Profit and Revenue Functions
Professor Scott Allan
March 11, 2015
Hello class, today we will be talking about the Profit and Revenue functions.
Background of the Profit and Revenue Functions:
Profit and Revenue functions are the everyday functions that every business has to deal with, and what people have to deal with when talking about managing their incomes. The profit function deals with the difference between the Revenue and Cost Functions (to be mentioned later,) and the Revenue function deals with the overall total amount of money a company or business can bring in. The two formulas are widely used in Economic applications as well.
Recall:
The Cost Function
Cost Function = fixed costs + variable costs
Fixed Costs are the costs that the business or company is forced to pay, which could include payments like rent on buildings, lighting, water, and machinery costs, as well as payroll. On the other hand, Variable Costs are costs that can range, such as the costs of company outings, travel, materials, and packaging.
Formulas:
Profit Function:
Profit = Total Revenue (R(q)) - Total Costs (C(q))
Profit is the total amount of money a company makes after subtracting all the costs out of the total revenue.
Revenue Function:
Revenue (R(q)) = Price (P) x Quantity (Q)
By multiplying the price of the product being sold and the quantity sold, the result is a a total sum in dollars, a company makes.
**Notice that all three formulas are related in one way or another, and one cannot be accounted for without accounting for the others as well. See below: The cost and revenue functions plotted against each other to create the profit, and the break-even point which indicates where costs turn into profits.
Example:
A toy store pays $10.25 for a video game. The fixed costs for the game are $1302 total, and the store sells each game for $15.
a. Find the cost function.
b. Find the revenue function.
c. Find the profit function.
d. What is the break-even point?
a. Costs = Fixed + Variable
C(q) = $1302 + $10.25x
b. Revenue = PQ
R(q) = $15x
c. Profit = R(q) - C(q)
P(q) = $15x - $1302 + $10.25x
P(q) = $4.75x -$1302
d. Break-Even point (set profit equation = 0)
$4.75x-$1302=0
Break - Even point = x = 274.10
**In this example, the toy store must sell around 274 video games to "break-even" and start to make profits.
Thank you everyone!
