How to Find the Equilibrium Point Mathematically ?

Supply and demand can be written as mathematical functions,

and in simple examples, they are often straight lines. They could, for instance, be:

                            QS = 85 + 30p

                            QD = 185 - 20p

Here, QD is the quantity demanded, QS is the quantity supplied, and p is the price. We now want to find the price, p*, that makes QD = QS. If the left-hand sides above are equal, the right-hand sides must also be so. Therefore, substitute p*

for p and set the right-hand sides equal to each other:

                            85 + 30p* = 185 - 20p*

To get p* alone on the left-hand side, we add 20 p* on both sides and subtract 85 from both sides. Then we have that

                                  50p* = 100

Dividing by 50 on both sides yields the result that

                                       p* = 2

If we then want to know the equilibrium quantity, Q*, we substitute the result we got for p* into either the supply or the demand function above. (Note that they must yield the same quantity, since p*, by definition, is the price that makes QD = QS)



Consequently, we have the equilibrium price, p* = 2, and the equilibrium quantity, Q* = 145.