### Integrals in Business

In the world of business, integrals are used to determine many numbers that may mean the success or the failure of a company.

With integrals and some statistics, we as the CEO's of companies can determine the consumer surplus, the producer surplus, and the market price

where P is the price, and x is the amount of products, the following graphs portray the relationships between price and goods.

for consumer surplus:

The Producer Surplus:

The Marketing Price curve:

A sample problem: given the following information find the producer surplus

Pd = D(x) = -.001x^2 + 250

Ps = S(x) = .0006x^2 + .02x + 100

x = 300

P = 160

PS =

on your calculator: you should put the equation in the parenthesis in the Y1 function and input fnInt(Y1,x,0,300) and you will get a number: 36300 which is the producer surplus because we used the producer surplus function as the Y1.

Future and present value of an Income Stream:

T = time frame

R(t) = rate of income generated

r = Interest rate for reinvestment

this tells you how much you would have if you put your money in a bank and had interest on top of reinvestment.

Present Value function: which is the exact value of the money at the moment is described by

and the Amount Annuity is the future output of your investment and is described by functions

m: payments per year P : amount of payment

Lorentz Curve: Income Distribution

f(x) = proportion of the total income recieved by the poorest 100x% of the population

Domain: [0,1] f(0) = 0 <- if nobody is counted, nobody has money.

Range: [0,1] f(1) = 1 <- if everybody is counted all the money is in one way or another, distributed.

the proportions are shown in between the two extremes of nobody and everybody.

It is always increasing because a person's income cannot be negative.

the GINI index which shows the coefficient of the inequality is

some more reference is here

Thou art next DANICA

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