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 ​$_______ and the equlibrium price of siliver will be​$________.

Answer 1

Answer:

a) Gold = $1,380; Silver = $1,020

b) Gold = $1,300; Silver = $980

Explanation:

a) At first, with Qg = 60 and Qs = 270, the equilibrium prices for gold and silver are found by solving the following linear system:

$P_g = 930-60 +0.50 P_s\\P_s = 600 - 270 + 0.50P_g\\\\-P_s=1740 -2P_g\\P_s = 330+ 0.50P_g\\P_g = 1,380\\P_s = 1,020$

Equilibrium price of gold is $1,380 and the price of silver is $1,020.

b) If the supply of gold increases to 120, since the goods are substitutes, there will be an increase in overall supply and the equilibrium price of gold and silver will decrease as follows:

$P_g = 930-120 +0.50 P_s\\P_s = 600 - 270 + 0.50P_g\\\\-P_s=1620 -2P_g\\P_s = 330+ 0.50P_g\\P_g = 1,300\\P_s = 980$

Equilibrium price of gold is $1,300 and the price of silver is $980.