The market of natural gas is described by the following supply and demand equati

Question

The market of natural gas is described by the following supply and demand equations:

                                    Qs = 14 + 2 PG + .25 P0           Qd = -5 PG + 3.75 P0

    where Qs represent the quantities supplied and demanded of natural gas (in millions of cubic feet), PGrepresents the price of natural gas (per cubic foot) and P0represents the

    price of oil (per barrel).

a. If P0 = 8, find the equilibrium price and quantities of natural gas.

b. Find the new equilibrium price and quantities if P0 doubles (from 8 to 16).

Explanation / Answer

a. If P0 = 8, then the equations become:
Qs = 14 + 2PG + 0.25*8 = 16 + 2PG
and Qd = -5PG + 3.75*8 = -5PG + 30

At equilibrium, Qs = Qd

16 + 2PG = -5PG + 30
2PG + 5PG = 30 - 16 = 14
PG = 14/7 = 2

Qs = 16 + 2*2 = 20

Equilibrium price of gas is $2 per cubic foot and quantity demanded is 20 million of cubic feet.

b. If P0 = 16,
Qs = 14 + 2PG + 0.25*16 = 18 + 2PG
and Qd = -5PG + 3.75*16 = -5PG + 60
At equilibrium, Qs = Qd

18 + 2PG = -5PG + 60
7PG = 60 - 18 = 42
PG = 42/7 = 6

and Qs = 18 + 2 *6 = 30

Equilibrium price of gas becomes $6 per cubic foot and quantity demanded is 30 million of cubic feet.

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