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The Algebraic Approach
We have worked with supply and demand equations separately, but they can also be combined to
find market equilibrium. We have already established that at equilibrium, there is one price, and
one quantity, on which both the buyers and the sellers agree. Graphically, we see that as a single
intersection of two curves. Mathematically, we will see it as the result of setting the two
equations equal in order to find equilibrium price and quantity.
If we are looking at the market for cans of paint, for instance, and we know that the supply
equation is as follows:
QS = -5 + 2P
And the demand equation is:
QD = 10 - P
Then to find the equilibrium point, we set the two equations equal. Notice that quantity is on the
left-hand side of both equations. Because quantity supplied is equal to quantity demanded at
equilibrium, we can set the right-hand sides of the two equations equal.
QS = QD

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