Profit Function Calculus

Introduction to profit function calculus:

In this article we are study about profit function calculus. The profit function is also referred to income statement or financial performance statements.The profit is defined by money received from investment or sales product then subtracting for the cost price or all expenses. I like to share this Composition of Functions Examples with you all through my article.

Calculus is included for functions, limits, integrals, and derivatives. It is branch of mathematics.

Profit=Sales price-Cost price
The loss is defined by,

Loss=Cost price-Sales price

Properties of Profit Function Calculus:

The profit function is denoted as `pi(w, p)` , it is defined as we gain maximum amount of  profit  we are facing two prices ,

Input prices `w` and
Output prices `p` .
The  profit function calculus equations  is given below,

` pi(w, p)=m a x _z(pf(z)-w^'z)`

Some properties of profit function calculus:

Input prices ` w` is non-increasing and
Output prices `p` is non-decreasing
Homogeneous of degree one(1) in (input price, outputprice) or `(w,p)`
Curved in output price(p) and input price(w)
Non-stop in p and w, for positive prices.
We are using one formula to calculate profit function calculus:

Hotelling’s Lemma
`(delpi(w,p)) / (delp)=q(w,p)` and

`(delpi(w,p))/ (delw_i)=-z_i(w, p)`

Cost function calculus:

The cost function is defined as `C(w,q).` Some cost function properties is given below,

Non-decreasing in `w, q`
Homogeneous of degree one(1) in input price`(w)`
Continuous in `w,` for positive ` w.`
We using one formula for cost function calculus,

Shephard’s Lemma
` (delc(w,q)) / (delw_i)=z^c(w,q)`

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Sample Problems of Profit Function Calculus:

Profit function Example problem 1:

Find the percent profit on cost. If a selling price is 70 %.

Solution:

We are using the formula: (% profit on selling price) / (100% - % profit on selling price) = (% profit on cost)

Or

` (sp)/(100-sp)=cp`

`(70%)/((100-70)% )= 2.3`

The value is` 230 %` profit on cost.

Profit function Example problem 2:

Find the percent profit on cost. If a box selling price is 90 %.

Solution:

We are using the formula: % profit on selling price / (100% - % profit on selling price) = % profit on cost.

Or

` ( sp)/(100-sp)=cp`

`( 90%)/((100-90)%) =( .90)/(.10)=.9`

The value is `90 %` profit on cost.