# Demand and Supply

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1. 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 OPECʹs level of production in this long-run equilibrium to maintain the price of \$30?

Ed= -0.906 Es= 0.515
Equilibrium: Price = \$30 per barrel, Quantity= 16.88 billion barrels per year.
a. Derive the (linear) long-run demand and supply equations.

Q=a+bP P= (Q-a)/P
Supply:
Es=dQ/dP * P/Q  .515= dQ/dP *30/16.88 dQ/dP=Es*Q/P = .515 *16.88/30 = 0.2898 -> b= 0.2898
Q= a+bP -> 16.88=a+0.2898*30 a=16.88-0.2898*30 -> a= 8.186
Linear long run supply equation: Q= 8.186+0.2898P
Demand:
Ed=dQ/dP * P/Q  -0.906= dQ/dP *30/16.88 dQ/dP=Ed*Q/P = -0.906 *16.88/30 = 0.2898 -> b= -0.5089
Q= a+bP -> 16.88=a-0.5089*30 a=16.88+0.5089*30 -> a= 32.147
Linear long run demand equation: Q= 32.147-0.5089P
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 OPECʹs level of production in this long-run equilibrium to maintain the price of \$30?

Qs(without OPEC)= 7.78+.29*30 = 16.48
OPECʹs level of production in this long-run equilibrium to maintain the price of \$30=16.88-16.48 = 0.4 billion barrels per

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