Question

The demand curve and supply curve for one-year discount bonds with a face value of $\$1050$are represented by the following equations:$B^d:Price=-0.8\times Quantity+1160B^s:Price=Quantity+720$Suppose that, as a result of monetary policy actions, the Federal Reserve sells 90 bonds that it holds. Assume that bond demand and money demand are held constant.

a. How does the Federal Reserve policy affect the bond supply equation? b. Calculate the effect on the equilibrium interest rate in this market, as a result of the Federal Reserve action.

Short answer

a) Price = quantity $+620$is the new supply equation.

b) Equilibrium interest rate is$5.28\%$

Step-by-step solution

Part (a) - Step 1: To determine

Effect of federal policy on bond supply equation.

Part(a) - Step 2: Explanation

If the Federal Reserve raises bond supply in the market by $80$percent, the bond supply equation becomes $Price=Quantity+620.$

The calculation for new supply equation:

Given,

Increase in supply is 80 .

Formula to determine the new supply equation is:

$$\begin{gathered} \text{Quantity supplied}=\text{Price}-700+80 \\ =\text{Price}-620 \\ \text{Price}=\text{Quantity supplied}+620 \end{gathered}$$

Hence$\text{Price}=\text{Quantity supplied}+620$is new supply equation.

Part (b) - Step 3: To determine

Federal policy has an effect on the equilibrium interest rate.

Part (b) - Step 4: Explanation

Equilibrium quantity of bonds

Given,

$$\begin{gathered} B^d:Price=-0.6\times Quantity+1140 \\ {B}^s:Price=Quantity+620 \end{gathered}$$

To solve the equation

$$\begin{gathered} \text{Quantity}+620=-0.6\times \text{Quantity}+1,140 \\ \text{Quantity}+0.6\text{Quantity}=1,140-620 \\ 1.6\text{Quantity}=520 \\ \text{Quantity}=325 \end{gathered}$$

Equilibrium quantity of bonds is $325$

Now to find the equilibrium price:

Given,

Quantity is $325$

$$\begin{gathered} B^s:Price=Quantity+620 \\ {B}^s:Price=325+620 \\ =\$945 \end{gathered}$$
The equilibrium price is: $945

Now to find the Expected interest rate:

Given,

Current price is$\$945$and face value is$\$1000$

So, formula to determine the expected interest rate is :

$Expectedinterestrate=\frac{Facevalue-Currentprice}{Currentprice}\times 100$

Substitute $\$945$for current price and $\$1000$for face value in the above equation, $Expectedinterestrate=\frac{(\$1,000-\$945)}{\$945}\times 100$

$=5.82\%$

Expected interest rate is $5.82\%$

The interest rate will rise to$5.82\%$