Principles of Microeconomics / Unit 2 MIC 0109 worked example, 60 to 90 seconds
Solving a Market with Algebra
The idea
When demand and supply are written as equations, set the quantity demanded equal to the quantity supplied and solve for the price. Then substitute that price back into either equation to get the quantity, and into the other to check: both must return the same number, and if they do not, the arithmetic is wrong. Price is the unknown you solve for first because it is what both sides share.
In practice
Worked example: quantity demanded is one hundred minus five times the price, and quantity supplied is twenty plus three times the price. Setting them equal, one hundred minus five p equals twenty plus three p, so eighty equals eight p and the price is ten. Demand at ten gives one hundred minus fifty, or fifty; supply at ten gives twenty plus thirty, also fifty. The market clears at ten dollars and fifty units.
Where people slip
Two cautions. The demand equation has a negative slope and the supply equation a positive one; a sign error turns the market into two lines that never meet. And when the diagram puts price on the vertical axis, each equation is drawn with price solved out, which is the reverse of how it is written here.
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