We have already seen that demand and supply relationships can be expressed graphically, mathematically, and in tabular form. Graphically, we saw that an equilibrium occurs at the intersection of the demand and supply curves. Mathematically, we find the equilibrium by solving for the price that equates demand and supply.

Suppose in some market the demand curve can be represented with the following mathematical expression:

Q_{D} = 100 - 2P

Suppose supply can be represented by:

Q_{S} = -20 + 4P

We can find the equilibrium price for this market equating the demand and supply relationships and solving for the price that equates the two:

Q_{D} = Q_{S}

100 - 2P = -20 + 4P

120 = 6P

P = 20

100 - 2P = -20 + 4P

120 = 6P

P = 20

By substituting 20 for P in either of the expressions for demand or supply (we can use either one since at P = 20 they are equal) we can find the equilibrium quantity for this market. Let's substitute it into the supply equation to find:

Q_{S} = -20 + 4(20) = 60 = Q_{D}

So, for this market, the **equilibrium price is 20** and the **equilibrium quantity is 60.**

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