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THE MATHEMATICS PART OF IT MARKET EQUILIBRIUM

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- 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 = + x quantity of demand y price per unit = + 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 eP eQ 1P 1sQ 1dQ 2PWhen P is below , there is shortage of 1 1 When P is above , there is a glut (over supply) of 2 2
- 4. 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
- 5. MARKET EQUILIBRIUM Example. Demand equation: + 25 425 = 0 Supply equation: 50 + 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. + 25 = 425 50 = 400 b. Solve the system . ( Recall the methods to solve systems of equations) + 25 = 425 - 50 = 400 75 = 825 Solve by elimination method = 11
- 7. MARKET EQUILIBRIUM b. Get the market equilibrium quantity x by substitution + 25 = 425 + 25 11 = 425 = 150
- 8. MARKET EQUILIBRIUM c. Graph (Two points determine a line) (425,0) (0,11) (0,8) (-400,0) (150,11) + 25 = 425 50 = 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: = 3 + 20 Demand equation: = + 44 a. How many units are available at y = 40php 40 = 3 + 20 = 20 3 = 6.67 b. How many units are demanded at y = 28 28 = + 44 = 16
- 11. MARKET EQUILIBRIUM c. Find the market equilibrium point = 3 + 20 = + 44 0 = 4 24 = 6 Solve for y when x = 6 = + 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) = 3 + 20 = + 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) = = 75 25 = 3 = 3 + 60
- 14. MARKET EQUILIBRIUM Demand Curve equation: Find a point, find the slope (150,60). MEP(25,135) = = 75 125 = 3 5 135 = 3 5 25 = 3 5 + 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 + 150 Solve for x: = 60 5 3 = 100
- 16. MARKET EQUILIBRIUM At y = 90, quantity supplied is: = 3 90 + 60 = 330
- 17. MARKET EQUILIBRIUM d. graph (0, 60) (-20, 0) (0,150) (250, 0) (25, 135) = 3 5 + 150 = 3 + 60 3 60 = 0 5 + 3 750 = 0