Suppose gold (G) and silver (S) are substitutes for each other because both serv
ID: 1226740 • Letter: S
Question
Suppose gold (G) and silver (S) are substitutes for each other because both serve as hedges against inflation. Suppose also that the supplies of both are fixed in the short run (Qg =60 and Qs=270) and that the demands for gold and silver are given by the following equations:
Pg = 930 Qg +0.50 Ps and Ps = 600 Qs S + 0.50 Pg.
What the the equilibrium prices of gold and silver?
The equilibrium price of gold is $_______and the equlibrium price of siliver is $________. (Enter your responses rounded to two decimal places.)
What if a new discovery of gold doubles the quantity supplied to 120? How will this discovery affect the prices of both gold and silver?
The equilibrium price of gold will be $_______ and the equlibrium price of siliver will be $________.
Explanation / Answer
Pg = 930 - Qg + 0.5Ps
Ps = 600 - Qs + 0.5Pg
(1) Qg = 60, Qs = 270
Pg = 930 - 60 + 0.5Ps
Pg - 0.5Ps = 870 ......(1)
Again,
Ps = 600 - 270 + 0.5Pg
Ps - 0.5Pg = 330 ......(2)
Equilibrium price is obtained by solving (1) and (2):
Pg - 0.5Ps = 870 ......(1)
(2) x 2 yields:
2Ps - Pg = 660 .........(3)
Adding (1) and (3) we get:
1.5Ps = 1,530
Ps = 1,020.00
Pg = 2Ps - 660 = (2 x 1,020) - 660 = 2,040 - 660 = 1,380.00
(2) Qg = 120, Qs = 270
Pg = 930 - 120 + 0.5Ps
Pg - 0.5Ps = 810 ......(1)
Again,
Ps = 600 - 270 + 0.5Pg
Ps - 0.5Pg = 330 ......(2)
Equilibrium price is obtained by solving (1) and (2):
Pg - 0.5Ps = 810 ......(1)
(2) x 2 yields:
2Ps - Pg = 660 .........(3)
Adding (1) and (3) we get:
1.5Ps = 1,470
Ps = 980.00
Pg = (2 x 980) - 660 = 1,960 - 660 = 1,300.00