T H E M AT H E M AT I C S PA RT O F I T

MARKET EQUILIBRIUM

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

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

eP

eQ

1P

1sQ 1dQ

2PWhen P is below , there is shortage of

When P is above , there is a glut (over supply) of

MARKET EQUILIBRIUM

Given the demand and supply curves defined by the system

222

111

cybxa

cybxa

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 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

MARKET EQUILIBRIUM

Example. Demand equation: Supply equation: x- number of units producedy- price per unit

1. Find the market equilibrium quantity and price.

MARKET EQUILIBRIUM

Solutiona. Identify and set up the system of equations.

𝑥+25 𝑦=425

b. Solve the system . ( Recall the methods to solve systems of equations)

𝑥+25 𝑦=425-

75 𝑦=825

Solve by elimination method

𝑦=11

MARKET EQUILIBRIUM

b. Get the market equilibrium quantity x by substitution

𝑥+25 𝑦=425→ 𝑥+25 (11)=425𝑥=150𝑢𝑛𝑖𝑡𝑠

MARKET EQUILIBRIUM

c. Graph (Two points determine a line)

(425,0)

(0,11)

(0,8)

(-400,0)

(150,11)

𝑥+25 𝑦=425

MARKET EQUILIBRIUM

QuizAnswer Page 48, problem 4 – a,b,c,d

Page 50, problem 5 – a,b,c,d

MARKET EQUILIBRIUM

Solution and answer4.a. Given Supply equation: Demand equation:

a. How many units are available at y = 40php

b. How many units are demanded at y = 28

MARKET EQUILIBRIUM

c. Find the market equilibrium point

𝑦=3 𝑥+20𝑦=−𝑥+44

0=4 𝑥−24→𝑥=6

Solve for y when x = 6

𝑦=−𝑥+44→=−6+44=38

Market equilibrium point (x,y)=( 6, 38)

MARKET EQUILIBRIUM

(0,20)

(-20/3, 0)

(0, 44)

(44, 0)

(6,38)

𝑦=3 𝑥+20

𝑦=−𝑥+44

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 slopeSupply curve: (25,135), (0,60)

𝑚=∆ 𝑦∆ 𝑥

=7525

=3

𝑦=3 𝑥+60

MARKET EQUILIBRIUM

Demand Curve equation: Find a point, find the slope(150,60). MEP(25,135)

MARKET EQUILIBRIUM

b. Highest price to be paid for the commodity. ( y-intercept of the demand curve)

(0,150) or 150phpc. At y = 90, the quantity of demand is

90=−35𝑥+150

Solve for x:

MARKET EQUILIBRIUM

At y = 90, quantity supplied is:

𝑦=3 (90 )+60=330

MARKET EQUILIBRIUM

d. graph

(0, 60)

(-20, 0)

(0,150)

(250, 0)

(25, 135)

𝑦=−35𝑥+150

𝑦=3 𝑥+60𝑦−3𝑥−60=0

5 𝑦+3 𝑥−750=0