Calculation of equilibrium price and equilibrium quantity .

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Calculation of equilibrium price and equilibrium quantity using  Functions 


Market Equilibrium refers to the  point where quantity demanded equals quantity supplied 

For example ,Given:                  Demand function as : 40 - 6P    Supply function as : 12P -32

(1) Calculate the equilibrium price 
Solution 
Note : At equilibrium,                          Quantity demanded  = Quantity supplied 
Thus, 40 - 6P  = 12P - 32
Collect like terms : 
40 + 32 = 12P + 6P
          72 = 18P
Divide both sides by 18
72/18 = 18P/18
       P = 4.                                                  Therefore ,equilibrium price (P) is $4

(2)Determine the equilibrium quantity in kilogram (kg)

Solution.                                                 Substitute the calculated equilibrium price in the given functions

Note : Calculated Equil.price is $4.                  Given 
QD = 40 -  6P              QS = 12P - 32
       = 40 - 6(4).                 = 12(4)  - 32
       = 40 - 24.                    = 48 - 32 
        = 16                            = 16
Therefore, equilibrium quantity is 16 kilograms                   

 (3 ) Calculate the excess demand at $3
Solution : At $3,                                       Substitute 3 for Price (P)
       = 40 - 6(3).                 = 12(3)  - 32.                          = 40 - 18                    = 36 - 32.                        QD  = 22                   QS    = 4 
From the calculation above 
Excess demand. = QD - QS 
                               = 22. -  4
                               =18 
Therefore, Excess demand at $3 is  18kg 

(4) Determine the Excess supply at $6.
Solution 
Substitute 6 for Price (P)
QD = 40 - 6P                 QS = 12P - 32 
       = 40 - 6(6).                   = 12(6) - 32.                         = 40 - 36.                      = 72- 32.                  QD  = 4                        QS = 40
From the calculation above 
Excess Supply. = QS - QD
                            = 40 - 4                     
                            =36
Therefore, Excess supply at $6 is 36kg 


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