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), PG represents the price of natural gas (per cubic foot) and P0 represents the price of oil (per barrel).

a) If P0 = 6, find the equilibrium price and quantities of natural gas.

b) Find the new equilibrium price and quantities if P0 doubles (from 6 to 12).

Answer 1

a)

Qs = 14 + 2 Pg + .25 Po.......................1

Qd = -5 Pg + 3.75 Po...........................2

For equilibrium price and quantity

Qs =Qd   so from Equation 1 and 2

14 + 2 Pg + .25 Po = -5 Pg + 3.75 Po ; we are given Po =6 Plug the value

14 + 2 Pg + .25 *6 = -5 Pg + 3.75*6

7Pg = 3.75*6-0.25*6-14 =7

Pg =7/7 = 1 (equilibrium price of natural gas); plug Pg = 1 in Eqn 1 to get the

Qs = 14 + 2 Pg + .25 Po. =14+2*1+.25*6 =17.5

(Pg =1 ,Q =17.5)

b)

Qs =Qd   so from Equation 1 and 2

14 + 2 Pg + .25 Po = -5 Pg + 3.75 Po ; we are given Po =6 Plug the value

14 + 2 Pg + .25 *12 = -5 Pg + 3.75*12

7Pg = 3.75*12-0.25*12-14 =28

Pg =28/7 = 4 (equilibrium price of natural gas); plug Pg = 1 in Eqn 1 to get the

Qs = 14 + 2 Pg + .25 Po. =14+2*4+.25*6 =23.5

(Pg =4 ,Q =23.5)