm. If the market demand is given by $x=2500-3p,$ where $x$ is the

quantity demanded by consumers and $p$ is the price. Calculate the long$-$run competitive

equilibrium. If the competitive industry faces an increase in demand such that the new

demand is given by $x=3000-3p,$ what are the effects of the increase in the demand in the

short run and in the long run?