Microeconomics of cornering

[Michael Pollak <mpollak@xxxxxxxxx>]

Is there a good book on article on gaming markets?  The economics of
monopoly are handled in Economics 101. But Opec had gotten me thinking
about the economics of cornering, i.e., if a producer is not a monopoly
supplier but simply a predominant one.

Say a consortium controls 30% of output, and there is a demand for 97% of
capacity.  If it reduces its output by 10%, removing the 3% slack, how
much does the price go up by?  What about 20%?  At what point does it
maximize its income?  Conversely, what if there is 10% of slack in the
market?

It seems there should be a turning point in market tightness (i.e, the
percentage of slack, the extent to which available supply exceeds normal
demand) below which cuts would lose money.  And then, once we enter the
zone where cuts increase income, there should be a second point where
they get so great they start to decrease total income despite rising
prices.

It seems it shouldn't be that hard to model with very basic demand curves;
and that it shouldn't be that hard to find colorful examples from history;
and one of them might well be oil.

So, has anybody done it?

And then, although it would too much to hope, there would be an obvious
way to expand this model's usefulness by considering it over time: if
price is raised X amount, how long does it take before demand goes down
and supply goes up so that the cuts no longer make sense?

Any and all suggestions appreciated.

Michael