Sunday, January 20, 2013

OPEC in Cournot Equilibrium

Here is my Alzheimer's problem of the day.

Assume there are only two producers of oil, OPEC and non-OPEC.  The costs of production for a barrel of oil for non-OPEC producers is $10 and OPEC producers is $5.  The demand curve for the world oil is given by: P = 65 - ((Qo + Qn)/3) where Qo is OPEC's production and Qn is non-OPEC.  Calculate the rivals best response functions, find the OPEC quantity, price, and profit.  Do the same for non-OPEC.

I hastily graphed the reaction functions and found 50 for non-OPEC and 65 for OPEC.  Direct computation yeilds a price of $26 2/3.  The profit is equal to PQ - TC.  Profit equals $1408 1/3. Non-OPEC equals $833 1/3.

I loved working this problem.  I can't believe the amount of trouble I had with fractions.  I am always amazed how the basics seem to disappear when the level of difficulty increases.  The question I have for educators is "what level of rigor is needed for learning?"  What I mean is should teachers make the problems so hard that students must take hours to solve the problem or show the work be easy so that a lot more ground can be covered?

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