Market equilibrium

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  1. 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. 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. 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. 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. 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. 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. 7. MARKET EQUILIBRIUM b. Get the market equilibrium quantity x by substitution + 25 = 425 + 25 11 = 425 = 150
  8. 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. 9. MARKET EQUILIBRIUM Quiz Answer Page 48, problem 4 a,b,c,d Page 50, problem 5 a,b,c,d
  10. 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. 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. 12. MARKET EQUILIBRIUM (0,20) (-20/3, 0) (0, 44) (44, 0) (6,38) = 3 + 20 = + 44
  13. 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. 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. 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. 16. MARKET EQUILIBRIUM At y = 90, quantity supplied is: = 3 90 + 60 = 330
  17. 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