Question

Assume this is a demand and supply schedule for a one-year discount bond with face value of $1,000. Complete the column for corresponding interest rate.

Interest rate (%)	Price bond	Quantity demanded	Quantity supplied
_______	1000	0	900
________	900	200	850
________	800	400	800
________	700	600	750
________	600	800	700
________	500	1000	650

b. Given the above demand and supply schedules for the discount bond market, solve for equilibrium price, quantity, and interest rate.

Demand equation:   P_B = ________________________

Supply equation:    P_B = _________________________

Equilibrium price P* = _________________________

Equilibrium quantity Q* = _______________________

Equilibrium interest rate r* = _______________________

Answer 1

(a) If bond interest rate is R% per year, then

R = [(Face value / Bond price) - 1] x 100 = [($1,000 / P)] - 1] x 100 [Where P: Bond price]

(i) P = $1,000

R = [(1,000 / 1,000) - 1] x 100 = (1 - 1) x 100 = 0 x 100 = 0%

(ii) P = $900

R = [(1,000 / 900) - 1] x 100 = (1.1111 - 1) x 100 = 0.1111 x 100 = 11.11%

(iii) P = $800

R = [(1,000 / 800) - 1] x 100 = (1.25 - 1) x 100 = 0.25 x 100 = 25%

(iv) P = $700

R = [(1,000 / 700) - 1] x 100 = (1.4286 - 1) x 100 = 0.4286 x 100 = 42.86%

(v) P = $600

R = [(1,000 / 600) - 1] x 100 = (1.6667 - 1) x 100 = 0.6667 x 100 = 66.67%

(vi) P = $500

R = [(1,000 / 500) - 1] x 100 = (2 - 1) x 100 = 11 x 100 = 100%

(b)

(i) Demand equation: PB = a - bQ

When Q = 0, PB = 1,000

1,000 = a - 0

a = 1,000

When Q = 200, PB = 900

900 = a - 200b

900 = 1,000 - 200b

200b = 100

b = 0.5

Demand equation: PB = 1,000 - 0.5Q

(ii) Supply equation: PB = c + dQ

When Q = 900, P = 1,000

1,000 = c + 900d......(1)

When Q = 850, P = 900

900 = c + 850d.........(2)

(1) - (2) yields: 50d = 100

d = 2

c = 1,000 - 900d [From (1)] = 1,000 - (900 x 2) = 1,000 - 1,800 = - 800

Supply equation: PB = - 800 + 2Q

(iii) In equilibrium, quantity demanded equals quantity supplied.

1,000 - 0.5Q = - 800 + 2Q

2.5Q = 1,800

Q* = 720

P* = 1,000 - (0.5 x 720) = 1,000 - 360 = 640

(iv) When P = 640,

r* = [(1,000 / 640) - 1] x 100 = (1.5625 - 1) x 100 = 0.5625 x 100 = 56.25%