You are the oil minister of one of 5 key OPEC countries. The world demand for oil can be reduced to Q = 100 – p and therefore p = 100 – Q (where p is dollars and Q is in millions of barrels/day). The TC of production for you and all your OPEC brethren is 10q. Assume that each of the OPEC countries has plenty of oil so each can sell as much as it wants.
a. Given that there are 5 identical countries, each with a TC(q) = 10q, derive the aggregate profit maximizing quantity for the cartel (e.g. the total production from all 5 countries that would maximize the sum of all your profits).
b. Assume that each of the 5 firms gets a production quota equal to 1/5 the total supply you derived in part a. Further assume that each of the other countries is true to the agreement and produces at their quota. Derive the Residual Demand for your country. (this would be the demand left over after all the production from all the other countries is accounted for).
c. You are considering cheating on the rest of the cartel, what would your optimal production quantity be – assuming everyone else sticks to the agreement and therefore your residual demand looks like the answer to part b. This is your Best Response.
c. In a graph, show the response functions of firm 1 and firm 2 and identify the Cournot equilibria. One axis of the graph should be the output of firm 1 and the other axis the output of firm 2.