FUNCTIONS IN BUSINESS AND

ECONOMICSApplications

Functions

Y – dependent variable RevenueCost of productionProfit

X – independent variableGoods/merchandize manufacturedGoods/merchandize soldTicket sales

Functions

Function of one variable

Example: Profit from sales of tickets (as a retail seller)

Function of two or more variables

y- Human development indexx- Life Expectancy, w – purchasing power of money, z - Literacy

Demand Function

Demand function describes consumer behavior in relation

to the price of goods. the quantity y of goods a consumer is

willing to buy at price x

What are your common observations about the behavior of consumers in relation to price of goods?

Demand Function

Case 1 Negative slopey - price

x- demand

Slope (m, rate of change) is negative

An increase in price results in a decrease in demand

A decrease in price results in an increase in demand

x- demand

y - priceCase 2 Constant slope

Slope (m, rate of change) is constant

An increase/decrease in demand does not affect price

A change in demand leaves price unchanged

Demand Function

Case 3 Undefined slope

y- price

x demand

Slope m is undefined

Quantity demanded is not affected by priceThe rise and fall in price does not affect demand

Demand function

Case 4 Increasing slope

y- price

x demand

Slope is increasing

The demand for the product increases when the price increases

An increase in price encourages consumption of the good/merchandize

Demand Function

Mathematical Model for Demand Function Point-Slope form

Slope-Intercept form General form

ExampleFind the equation of the line that has the slope of 6 and which passes through the point ( 4, 7)𝑦−7=6 (𝑥−4 )

Demand Function

Find the equation of the line with slope -5 and is equal to 3 when x = 0.

Demand Function applicationA business sells 20,000 units each month at a price of 100php each. It is projected that monthly sales will increase by 2,500 units for each 2.50php reduction in price.a. Construct the demand equation.

?(20,000, 100)

Demand FunctionApplication

𝑦−100=−11000

(𝑥−20,000 )How do you transform it to slope-intercept form?

How do you transform it to general form

Demand Function Application

b. What is the highest price to be paid for this commodity?How would the graph look like?

How do you interpret mathematically the question?

x - demand

y- price(0 , 𝑦 )

𝑦−100=−11000

(𝑥−20,000 )

𝑦−100=−11000

(0−20,000 )

𝑦=120

Demand Function Application

c. What is the highest quantity demanded for this product?

y- price

x - demand

0,x 𝑦−100=−11000

(𝑥−20,000 )

0−100=−11000

(𝑥−20,000 )

𝑥=120,000

Demand Function Application

d. How many units will be bought if the price is 80php per unit?

What is x when y is 80php?

Equation in slope intercept form

Solve for x 𝑥=40,000𝑢𝑛𝑖𝑡𝑠

Demand Function Application

e. What is the price per unit if 25,000 units were demanded?

What is y when x is 25,000 units?

Equation in slope intercept form

Solve for y 𝑦=95 h𝑝 𝑝

Demand Function Application

f. Sketch the graph of the demand equation

𝑦=120−𝑥1000

x -demand

y price

Supply Function

Case 1 Positive slope

x – quantity supplied

y price

Slope is positive

As price increases, the supply for the product increases

As price decreases, the supply for the product decreases.

Supply Function

Case 2 Constant Supply

y price

x – quantity supplied

Slope is constant

The price stays the same regardless of the amount of supplyThe quantity of supply does not affect the price

Supply Function

Case 3 Slope is undefined

y price

x – quantity supplied

Slope is undefined

Quantity supplied is constant, is not affected by the price

Supply Function

Case 4 Negative Slope, Decreasing supply

x – quantity supplied

y priceSlope is negative As the price

decreases, supply increases A price decrease is an incentive to produce more

Meron bang ganitong pangyayari in real business situations?

Supply Function

Yes!