(i) A competitive firm's short run total cost function is given by
TC = Q2 + 40 Q + 81
(a) Determine the range of prices for which the firm incurs a loss but continues to produce. Also determine the range of prices for which the firm earns a profit.
(b) Calculate the profit maximizing output and the resulting profit when price is $100.

(ii) 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 = 1/3Q^3  6Q^2 + 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.

(iii) Suppose that Saudi Arabia lets other members of OPEC sell all the oil they want at the existing price which the Saudis set and other members accept. The daily world demand for OPEC oil is given by:
P = 88 2Q
where P is the price per barrel of oil and Q the total quantity of OPEC oil (in millions of barrels per day). The supply function for other members of OPEC who behave like a %u201Ccompetitive fringe is given by:
Qr = .6P

The Saudis cost of production of oil is given by:
TCs = 15Qs +20
where Qs is the daily output of oil produced by the Saudis.

Calculate the price that Saudi Arabia will set to maximize its own profit. Also calculate the optimal output and profit of the Saudis. Determine the output produced by other members of the OPEC as well as the total market output.