Supply and Demand Curves

Business Calculus · Axiom Academy

LESSON Supply and Demand Curves Understanding the mathematical functions that govern markets The Foundation of Market Economics Every time you buy something, you're participating in a fascinating dance between supply and demand . These two forces determine prices for everything from coffee to cars, and they can be described using simple mathematical functions. In this lesson, we'll learn how to express supply and demand as functions of price, interpret their graphs, and understand why they behave the way they do. The demand function D(p) gives the quantity of a product consumers are willing to buy at price p . Where a is the maximum demand (when price is zero) and b is the rate at which demand decreases as price increases. As price increases, fewer people can afford or are willing to buy the product. This is the Law of Demand : there's an inverse relationship between price and quantity demanded. A coffee shop finds that their demand function is: At p = \ 2 : D(2) = 200 - 40(2) = 120 cups per day At p = \ 4 : D(4) = 200 - 40(4) = 40 cups per day The supply function S(p) gives the quantity of a product producers are willing to sell at price p . Where c is the base supply and d is the rate at which supply increases as price increases. As price increases, producers can make more profit, so they're willing to produce more. Higher prices may also attract new producers to the market. This is the Law of Supply . The same coffee shop has a supply function:

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