Propylene is used to make plastic. The propylene industry is perfectly competitive and each producer has a long run total cost function given by
LTC = 1 /3 Q3- 6Q2 + 40Q
Where Q denotes the output of the individual firm.

The market demand for propylene is
X = 2200 – 100P
Where X and P denote the market output and price respectively.
(a) Calculate the optimal output produced by each firm at the long run competitive equilibrium (LRCE).
(b) Calculate the market price and market output at the LRCE.
(c) Calculate the number of firms at the LRCE.
(d) Suppose the demand curve shifts to
X = A – 100P
Where A is a positive number.
Calculate how large A would have to be so that in the new LRCE, the number of firms is twice what it was in the initial equilibrium.