Assignment:
1. 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.
2. Southwest Airlines is by far the low cost carrier on the Sacramento to Los Angeles Air Travel Route. Their marginal costs are a constant $20 dollars per seat. All the other airlines (United, Delta, Alaska) have marginal costs of $100 per seat. The daily inverse demand for seats on this route is P(q) = 160 - Q, where Q is the number of seats offered by ALL airlines combined.
a. You are the Southwest marketing director and are in charge of setting prices. You know that all the other airlines with set quantity as if they were PERFECTLY COMPETITIVE. Draw your residual demand (e.g. demand left over after other airlines provide their supply of seats)
b. Derive the profit maximizing number of seats to provide on this route. How many seats do your competitors provide at this equilibrium quantity and price?
3. Two firms compete in the emerging market for energy drinks/cold medicine hybrids that feature caffine, alcohol, and cough suppressant. Consider that the two firms compete as Cournot competitors. Firm 1 has production cost of c1(q1) = (q1)^2. Firm two is less efficient and has costs of c2(q2) = 2(q2)^2.
The inverse demand for the good is given by P(Q) = 440 - 2Q, where Q=q1 + q2.
a. What is the best response function of firm 1 (as a function of q2)?
b. What is the best response function of firm 2 (as a function of q1)? Remember that the two firms ARE NOT THE SAME.