An algebraic approach to Market Equilibrium

Market Equilibrium - Algebraically

As teachers of Economics, we often limit ourselves to one approach of teaching Market Equilibrium. We frequently use the theoretical approach with the aid of a graph. I too was very guilty of this, until I discovered that it can also be taught or supplemented using an Algebraic approach.

Market equilibrium can be determined algebraically using a demand function and a supply function. The demand function shows the exact relationship between price and quantity demanded and the supply function shows the exact relationship between supply and quantity supplied. These two functions represent the exact intentions of buyers and sellers in the market and can be used to determine equilibrium quantity and equilibrium price without having to visually scope where it is on a graph.

EXAMPLE:

A demand function and supply function for carrots is given by:

Q_d  =  50   -   2p           (demand function)

Q_s  =  -6   +   12p         (supply function)

Where                         :  Q_d =  quantity demanded

                                    Q_s  =  quantity supplied

                                    p    =  price     

Since equilibrium is where quantity demanded is equal to quantity supplied (Q_d  =  Q_s ), then the equilibrium price can be determined by equating the demand and supply functions and then solving for price.

STEP I : Equate the demand and supply functions

            Q_d    =   Q_s

   50  -  2p    =  -6   +   12p

STEP II : Put all like terms together

    50  -  2p    =  -6   +   12p

    50  +  6   =   2p   +   12p

   56   =   14P

STEP III            :  Solve for p by dividing both sides by 14

       =   

   4      =     p

The equilibrium price is therefore $4.00

So what is equilibrium quantity?

We can use any of the functions to determine equilibrium quantity by simply substituting the price of $4.00 into the respective equations, then solve them to determine the equilibrium quantity.

Example One:                                                             Example Two:

Q_d  =  50  -  2p                                                                        Q_s   =   -6  +  12p

Q_d  =  50 -  2($4)                                                    Q_s    =   -6   +   12 ($4)                                                                        

Q_d   =   50   -   8                                                           Q_s    =   -6   +   48

Q_d   =  42                                                                     Q_s    =   42

Equilibrium quantity at the Market price of $4.00 is 42 carrots