Principles of Macroeconomics / Unit 2 MAC 0109 worked example, 60 to 90 seconds
Solving a Market with Algebra
The idea
When demand and supply are given as equations rather than a table, set the two quantities equal and solve. Write quantity demanded and quantity supplied each as a function of price. Set them equal, because equilibrium is where they are equal. Solve for price. Then put that price back into both equations separately. If the two give the same quantity, the arithmetic is right and that number is the equilibrium quantity. If they disagree, something has gone wrong and the check has caught it.
In practice
Worked example: quantity demanded equals one hundred minus four times price, and quantity supplied equals twenty plus two times price. Setting them equal gives one hundred minus four price equals twenty plus two price, so eighty equals six price, and price is thirteen and a third. Putting that back gives about forty-six and two thirds from each equation, so the answer checks.
Where people slip
Economists put price on the vertical axis although quantity is the variable being explained, which reverses the usual convention from unit one. When solving algebraically the axis does not matter, but when reading a graph it does.
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