Flashcards in Term 2 Deck (51):

1

## Discuss Exponential Graphs

###
b>1 and a>0 = backwards L

0**0 = L**

if a<0 flipped over x

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