Suppose that the longrun world demand and supply elasticitie

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. Derive the linear long-run demand and supply equations. Next, suppose the long-run supply curve you derived above consists of competitive supply and OPEC supply. If the long-run competitive supply equation is: S_C = 7.78 + 0.29P, what must be OPEC\'s level of production in this long-run equilibrium?

Solution

Answer to 1st question:

If the demand curve is linear, it is in the form of Q_D = a + bP

Also, we know that

E_d = b P/Q

b = E_d (Q/P )= -0.906 (16.88/30)= -0.509.

Rearranging the linear expression for demand allows us to solve for a as follows:

a = Q_D- bP

a = 16.88 + 0.509(30) = 32.15.

We may now write the linear expression for demand as

Q_D = 32.15 - 0.509P.

If the supply curve is linear, it is in the form of

Q_S = c + dP.

Also, we know that E_s = d (P/Q)

d = E_s (Q/P) = 0.515 (16.88/30) = 0.290.

Rearranging the linear expression for demand allows us to solve for c as follows:

c = Q_S- dP

c = 16.88 - 0.290(30) = 8.18.

We may now write the linear expression for supply as

Q_S = 8.18 + 0.290P

Answer to 2nd question:

OPEC\'s supply is the difference between the world supply and competitive supply at $30. We know that world supply at $30 is 16.88. Competitive supply at $30 is 7.78 + 0.29(30) = 16.48. This implies that OPEC\'s supply is 0.4 billion barrels per year at $30 in this long-run equilibrium.