Question

1. Suppose Y = 18 and Yn = 22. What is the output gap?

2. Suppose π e = 2%, α = 0.4, U = 8%, and Un = 5%. Using the Phillips Curve, what is the numerical value of π?

3. Suppose Y = 18, Yn = 22, Un = 6%, and γ = 0.4. Using Okun’s Law, What is U?

4. Suppose i = 60%, π e = 30%. (a) What is r using the exact equation? (b) What is r using the approximate equation?

5. Consider a bond that pays $1000 in one year. Calculate the current interest rate if the current price of the bond is the following. (a) $600 (b) $700 (c) $800

Answer 1

Ans 1. Output gap = Yn - Y = 22 - 18 = 4

Ans 2 From Philips curve Equation,

Pie - Pie e = -a(u - un)

=> Pie = 2% - 0.4(8 - 5) = 0.8%

Ans 3. From Okun’s Law equation,

U - Un = -y(Y - Yn)

=> U = 6 - 0.4(18-22) = 6 + 1.6 = 7.6%

Ans 4. From exact formula,

r = (1+i)/(1+pie e) - 1 = (1+0.6)/(1+0.3) - 1 = 0.2307 or 23.07%

From approximation,

r = i - pie e = 60 - 30 = 30%

Ans 5. Price of the bond = P

Face value of the bond = 1000

Interest rate = r

General formula,

P = 1000/(1+r)

=> r = 1000/P - 1

a) P = $600

=> r = 1000/600 - 1 = 0.6667 or 66.67%

b) P = $700

=> r = 1000/700 - 1 = 0.4285 or 42.85%

c) P = $800

=>r = 1000/800 - 1 = 0.25 or 25%

*Please don’t forget to hit the thumbs up button, if you find the answer helpful.