Pharmaceutical companies develop medications that address important conditions like cancer and HIV. They also develop medications for conditions that are less dire but more prevalent.

In this lesson, students use linear and quadratic functions to explore how much pharmaceutical companies expect to make from different drugs, and discuss ways to incentivize companies to develop medications that are more valuable to society.

### Students will

• Given the graph of demand for a certain medication, write a linear function and interpret the slope in context
• Assign a value for how important a drug is, and write a linear equation to model the “total social benefit”
• Using the demand function and price, write and graph the quadratic equation for a medication’s revenue
• Use the parabola to determine the revenue-maximizing price and corresponding revenue
• Understand how the size of the market and price elasticity determine the revenue a pharmaceutical company expects to make
• Discuss strategies that might encourage companies to develop medications for more important conditions

### Before you begin

Students should be able to write a linear equation given a graph, and interpret the slope as a unit rate in context, e.g. “the number of additional people who will opt not to buy a drug for every dollar that its price increases.” In addition to linear functions, the lesson also includes quadratic functions. A prior understanding of quadratics is helpful but is not necessary. In fact, the lesson could be used to introduce quadratic functions, and in particular as the product of two linear functions.