Consider a model for world oil market, where OPEC fulfils a portion of the world oil demand and non-OPEC producers supply the rest. That is, the

demand for OPEC oil (D^O ) is equal to world demand (D^w) minus non-OPEC supply (S^NOP):

D^O = D^w - S^NOP.

Suppose the world demand for oil equation is specified as

D^w= 80 - 1.25 P

and the non-OPEC supply equation is

S^NOP=10 + 0.5 P.

a.Derive the demand equation for OPEC oil.

b.Assume OPEC operates as a monopoly and its marginal cost of oil production is zero. What is the profit-maximizing level of production for OPEC [Hint: Use the inverse demand function from (a)]?

c.What will be the market oil price?

d.What will be the total world demand and the OPEC market share?

e.If the average cost of oil production is $10 per barrel in OPEC, how much will be the OPEC's total profit?

f.Suppose that new technologies decrease the production cost in the non-OPEC producers. Which one of the three equations (D^w , S^NOP , D^O ) will change to reflect the new condition? What impact will this have on

-the oil prices?

-OPEC's profit?

-OPEC's market share?