A large department store is prepared to buy 3,950 of your...

A large department store is prepared to buy 3,950 of your neon-colored shower curtains per month for $\$ 5$ each, but only 3,700 shower curtains per month for $\$ 10$ each. What is the linear demand function for your neon-colored shower curtains?

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Key Concepts

Intercept Determination

The intercept in a linear demand function represents the theoretical price at which no units would be demanded (or alternatively, the maximum price a consumer is willing to pay when zero quantity is purchased). Determining the intercept from given points allows for the complete formation of the linear demand equation.

Slope Calculation

The slope of a linear demand curve measures the sensitivity of the price to changes in quantity demanded. It is calculated as the change in price divided by the corresponding change in quantity between two data points. This value tells us how much the price will drop for each additional unit of quantity demanded.

Linear Functions in Economics

In economics, a linear function is often used to model relationships with a constant rate of change. A linear demand function is typically expressed in the form p = a - bq, where p represents price, q represents quantity, a is the intercept (the price when quantity is zero), and b is the slope (the rate at which price changes with quantity).

Demand Function

A demand function describes the relationship between the price of a product and the quantity demanded by consumers. It shows how the quantity demanded varies inversely with price, meaning that as the price increases, the quantity demanded generally decreases, and vice versa.

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