The document discusses demand functions and supply functions. It provides examples of demand functions with different slopes: 1) Negative slope - as price increases, demand decreases. 2) Constant slope - a change in demand does not affect price. 3) Undefined slope - demand is not affected by price. 4) Increasing slope - demand increases as price increases. It also discusses cases of supply functions with positive, constant, or negative slopes and how quantity supplied relates to price in each case. Examples are provided of constructing a demand equation from data points and using the equation to solve for price, demand, or other variables.

1. Applications

2. Y – dependent variable
Revenue
Cost of production
Profit
X – independent variable
Goods/merchandize manufactured
Goods/merchandize sold
Ticket sales

3. Function of one variable
𝑦 = 𝑓 𝑥
Example: Profit from sales of tickets (as a retail
seller)
Function of two or more variables
𝑦 = 𝑓 𝑥, 𝑤, 𝑧
y- Human development index
x- Life Expectancy, w – purchasing power of money, z -
Literacy

4. 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
𝑦 = 𝑓 𝑥
What are your common observations about the
behavior of consumers in relation to price of
goods?

5. Case 1 Negative slope
y - price
x- demand
Slope (m, rate of
change) is negative
𝑚 < 0
An increase in price
results in a decrease
in demand
A decrease in price
results in an increase
in demand
x- demand
y - price
Case 2 Constant slope
Slope (m, rate of
change) is constant
𝑚 = 0
An increase/decrease
in demand does not
affect price
A change in demand
leaves price
unchanged

6. Case 3 Undefined slope
y- price
x demand
Slope m is undefined
𝑚 =
∆𝑦
∆𝑥
=
∆𝑦
0
Quantity demanded is
not affected by price
The rise and fall in price
does not affect
demand

7. Case 4 Increasing slope
y- price
x demand
Slope is increasing
𝑚 > 0
The demand for the
product increases
when the price
increases
An increase in price
encourages
consumption of the
good/merchandize

8. Mathematical Model for Demand Function
𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1 Point-Slope form
𝑦 = 𝑚𝑥 + 𝑏 Slope-Intercept form
𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0 General form
Example
Find the equation of the line that has the slope of
6 and which passes through the point ( 4, 7)
𝑦 − 7 = 6 𝑥 − 4

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

10. A 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.
𝑥, 𝑦 →?
(20,000, 100)
𝑚 =
∆𝑦
∆𝑥
=?
𝑚 =
−2.50
2,500
=
−1
1000

11. 𝑦 − 100 =
−1
1000
𝑥 − 20,000
How do you transform it to slope-intercept
form?
How do you transform it to general form

12. 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 =
−1
1000
𝑥 − 20,000
𝑦 − 100 =
−1
1000
0 − 20,000
𝑦 = 120

13. c. What is the highest quantity demanded for this
product?
y- price
x - demand
 0,x 𝑦 − 100 =
−1
1000
𝑥 − 20,000
0 − 100 =
−1
1000
𝑥 − 20,000
𝑥 = 120,000

14. d. How many units will be bought if the price is
80php per unit?
What is x when y is 80php?
𝑦 = 120 −
𝑥
1000
Equation in slope intercept form
80 = 120 −
𝑥
1000
Solve for x
𝑥 = 40,000 𝑢𝑛𝑖𝑡𝑠

15. e. What is the price per unit if 25,000 units were
demanded?
What is y when x is 25,000 units?
𝑦 = 120 −
𝑥
1000
Equation in slope intercept form
𝑦 = 120 −
25,000
1000
Solve for y
𝑦 = 95𝑝ℎ𝑝

16. f. Sketch the graph of the demand equation
𝑦 = 120 −
𝑥
1000
x -demand
y price

17. Case 1 Positive slope
x – quantity supplied
y price
Slope is positive
𝑚 > 0
As price increases,
the supply for the
product increases
As price decreases,
the supply for the
product decreases.

18. Case 2 Constant Supply
y price
x – quantity supplied
Slope is constant
𝑚 = 0
The price stays the
same regardless of the
amount of supply
The quantity of supply
does not affect the
price

19. Case 3 Slope is undefined
y price
x – quantity supplied
Slope is undefined 𝑚 =
∆𝑦
∆𝑥
=
∆𝑦
0
Quantity supplied is
constant, is not
affected by the price

20. Case 4 Negative Slope, Decreasing supply
x – quantity supplied
y price
Slope is negative
𝑚 < 0
As the price decreases,
supply increases
A price decrease is an
incentive to produce
more
Meron bang ganitong pangyayari in real
business situations?

21. Yes!