Demand and elasticity Based on sales data o​​ver the past year, the owner of a DVD store devises the demand function $D\left(p\right)=40-2p$ , where D(p) is the number of DVDs that can be sold in one day at a price of p dollars.
a. According to the model, how many DVDs can be sold in a day at a price of $10?

Key Concepts

Demand Function

A demand function expresses the relationship between the price of a good and the quantity demanded by consumers. In this case, the function D(p) = 40 - 2p indicates that as the price (p) increases, the quantity of DVDs sold (D) decreases. This linear relationship helps predict sales at different price points.

Elasticity of Demand

Elasticity of demand measures how sensitive the quantity demanded is to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. Understanding elasticity helps businesses make informed pricing decisions to maximize revenue.

Substitution and Revenue Maximization

Substitution refers to how consumers may switch to alternative products as prices change. For the DVD store, if prices rise significantly, customers might choose digital streaming instead. Revenue maximization occurs when the price is set at a level where the product's demand is balanced with consumer willingness to pay, ensuring optimal sales and profit.