Suppose that the long-run world demand and supply elasticities of crude oil are -0.906 and 0.515, respectively. The current long-run equilibrium price is $30 per barrel and the equilibrium quantity is 16.88 billion barrels per year.

a. (10 points) Derive the (linear) long-run demand and supply equations.

b. (5 points) Suppose the long-run supply curve you derived above consists of competitive supply plus the quantity of OPEC supply.

If the long-run competitive supply (not including OPEC's production) is: QS = 7.78 + 0.29p, what must be OPECs level of production in this long-run equilibrium to maintain the price of $30?