Market Equilibrium

1. T H E M A T H E M A T I C S P A R T O F I T
MARKET EQUILIBRIUM

2. MARKET EQUILIBRIUM
Demand Curve vs. Supply Curve
x – quantity of
demand
y – price per
unit
𝑦 = 𝑚𝑥 + 𝑏
x – quantity of
demand
y – price per
unit
𝑦 = 𝑀𝑥 + 𝐵
Model for consumer and producer behavior
in relation to price under “normal” free
market conditions

3. MARKET EQUILIBRIUM
Market - the “place” where buyers and sellers
exchange money for goods
Under free-market conditions, there is a “right price”
that will get demand and supply into “balance”.
x quantity of goods
y-price per unit
e
P
e
Q
1
P
1
s
Q 1
d
Q
2
P
When P is
below 𝑃𝑒,
there is
shortage of
𝑄𝑑1 − 𝑄𝑠1
When P is above
𝑃𝑒, there is a glut
(over supply) of
𝑄𝑠2 − 𝑄𝑑2

4. MARKET EQUILIBRIUM
Given the demand and supply curves defined by the
system







2
2
2
1
1
1
c
y
b
x
a
c
y
b
x
a
Where x is the quantity of product and y the price per unit
of the product. The equilibrium quantity and equilibrium
price is the point 𝑥, 𝑦 which is the solution to the system.
Given the demand and supply equations, to find the
equilibrium price and quantity, find the solution to the
system

5. MARKET EQUILIBRIUM
Example.
Demand equation: 𝑥 + 25𝑦 − 425 = 0
Supply equation: 𝑥 − 50𝑦 + 400 = 0
x- number of units produced
y- price per unit
1. Find the market equilibrium quantity and price.

6. MARKET EQUILIBRIUM
Solution
a. Identify and set up the system of equations.
𝑥 + 25𝑦 = 425
𝑥 − 50𝑦 = −400
b. Solve the system . ( Recall the methods to solve
systems of equations)
𝑥 + 25𝑦 = 425
- 𝑥 − 50𝑦 = −400
75𝑦 = 825
Solve by elimination
method
𝑦 = 11

7. MARKET EQUILIBRIUM
b. Get the market equilibrium quantity x by
substitution
𝑥 + 25𝑦 = 425 → 𝑥 + 25 11 = 425
𝑥 = 150 𝑢𝑛𝑖𝑡𝑠

8. MARKET EQUILIBRIUM
c. Graph (Two points determine a line)
(425,0)
(0,11)
(0,8)
(-400,0)
(150,11)
𝑥 + 25𝑦 = 425
𝑥 − 50𝑦 = −400

9. MARKET EQUILIBRIUM
Quiz
Answer
Page 48, problem 4 – a,b,c,d
Page 50, problem 5 – a,b,c,d

10. MARKET EQUILIBRIUM
Solution and answer
4.a. Given
Supply equation: 𝑦 = 3𝑥 + 20
Demand equation: 𝑦 = −𝑥 + 44
a. How many units are available at y = 40php
40 = 3𝑥 + 20 → 𝑥 =
20
3
= 6.67
b. How many units are demanded at y = 28
28 = −𝑥 + 44 → 𝑥 = 16

11. MARKET EQUILIBRIUM
c. Find the market equilibrium point
𝑦 = 3𝑥 + 20
𝑦 = −𝑥 + 44
0 = 4𝑥 − 24 → 𝑥 = 6
Solve for y when x = 6
𝑦 = −𝑥 + 44 →= −6 + 44 = 38
Market equilibrium point (x,y)=( 6, 38)

12. MARKET EQUILIBRIUM
(0,20)
(-20/3, 0)
(0, 44)
(44, 0)
(6,38)
𝑦 = 3𝑥 + 20
𝑦 = −𝑥 + 44

13. MARKET EQUILIBRIUM
5. MEP ( 25, 135). At y = 60, no unit will be supplied,
but the quantity demanded x is 150 units.
Find the demand and supply equations
Point slope form: Find a point and find the slope
Supply curve: (25,135), (0,60)
𝑚 =
∆𝑦
∆𝑥
=
75
25
= 3
𝑦 = 3𝑥 + 60

14. MARKET EQUILIBRIUM
Demand Curve equation: Find a point, find the slope
(150,60). MEP(25,135)
𝑚 =
∆𝑦
∆𝑥
=
75
−125
= −
3
5
𝑦 − 135 = −
3
5
𝑥 − 25
𝑦 = −
3
5
𝑥 + 150

15. MARKET EQUILIBRIUM
b. Highest price to be paid for the commodity. ( y-
intercept of the demand curve)
(0,150) or 150php
c. At y = 90, the quantity of demand is
90 = −
3
5
𝑥 + 150
Solve for x: 𝑥 = −60 −
5
3
= 100

16. MARKET EQUILIBRIUM
At y = 90, quantity supplied is:
𝑦 = 3 90 + 60 = 330

17. MARKET EQUILIBRIUM
d. graph
(0, 60)
(-20, 0)
(0,150)
(250, 0)
(25, 135)
𝑦 = −
3
5
𝑥 + 150
𝑦 = 3𝑥 + 60
𝑦 − 3𝑥 − 60 = 0
5𝑦 + 3𝑥 − 750 = 0