Market Equilibrium

Business Calculus · Axiom Academy

EXAMPLE Finding Market Equilibrium A step-by-step worked example solving for equilibrium price and quantity A market for widgets has the following supply and demand functions: Find: The equilibrium price p^* and equilibrium quantity Q^* . At equilibrium, the quantity demanded equals the quantity supplied. This means: What equation should we set up? Starting with 300 - 25p = 50 + 15p , we move all p terms to one side: What is the equilibrium price p^* ? Now that we know p^* = 6.25 , substitute into either function. Let's use demand: Let's double-check by substituting p^* = 6.25 into the supply function: At equilibrium, D(p^*) = S(p^*) . Getting the same quantity from both functions confirms our solution is correct. This is a crucial check! At 6.25, consumers want to buy exactly 143.75 widgets At 6.25, producers want to sell exactly 143.75 widgets The market "clears"—no shortage, no surplus This is the natural resting point of the market Finding equilibrium is about solving the equation D(p) = S(p) . The solution gives you the price where quantity demanded equals quantity supplied.

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