2.3 : Mathematical Representation of the Demand Curve

Demand curves can be mathematically represented to quantify the law of demand and predict consumer behavior more accurately. Usually, it depicts a linear demand curve as Q_d = a - bP.

Where,

• Q_d stands for the quantity demanded
• P represents the price
• a is the intercept on the quantity axis, and
• b symbolizes the slope of the demand curve
• The negative sign in front of 'b' signifies the inverse relationship between price and quantity demanded, as stipulated by the law of demand.

Let's consider the consumer demand for a specific book. This might be represented by the equation Q_d = 500 - 100P.

Usually, economists rearrange this equation to make price a function of quantity, such as P = (500 - Q_d)/100. When the price per book reaches $5, the consumer stops purchasing. This point, which marks the vertical intercept on the demand curve, is known as the choke price. It designates the highest price the bookstore owner is willing to pay for the book, which can assist in developing pricing strategies.

However, it's crucial to remember that real-world demand curves tend to be more complex and non-linear.