Question

The demand curve and supply curve for one-year discount bonds with a face value of $1,000 are represented by the following equation

BD ? P = ?QD + 1100

BS ?P=QS +500.

A. What is the equilibrium price and quantity of bonds? [Hint: The equilibrium condition is that QD = QS.]

B. Given your answer to part (a), what is the interest rate of the discount bond?

Suppose that the economy is expanding now. The borrowers issue 80 more bonds and the lenders purchase 50 more bonds at any given prices. Assume that money demand is held constant.

C. How does the economic boom affect the bond demand and supply equation? [Note: You need to provide the new demand and supply functions to receive full credit.]

D. Calculate the effect of expansion on the equilibrium interest rate in this market. To calculate the effect, you need to calculate the new market equilibrium interest and the percentage change in the interest rate.

Answer 1

(A) In equilibrium, BD = BS and QD = QS = Q

- Q + 1100 = Q + 500

2Q = 600

Q = 300

P = 300 + 500 = $800

(B) If Interest rate = R%, then

$800 x (1 + R) = $1,000

1 + R = $1,000 / $800 = 1.25

R = 0.25

R = 25%

(C) Bond supply (QS) increases by 80 and bond demand (QD) increases by 50.

From demand function,

P = - QD + 1,000

QD = 1,000 - P

New bond demand: Q'D = QD + 50 = 1,000 + 50 - P = 1,050 - P

From supply function,

P = QS + 500

QS = P - 500

New bond supply: Q'S = QS + 80 = P - 500 + 80 = P - 420

(D) In new equilibrium,

Q'D = Q'S

1,050 - P = P - 420

2P = 1,470

P = $735

If new Interest rate = R%, then

$735 x (1 + R) = $1,000

1 + R = $1,000 / $735 = 1.3605

R = 0.3605

R = 36.05%

% Change in interest rate = (36.05% / 25%) - 1 = 1.4420 - 1 = 0.4420 = 44.20% (Increase)