Question

1. 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 75 and Qs 300) and that the demands for gold and silver are given by the following equations: P6 975-Q0.5Ps and Ps 600-Qs0.5PG a. What are the equilibrium prices of gold and silver b. What if a new discovery of gold doubles the quantity supplied to 150. How will this discovery affect the prices of both gold and silver? 2. Fill in the missing information in the following tables. For each table, use the information provided to identify a possible trade. Then identify the final allocation and a possible value for the MRS at the efficient solution. (Note: there is more than one correct answer.) Illustrate your results using Edgeworth Box diagrams. Norman's MRS of food for clothing is 1 and Gina's MRS of food for clothing is 4. Initial allocation for Norman is 6F and 2C while initial allocation for Gina is 1F and 8C Michael's MRS of food for clothing is 1/2 and Kelly's MRS of food for clothing is 3. Initial allocation for Michael is 10F and 3C while initial allocation for Kelly is 5F and a. 15C

Answer 1

I will assume that you want me to answer only question 1 (since all information with regard to question 2 has not been provided).

You're given two demand equations:

$P_G=975-Q_G+0.5P_S$

and

Ps = 600-Qs + 0.5PG

At equilibrium, quantity demanded equals quantity supplied. So you get the following:

All you need to do is substitute these values of quantity in the price equations and solve for the prices.

$P_G=975-(75)+0.5P_S=900+0.5P_S$

and

600-(300) + 0.5Pa = 300 + 0.5Pa P.

If I multiply 0.5 to both sides of the second equation, I'll get:

$0.5P_S=150+0.25P_G$

Substituting for 0.5P_S in the first equation, I'll get:

Pc 900+150+0.25Po

Solving the above, you get:

$P_G=1400$

And using this, you find

$P_S=1000$

So the equilibrium price of gold is 1400 and that of silver is 1000.

b) Now if you double the quantity supplied of gold to 150, the two equations you now need to solve to get the prices are:

$P_G=975-(150)+0.5P_S=825+0.5P_S$

and

$P_S=300+0.5P_G$

Follow the same steps as before. Multiply 0.5 to both sides of the second equation to get:

$0.5P_S=150+0.25P_G$

Substitute this in the first equation and you have:

$P_G=825+150+0.25P_G$

Which solves to

$P_G=1300$

And substituting for this in the equation for P_S you get:

$P_S=950$

So, when the quantity supplied of gold rises, you see that the price of both gold and silver fall. The price of gold falls from 1400 to 1300 while that of silver falls from 1000 to 950.