EC125 (CDA) Assignment 1 Moses Tan (STU:1400320)

1. Reproduce the following equations (without the watermark) using MathType:

a) 3

1 1 2 1 1

1

1 if in quarter j, where

0 otherwiset t t j jt t jt

j

y x x Q Q

.

b)

1 if individual is <16 years old

2 if individual is 17-25 years old

3 if individual is 26-40 years old

8 if individual is >75 years old

ix

c)

,1 ,1

,2 ,2

, ,

ˆ ˆ 0 0

ˆ ˆ0 0ˆ

ˆ ˆ0 0

i j

i j

ijT T

i T j T

u u

u u

u u

d)

ln

1 ln

p r pd u y

d y p r p y b

e)

, ( , ) , y

, ( , )

x y x y x y

x y y x x y

p yp x

E X Y x y p x y xp x y yp x

x p x y y p x y xp x yp y E X E Y

f) 1

1 2, ,x

1

max , , , s.t. ; 0 1,2, ,n

n

n i ix

i

U x x x p x M x i n

EC125 (CDA) Assignment 1 Moses Tan (STU:1400320)

MR

y

π PC’

PC

PC’’

y

π

PC’ PC

PC’

’

MR

Figure 1 – The Role of Central Banks – Monetary Rule.

2. Reproduce the following equations (without the watermark) using Microsoft Word: