Cusack U.S Economy Equation | OMICS International
ISSN: 2375-4389
Journal of Global Economics

# Cusack U.S Economy Equation

Paul T E Cusack*

*Corresponding Author:
Cusack PTE
Independent Researcher
BSc E, DULE, 1641 Sandy Point Rd
Saint John, NB, Canada E2K 5E8
Tel: (506) 214-3313
E-mail: [email protected]

Received Date: January 17, 2017; Accepted Date: February 23, 2017; Published Date: March 02, 2017

Citation: Cusack PTE (2017) Cusack U.S Economy Equation. J Glob Econ 5:239. doi:10.4172/2375-4389.1000239

Copyright: © 2017 Cusack PTE. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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#### Abstract

Here is a paper that uses 11 variables in an equation that describes the US economy. It can be used to predict the peaks to crash and where it is in the economic cycle.

#### Introduction

GDP=e^x

Dow Jones Industrial Average=sin

Standard and Poor`s 500 Index=sin/e^x

CPI=e^x

Unemployment=sin

Commodities Index

Oil linear

Gold Production=constant

New Residential Construction=linear

Personal Income=linear

Global Stock Market=e^x sin

Each one of these indicates is a sin, cos or exponential function.

SO,

y=y'

y=e^x

y=y'

y=sin x+C1=cos x+C2

x=1, Y=0.8415 cf 0.86

0.8415+C3=e^x

Boundary condition

x=1

C3=c=1.8768

Y=e^x-1.8768

Now for the Fourier series:

y=e^x-1.8768

y=asin x+bcos x

asin x+b cos x=e^x-1.8768

a(0.86)+b(0.86)=0.8415

(a+b)=1

a=1-b

(1-b)sin x+b cos x=e^x-1.8768

0.86-b(0.86)-b(0.86)=e^1-1.8768

y=e^1-1.8768

Y=0.8415

For a full cycle:

1/2Pi=0.1592

0.1592x=6.28

x=39.467

So from peak to trough=39.4627(2)=78.93 years

October 29,1929+78.93=2007.9

November 4, 2007 Peak to crash

GDP=e^x

Dow Jones Industrial Average=sin

Standard and Poor`s 500 Index=sin/e^x

CPI=e^x

Unemployment=sin

Commodities Index

Oil linear

Gold Production=constant

New Residential Construction=linear

Personal Income=linear

Global Stock Market=e^x sin

S&P500=-(GDP*CPI) e^x+0.8415(sin TDJIA*sin T UnEmploy*sin T US Trade Balance) sin x+x(oil production+mean house price +Personal Incxome)

For Annum 1990 X=1 Maximum:

400=(7113*391.4)e^Y * 0.7460+ (30,000+92,000+4878.6)X/1000

E^Y=0.1315 x=0.202=Y Output Energy

S&P500=-(GDP*CPI) e^Y+0.8415(sin TDJIA*sin T UnEmploy*sin T US Trade Balance) sin X+x (oil production+mean house price +Personal Incxome)

400=(7113*391.4)e^Y * 0.7460+ (30,000+92,000+4878.6)X/1000

e^Y=0.1315 x=0.202=Y Output Energy

Since Y=e1-1.8768

Y=2.71828-1.8768

0.202=2.71828 -1.8768 (Pi/2)=e^Y

Pi/2 *Y=e^Y =Pi

Y=Ln Pi

Y=e^1-1.8768 Refer to Figure 1.

Figure 1: Dampened cosine curve.

Y=0.8415

But Y=0.202 (dampened sine wave)

So,

Y=e^0.1315=1.1405

y=1/y

Ln x=1/x

#### Conclusion

y=y' for the economy.

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