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Consider
the global market for crude oil, consisting of Saudi Arabia, Iran, and the rest
of the world.  Suppose that price-taking
consumers in the rest of the world have demand for crude oil given by:

.P = 2500 – 1.5Q

Assume that price-taking fringe
suppliers of crude oil in the rest of the world have marginal costs given by:

.p = 2000+0.4Q

Suppose that Saudi Arabia has
marginal costs given by:

,p = 50+0.1Q

And that Iran has marginal costs given
by:

.p = 100+0.2Q

Assume that neither Iran nor
Saudi Arabia has demand of their own

Suppose
that Saudi Arabia and Iran are contemplating forming a Cournot duopoly
cartel.  (Hint: assume residual demand
reflects case 3).

a.
What is the optimal amount of crude oil
that Saudi Arabia, Iran, and the rest of the world produces?

b.
What is the equilibrium price of crude
oil in the market?

c.
What is the mark-up charged by Saudi
Arabia and Iran?

d.
What are the profits to Saudi Arabia and
Iran?

e.
What is the share of Saudi Arabia’s
production to total duopoly production?

f.
How does the Cournot mark-ups compare to
the full enforcement (multi-plant monopoly consisting of Saudi Arabia and Iran)
mark-ups?

Now suppose instead that rest of world
fringe supply is given by:
Suppose
that Saudi Arabia and Iran are again contemplating forming a Cournot duopoly
cartel.  (Hint: assume residual demand
reflects case 1).

g.
What is the optimal amount of crude oil
that Saudi Arabia, Iran, and the rest of the world produces?

h.
What is the equilibrium price of crude
oil in the market?

i.
What is the mark-up charged by Saudi
Arabia and Iran?

j.
What are the profits to Saudi Arabia and
Iran?

k.
What is the share of Saudi Arabia’s
production to total duopoly production?

l.
How does the Cournot mark-ups compare to
the full enforcement (multi-plant monopoly consisting of Saudi Arabia and Iran)
mark-ups?

Compare your results for these two cases.  What insights might this question have for
the OPEC strategy game

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