Question

The demand curve and supply curve for one- year discount bonds with a face value of $1000 are as follows, respectively. Bd: P = 1200 - 0.5 Q Bs: P = 400 + 0.3 Q Where P = price and Q = quantity. a. What is the expected equilibrium price and quantity of bonds in this market? (2.5 marks) b. Given your answer to part (a), what is the expected interest rate in this market? (2.5 marks) As a monetary policy action, suppose the central bank purchases 100 of the bonds. Assuming the bond demand and money demand are held constant, answer the next two questions. c. How does the central bank's action affect the bond demand and supply equations? (2.5 marks) d. Calculate the effect on the equilibrium interest rate in this market as a result of the central bank's action. (2.5 marks)

Answer 1

a. To find the equilibrium price and quantity, we need to set the demand and supply equations equal to each other and solve for Q:

1200 - 0.5Q = 400 + 0.3Q

800 = 0.8Q

Q = 1000

Then we can plug this value of Q into either the demand or supply equation to find the equilibrium price:

P = 1200 - 0.5(1000) = $700

So the expected equilibrium price is $700 and the expected equilibrium quantity is 1000 bonds.

b. To find the expected interest rate, we can use the formula:

Interest rate = (Face value - Price) / Price x (1 / Years to maturity)

Since these are one-year discount bonds with a face value of $1000, the years to maturity is 1. Plugging in the equilibrium price of $700, we get:

Interest rate = (1000 - 700) / 700 x (1/1) = 0.43 or 43%

So the expected interest rate in this market is 43%.

c. If the central bank purchases 100 of the bonds, this will decrease the quantity of bonds available in the market, shifting the supply curve to the left. The new supply equation will be:

P = 400 + 0.3(Q-100)

where Q is the total quantity of bonds available in the market.

d. To calculate the new equilibrium interest rate, we need to find the new equilibrium price and quantity. Setting the new supply equation equal to the demand equation, we get:

1200 - 0.5Q = 400 + 0.3(Q-100)

Simplifying this equation, we get:

Q = 940

P = 676

Plugging these values into the interest rate formula, we get:

Interest rate = (1000 - 676) / 676 x (1/1) = 0.48 or 48%

So the effect of the central bank's action is to increase the interest rate from 43% to 48%.