The demand curve and supply curve for one-year discount bonds with a face value of$\$1000$are represented by the following equations:

$$\begin{gathered} B^d:Price=-0.8\times Quantity+1100 \\ {B}^s:Price=Quantity+680 \end{gathered}$$

a. What is the expected equilibrium price and quantity of bonds in this market?

b. Given your answer to part (a), what is the expected interest rate in this market?

What is the expected equilibrium price and quantity of bonds in this market?

Given,

$$\begin{gathered} B^d:Price=-0.8\times Quantity+1100 \\ {B}^s:Price=Quantity+680 \end{gathered}$$

Now,

$$\begin{gathered} \text{Quantity}+700=-0.6\times \text{Quantity}+1,140 \\ \text{Quantity}+0.6\text{Quantity}=1,140-700 \\ 1.6\text{Quantity}=440 \\ \text{Quantity}=275 \end{gathered}$$

Equilibrium quantity of bonds is $275$.

Given,

Quantity is$\$275$

${\mathrm{B}}^{\mathrm{s}}\text{: Price}=\text{Quantity}+700$

Substitute $275$for quantity in equation $B^s$

$$\begin{gathered} price=275+700 \\ =975 \end{gathered}$$

Equilibrium price is$\$975$

Therefore the equilibrium price and quantity are$\$975and\$275$respectively.

what is the expected interest rate in this market?

Given.

Current price is $\$975$

Face value is $\$1000$

Now, Expected interest is:

$Expectedinterestrate=\frac{facevalue-currentprice}{currentprice}\times 100$

Substitute the value of face value and current price

$$\begin{gathered} Expectedrate=\frac{\$1000-\$975}{\$975}\times 100 \\ =2.56\% \end{gathered}$$

So, Expected interest rate is$2.56\%$