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Flashcards in Term 2 Deck (51):
1

Discuss Exponential Graphs

b>1 and a>0 = backwards L
00 = L
if a<0 flipped over x

2

What is the formula for compound interest?

F=P(1+r/m)^mt
F=Pe^rt

3

What is the effective rate and how is it calculated?

The actual interest eared
(1+r/m)^m -1
i=e^r-1

4

How do you work out the present value of a future amount

P=F(1+r/m)^-mt
P=Fe^-rt

5

What is the formula for the sum of the total future value of an annuity?

F=d[(1+r/m)^mT -1 /(1+r/m)^m -1 ]

6

What is the formula for the present value of an annuity

P=d[1- (1+r/m)^mT /(1+r/m)^m -1 ]

7

What is the formula for a present value of a perpetuity?

d/(1+r)

8

How do you integrate an exponential function?

f(x)/DiffPower*LogBase

9

How do you integrate by substitution?

Set one part =U,
Diff and rearrange for dx=du/f'(x)
Sub back into original and solve

10

How do you integrate by parts?

Int(udv/dx)=uv-int(vdu/dx)

11

How do you find the capital stock?

Integrate the function

12

What is the formula for consumer surplus

Int-PQ

13

What is the formula for producer surplus

PQ-Int

14

How do you calculate the present value of dividends to be paid to a fund

Int(f(T)e^(-kt)

15

How do you work out a density function?

Differentiate a distribution function

16

How do you work out a distribution function?

Integrate a density function

17

How do you find the ER on continous functions?

Int( F(x)*P(X)

18

How do you find the ER on discrete probability functions?

Sum(R*P(I)

19

How do you find the variance?

Int(F(X)^2P(x) - [Int(F(x)P(x)]^2

20

What is the expected return of a European call?

Int(Sn-X)(P(sn)

21

What is the probability a call will be exercised?

P(Sn>x)=Int(P(sn)

22

What is the expected value of a call on the condition it will be exercised?

Int(Sn-x)P(x) / Int(Psn)

23

What is the general form of a differential equation?

dy/dt+vy=w

24

What is the Homogeneous case?

V is a constant and W=0

25

How do you solve the homogeneous case?

Take V to the other side
Divide By Y
Integrate
Simplify and e

26

What is the non-homogeneous case?

V is a constant, W has a value

27

How do you solve a non-homogeneous case?

The Complementary function is the normal:
Y=Ae^(-vt)

The Particular function is w/v

28

How do you solve a homogenous case if V is not a constant?

Simply integrate V
Y=Ae(-int(vt))

29

How do you solve a non-homogeneous case if V and W arenot Constants?

Y=e^(-int(v)) (A+Int(we^(Int(V)

30

What is dynamic stablility?

Equation has a long run solution, the particular integral

The complementary represents the deviation

For an equation to be stable, Yc must tend to zero

31

How do you check if an equation is dynamically stable?

The power of E must be negative

32

What is the formula for a growing annuity?

CF/K-g * (1-e^(g-k)n

33

How do you solve a non-linear equation with a separable variable?

Move one term to the other side and integrate

34

How do you prove an equation is an exact differential equation?

If dM/dt=dN/dy

Exact

35

How do you solve an exact differential equation?

Diff with respect to Y and T
Add together
Integrate with respect to Y and T
Add together, excluding common term once

36

How do you check if an equation is not exact?

dM/dt=!dN/dy

37

How do you solve a non-exact differential equation?

Multiply by mew

38

How do you calculate mew

If 1/N(dM/dt-dN/dY) = f(y)
Then =e^Int(fY)

If 1/M(dN/dy-dM/dt)=f(t)
Then =e^int(fT)

39

What is a Bernoulli equation

dy/dy+ay=by^n

40

How do you solve a bernoli function?

Z=y^1-n

Z=Ae^(-a(1-n)t) + b(1-n)/a(1-n)

41

How do you express the solow model in fundemental growth equation form?

dk/dt+k(n+d)=sk^a

This is a bernoli equation

In LR: K=s/n+d

42

What is a difference equation?

Yt=a+bYt-1

43

How do you solve a homogeneous difference equation?

yt=b^tY

44

How do you solve a non-homogeneous difference equation?

Y=a/1-b+(Yo-a/1-b)b^t

45

What are the values of B and how do they influence the equations convergence to a/1-b

B > 1 - Increasing and moving away
B < -1 Oscilating and moving away
-1 < B < 0 - Oscilating and converging
0 < B < 1 - Not oscilating and converging

Thus dynamic stability if |B| < 1

46

Represent a DS equilbrium using a difference equation?

Pt=g-c/d-h+ [P-g-c/d-h] (h/d)^t
g is interceptof supply
d is slopeof supply

47

What is the condition for stability under the DS model?

1/h>1/d

48

Under a HD model, what is the condition for stability?

k/k-s < 1

49

What is the difference between the waranted and actual growth rate?

Warranted is the level at which producers are contend
Actual is how much output has changed

50

How do you calculate warranted growth rate?

s/k-s

51

Discuss the interaction between actual and warranted growth?

G > Gw: Inflation as demand excees supply