Suppose That the Long-Run World Demand and Supply Elasticities of Crude

Essay

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.Derive the (linear)long-run demand and supply equations.
b.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:
Q_S = 7.78 + 0.29p,
what must be OPECʹs level of production in this long-run equilibrium to maintain the price of $30?