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:
QS = 7.78 + 0.29p,
what must be OPEC?s level of production in this long-run equilibrium to maintain the price of $30?
a. First derive the slope of the demand curve:
-.906 = -b(30/16.88 ) → b = .510
Find intercept: 16.88 = a - .510(30 ) → a=32.18
So demand is Q = 32.18 - .510p
Repeat this for supply:
0.515 = d(30/16.88 ) → d = .290
16.88 = c + .290(30 ) → c = 8.18
So Supply is Q = 8.18 + .290p
b. The world supply = 8.18 + .290p + QOPEC
Setting equal to demand at a world price of 30 solves for QOPEC
.818 + .290(30 ) + QOPEC = 32.18 - .510(30 )
QOPEC = 7.362
OPEC will need to supply 7.362 billion barrels per year.
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